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Mr. SQUID User`s Guide

1. TP1 TP2 Figure 7 7 Scope photos of the signals at TP1 and TP2 One should then adjust the 10 kQ potentiometer so that the signal at Test Point 2 no longer shows any dc offset In other words adjust the potentiometer until the sine wave at Test Point 2 has the same amplitude in the positive voltage direction as in the negative voltage direction while dc coupled to the scope Once you have obtained the above signals from your circuit you are ready to lock in the flux state of the Mr SQUID If this is not done properly you can cause the Mr SQUID to flux trap First turn off your flux locked loop circuit Second ground yourself to the Mr SQUID box by touching the BNC connectors labeled X or Y on the front of the Mr SQUID box Third carefully connect the circuit output to the BNC connector labeled EXT COIL on the back of your Mr SQUID box This BNC is a direct connection to the second gold coil on the Mr SQUID chip and so any small static discharges into the coil can create large magnetic fluxes in the SQUID Make sure the V output Test Point 1 still looks correct If not you have caused your Mr SQUID to flux trap and will need to warm it up and recool it If you need to do this try t
2. region 1 region 2 Substrate Figure 5 12 Schematic of bicrystal grain boundary Josephson junction showing the relationship between the fused substrate and relative orientations of the two regions of the YBCO film STAR Cryoelectronics LLC 45 Mr SQUID User s Guide 6 TROUBLESHOOTING AND GETTING HELP Mr SQUID has been designed to be a trouble free easy to operate system for the study of the physics and applications of SQUIDs It is however a complex instrument incorporating sensitive Josephson junction electronics and cryogenic packaging The SQUID probe itself undergoes tremendous thermal stresses during its repeated cycling between room temperature and liquid nitrogen The cryogenic packaging system has been designed with two goals in mind durability and visibility These goals are not necessarily complementary but we considered it important from an educational standpoint that the user be able to see the actual SQUID chip With this in mind there is the possibility that problems that you have encountered with Mr SQUID may be associated with a thermally induced failure in the probe If this is the case STAR Cryoelectronics will replace the defective probe at no cost for a period of two years from the purchase of the Mr SQUID system On the other hand it is possible that the troubles you are encountering are of a less catastrophic
3. spurring the development of photolithographically processed devices The type of de SQUID most commonly used today is the square washer configuration first produced in 1982 In this design the thin film body of the SQUID is covered with a thin insulating layer on top of which is grown a thin film spiral coil with as many as 50 turns This scheme produces very tight inductive coupling between the coil and the SQUID Devices of this kind with niobium superconducting films used throughout can be made in batches of as many as several hundred at a time on a four inch silicon wafer The development of SQUIDs like all other aspects of superconductivity received a tremendous boost from the advent of high temperature superconductivity in 1986 Within a few months of the first thin film depositions HTS de SQUIDs had been announced with junctions consisting of randomly occurring boundaries between superconducting grains in the films Despite the apparent crudity of these devices somewhat reminiscent of the early days of LTS SQUIDs much progress has been made in understanding their behavior and noise limitations STAR Cryoelectronics LLC 43 Mr SQUID User s Guide More recently more controlled junctions have been developed enabling one to produce dc SQUIDs with relatively predictable characteristics Your Mr SQUID chip is the first commercialization of this new technology 5 14 The SQUID in Mr SQUID The SQUID in t
4. hias 2 Figure 5 5 A dc SQUID in the presence of an applied magnetic field The applied magnetic field has lowered the critical current of the SQUID in other words it has reduced the amount of bias current we can pass through the SQUID without generating a voltage The reason is that the screening current superimposes itself on top of the bias current Suppose the critical current of each junction is 5 microamps and the screening current is STAR Cryoelectronics LLC 33 Mr SQUID User s Guide 1 microamp Since the junction on the left has to carry 1 microamp of screening current it can now carry only 4 microamps of bias current before it becomes resistive It doesn t distinguish between bias currents and screening currents it just detects the flow of the electron pairs When it carries a total of 5 microamps it becomes resistive When the junction on the bottom goes normal all the current goes through the junction on the top which makes it go normal That means both paths are now resistive so a voltmeter will register a voltage across the SQUID As we increase the applied magnetic flux the screening current increases But when the applied magnetic flux reaches half a flux quantum something interesting happens The junctions momentarily go normal The continuity of the superconducting loop is destroyed long enough for one quantum of magnetic flux to pop inside the loop Then superconductivity around the loop is restored
5. At room temperature this should be 300 400 Q Turn on the current source to the silicon diode and verify that it is indicating that it is near room temperature Connect the power supply to the chip resistor but leave the power supply set to zero volts into the resistor Turn the amplitude on the Mr SQUID electronics down to its minimum Slide the Mr SQUID probe all the way to the bottom of the dewar Wait until the Mr SQUID has cooled to 77 K about 5 minutes Change the Mr SQUID electronics to the V mode Slide the Mr SQUID probe up until the liquid nitrogen level is just below the bottom of the magnetic shield Keep watching both V curve and the temperature of the HTS coated chip as indicated by the silicon diode The Mr SQUID should stabilize at or just above 77 K with a clear V curve If it becomes too warm as indicated by a weakening of the V curve amplitude lower the probe by a few millimeters STAR Cryoelectronics LLC 80 Mr SQUID User s Guide Mr SQUID Probe Binder Clip An Diode sensor resistor Aluminum rae and coil wires a Foil Liquid Nitrogen Level 7 5 2 Inductive measurement of the transition temperature STEP 1 Start with power supply connected to the chip resistor at zero Volts The diode should indicate that the film is at 77 K TIP If your sine wave generator can put out square waves try using the square wave instead of a sine wave You will find it easier to
6. From ae TOE U6 AD7524 8 bit DAC Mr SQUID Box U7 LM1458 T ie ie 5V 1k 5V ie All chip s use 15uf tantalum bypass caps between 5V pa j R1 1kz the 5 and 5 volt power pins and the circuit ground Nf a S A 5V TTL Clock In i from a VV Function Generator 8 we pele 4 v Sd 4 8252 MSB 8252 8252 8252 INVERTER ADDED tie FLL Analog output l 1 V 100pA to Mr SQUID T external coil 825 825 825 825 F E LSB 4 gt tq a Light Emitting R2 5kz Diodes Figure 7 22 STAR Cryoelectronics LLC 102 Mr SQUID User s Guide U1 U2 OP 27 U3 LM311 Mr SQUID nee U4 U5 U6 74LS169 4 bit U D counter LI sy U7 AD563 12 bit DAC sev apv LM Eq Mij U8 LF 441 X 5V Std Sr All chip s use 15yf tantalum bypass caps between VY 5V the 5 5 and 15 volt power pins and circuit ground TTL Clock In from Function L Generator 4 8 9 s Us 4 TH 8 9 s Us z 4l 8 9 s Ue 3 i INVERTER ADDED ANZ FE elf cg al esp psy s ald ge fer oc sy gee aL 825z gt ee ie le 825z 825z 825z Light is V J 7 ee i gle oh lt lt 1 lt SS Le LSB Emitting Diodes to Mr SQUID 10k L external coil FLL Analog Output 1 V 100pA TP3 Figure 7 23 After you have added the inverter turn you circuit back on and verify that it is working as you did at the beginnin
7. e A digital volt meter DVM with sub millivolt resolution e A soldering iron and electronics grade solder e A binder clip available from any stationary supplier e One or two cotton balls e Masking tape e An active dc constant current source capable of supplying 10 pA of current with a voltage compliance of at least 2 volts If you do not have a constant current source then you will also need e A general purpose operational amplifier e g 74 7 e A zener diode in the range of 2 5 to 7 volts 8 e A selection of resistors in the range of 1 kQ through 100 kQ e A capacitor within the range of 100 pF to 100 nF e A 9 Volt transistor battery e A solderless breadboard 14Such as Radio Shack part number 276 1122 15Such as Belden Beldsol Solderable Magnet Wire Types 8081 through 8087 6Such as a Kiethley Model 197 microvolt DVM Millivolt resolution may be acceptable but will limit the accuracy of the temperature measurements 17Such as a LM741 Radio Shack part number 276 007 18Such as Radio Shack part number 276 565 19Such as Radio Shack part numbers 276 169 276 174 270 175 STAR Cryoelectronics LLC 55 Mr SQUID User s Guide In this experiment we will use a common silicon diode to measure the temperature of the SQUID in the Mr SQUID probe Silicon diodes are a common and accurate way to measure temperature from 300 K down to liquid helium temperatures 4 2 K They are simple to use inexpensive
8. By looking at Test Point 3 we can determine the applied flux that the flux locked loop is canceling out The voltage at Test Point 3 is across the 10 kQ resistor and the Mr SQUID external coil whose resistance is negligible compared to 10 kQ This means that the y axis for the Test Point 3 signal below is 20 uA per division For this Mr SQUID external coil this translates into a flux of about 0 43 o per division 49There is a trouble shooting section at the end of this experiment STAR Cryoelectronics LLC 97 Mr SQUID User s Guide TP2 TP3 Figure 7 19 Signal outputs of the 12 bit FLL in the locked mode at TP1 and TP2 A few words are in order concerning improvements to this elementary 12 bit flux locked loop circuit First this circuit is not significantly different from a real digital flux locked loop TP1 of Figure 7 15 would indicate that the coupling of our Mr SQUID coil was 44 1 A po The voltages which can appear at test point 3 TP3 are about 3 Volts that drive the external coil through a 10 kQ resistor So the maximum flux that the loop as constructed in Figure 7 17 can cancel out and hence measure is 7 o The 12 bit DAC step size is 1 part in 2 4096 which for a total span of 14 o gives a DAC flux step size of 0 0034 o 5 Second changing the value of the 10 kQ resistor between TP3 and the Mr SQUID external coil will allow one to trade off resolution for maximum flux cancellation
9. Mr SQUID External Coil l Figure 7 10 Equivalent circuit of the voltage source The 1 MQ resistor and Rs form a voltage divider which results in the voltage at point A of V4 given by V R Baas V oe i 4 TIMOER This voltage is fed into another voltage divider comprising another 1 MQ and the Mr SQUID coil resistance of Rcoil and the output resistor of the flux locked loop that is 1350 Q according to the previous experiment Since the Mr SQUID coil is electrically in parallel with the 1350 Q flux locked loop output resistor together they appear as one resistor R where 1350R Eqn 7 7 R cl _ Ohms 1350 R coil The second 1 MQ resistor and R form a second voltage divider which divides the voltage at point A resulting in the voltage at point B of 1350R E 7 8 V VD sot R Via set 1350 Rooi qn 7 ce Not IMQ R IMQ R IMQ R set set IMQ 1350R oi 1350 Roi STAR Cryoelectronics LLC 67 Mr SQUID User s Guide For a typical value of about 25 Q for Reoii V R Eqn 7 9 V 2 45x10 4 _ IMO R a So by knowing the resistance of your Mr SQUID external coil and knowing Rye we can calculate the voltage being fed to the Mr SQUID external coil Once you have constructed the above voltage source we can now try to use the flux locked loop to measure small dc and ac signals 7 3 1 Building a dc voltmeter STEP 1 If you have not already done so construct the flux locked loop
10. Mr SQUID fo conng tus Figure 2 2 Front panel of the Mr SQUID electronics box STEP 2 Add liquid nitrogen Eye protection and gloves are advisable for anyone working with liquid nitrogen Under all circumstances be sure to follow the safety regulations of your laboratory If you are uncertain about handling the liquid nitrogen check with responsible people in your laboratory The dewar supplied with Mr SQUID is manufactured specifically to handle liquid nitrogen but it contains a glass vacuum vessel that can shatter if mishandled Fill the dewar about 3 4 full with liquid nitrogen If you will be using the system for a long time more than a few hours the liquid nitrogen level in the dewar will decrease due to evaporation If the liquid level dips below that of the SQUID sensor simply refill the dewar to its original level with more liquid nitrogen STAR Cryoelectronics LLC 6 Mr SQUID User s Guide STEP 3 Cooling down the probe Carefully lower the sensor end of the probe into the dewar as shown in Figure 2 3 below The foam cap to the Mr SQUID dewar has a hole and a slot in it to support the Mr SQUID probe It will take several minutes for the SQUID sensor on the end of the probe to reach a stable temperature of 77 K You should wear eye protection and gloves during this procedure as the liquid nitrogen may splash as the probe is introduced into the dewar The critical temperature T for the YBC
11. SQUID User s Guide Figure 3 6 Photograph of the Mr SQUID version 8 chip showing the two modulation coils See Sec 9 2 for Mr SQUID specifications To find this point first adjust the flux bias control 2 for numbering see page 14 so that the critical current is at its largest value Then turn down the amplitude control 4 all the way so that only a point is visible on the oscilloscope screen or so that the pen is stationary on the plotter page In this mode you can then sweep the point up and down the V curve by adjusting the current bias control 3 as you did initially Set the current bias level so that the point rests at either knee in the V I curve Now turn the flux bias control 2 which controls the amount of magnetic flux through the hole in the SQUID loop You should see the point move back and forth vertically on the screen or page This periodic motion arises because the screening currents in the SQUID body depend on the applied magnetic flux in a periodic manner The period is determined by the magnetic flux quantum o This phenomenon is a manifestation of the macroscopic quantum nature of superconductivity Figure 3 7 The knee in the V Z characteristic STAR Cryoelectronics LLC 16 Mr SQUID User s Guide To automate this procedure switch the function switch 1 from V Z to V In this new mode all of the controls on the Mr SQUID control box work the same way as before except f
12. nature and can be remedied by corrective actions outlined in this section In the following table we list some common difficulties along with recommended actions STAR Cryoelectronics LLC 46 Mr SQUID User s Guide 6 1 Problems in V I Mode Output signal is Point on scope or plotter pen is stationary 1 Check connections of x y cables to regardless of settings oscilloscope or x y recorder 2 Check scale settings on output device 3 Check batteries replace if LED does not lights Horizontal line only regardless of settings 1 Check scale settings on scope or x y recorder 2 Check continuity and connection of y cable 4 Check batteries replace if LED does not light 3 OK Call STAR Cryoelectronics Vertical line regardless of setting 1 Check scale settings on scope or x y recorder 2 Check continuity and connection of x cable 3 Check the liquid nitrogen level 4 OK Call STAR Cryoelectronics Erratic or open loop scope trace 1 Check that both oscilloscope or x y recorder inputs are dc coupled 2 Check continuity and connection of both Veer x and y cables 3 OK Call STAR Cryoelectronics 6If the two batteries are unbalanced then the LED may still light even though replacing both batteries with fresh ones will solve the problem This will happen if the batteries are of significantly unequal age or strength Always use new alkaline batteries in your Mr SQUID unit and al
13. 3 4 A per division For this Mr SQUID external coil this translates into a flux of about 0 17 per division oe TP1 TP2 Figure 7 8 Scope photos of the signals at TP1 and TP2 in flux locked loop mode A few words are in order concerning improvements to this elementary flux locked loop circuit First the LM1458 s are essentially dual LM741 s and have noise specifications of 80 nV Hz at 10 Hz One can immediately improve this circuit by using low noise op amps such as OP 270 dual op amps 5 nV Hz at 10 Hz or OP 27 op amps 3 nV Hz at 10 Hz Second boosting the gain of U2a will allow the circuit to lock the flux in to better than 7 One cannot boost it arbitrarily however We would suggest that this be left to the students to determine how much they can improve the ability of the circuit to lock Third C1 can be increased to average longer This will have the result of decreasing the noise at Test Point 2 but at the cost of slowing down the circuit s response speed In other words it will not be able to react as fast to cancel quickly changing flux at the SQUID On the other hand the bandwidth of the Mr SQUID electronics is about 2 8kHz so shortening the averaging time to less than 0 4 milliseconds will not allow one to increase the ability of this circuit to cancel flux changing any faster than this STAR Cryoelectronics LLC 65 Mr SQUID Us
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15. 7 15 and Figure 7 18 to determine the x axis scale in terms of applied flux From Figure 7 15 and Figure 7 18 we can see that for the Mr SQUID that we used the x output of our Mr SQUID box was 2 3 cm for 1 p on the scope photo The scope x axis scale was 200 mV cm and the x output of the Mr SQUID box is the voltage across a 10 KQ resistor Then the x axis on our scope photos is in units of Bo 2 3cm 0 2V 1 Eqn 7 22 cm 10kQ 461A Both the internal Mr SQUID coil and the EXT COIL should have the same mutual inductance with the SQUID same coupling in o uA So we can use the above scale factor to tell us what the quantization error due to the discreteness of the current used to lock the loop should be 8 bit 12 bit l step 3 9 pA B 46nA l step 0 146nA o 46uA 0 085 Po 3 2 uo STAR Cryoelectronics LLC 99 Mr SQUID User s Guide Figure 7 20 One obvious question to ask is Is our digital flux locked loop limited by this quantization error or is the noise of the Mr SQUID chip and electronics the limiting factor If we look at Figure 7 20 we can see that a given step is spread out over a range of 50 mV on the x axis and that the steps overlap on the x axis This corresponds to 50 mV 10 KQ Po 46uA or 0 11 Bo which is about the same as our step size above Is this true for your digital flux locked loop How would you go about changing the quantization error Hint Look at
16. Critical Current Figure 3 5 Determining the junction parameters from the V characteristic You can determine the critical current of the junctions in Mr SQUID by measuring the width in volts of the flat part of the V J curve and dividing that number by 10 000 Q to convert your answer into amperes of current If the flat region is 1 volt wide for example then the corresponding current is 100 microamps However you are looking at the current through both of the junctions in the SQUID not just one Therefore assuming the junctions are identical the current through one junction is half the value you are measuring in our example 50 microamps Is this the critical current of the junction Not quite The curve you are looking at drives the current symmetrically about zero marked in the drawing The current you have measured is actually composed of a contribution in the positive direction and a contribution in the negative direction If the curve is symmetric they are equal As a result the real critical current of the junction is half the value you infer from the measurement Thus in our example the critical current is 25 microamps 1 4 of the original measurement The flat region on the curve corresponds to 4 times the junction critical current Apart from the critical current of the junction usually written as Z there is also a parameter of the junction known as the normal state resistance or Ry You can determine it by measuring th
17. Mr SQUID User s Guide 7 6 SQUID Properties in Pumped Liquid Nitrogen Purpose Although Mr SQUID is designed to show excellent superconducting properties at 77 K in liquid nitrogen it must be remembered that this operating temperature is about 85 of the critical temperature of 90 K for YBCO Many of the superconducting properties of Josephson junctions such as Z scale with the parameter 1 4 where t is the dimensionless reduced temperature defined as t T T Liquid nitrogen boils at 77 K at atmospheric pressure By decreasing the ambient pressure the boiling point can be reduced easily to around 68 K All of the previous experiments can be done using pumped liquid nitrogen as most SQUID properties are improved by operation at a lower temperature The performance of various devices such as the flux locked loop and voltmeter will be improved In this experiment we will measure the standard SQUID parameters at this lower reduced temperature and explore the theory that explains how superconducting properties scale with temperature Equipment For this experiment you will need e lt A calibrated silicon diode temperature sensor attached to the Mr SQUID probe see Section 7 1 1 for instructions e A gt 3 diameter rubber stopper size number 14 with a hole for tubing preferably 1 4 36 e A vacuum source capable of less than 100 mTorr over the volume of the Mr SQUID dewar lt 1 liter To design the pumping cap
18. Next we need to attach the HTS coated sapphire chip on the Mr SQUID probe Since we want the HTS coated sapphire chip to be able to change temperature without perturbing the temperature of the SQUID chip we need to do a few things to thermally isolate them We will do this by using a 1 cm x 1 cm square piece of felt cloth to insulate the HTS coated chip from the Mr SQUID platform and we will use a 1 cm x 7 cm strip of aluminum foil to create a 77 K thermal shield between the felt insulation and the Mr SQUID platform Since we do not want the chip to be permanently mounted on the probe we will use paper tape masking tape to hold the chip felt and aluminum foil on backside of the probe as shown below Try to avoid getting tape onto any part of the chip housing side of the Mr SQUID probe Note that the aluminum foil should extend 2 to 3 cm beyond the end of the Mr SQUID printed circuit board Arrange the wires to trail downward under the magnetic shield and out the bottom of the probe Place the Mr SQUID magnetic shield on the Mr SQUID probe so that the diode wires come out of the bottom Felt Pad HTS Film N with coil diode and resistor Mr SQUID chip lt housing 4 layers of lt Aluminun Foil Connect the silicon diode leads to the 10 pamp dc constant current source and DVM as shown below If you do not have a suitable constant current source available a procedure to make one is given in Section 7 1
19. Polystyrene cement model glue such as Duco Cement gt 30This experiment works best if the HTS film is on a high thermal conductivity substrate such as sapphire Although any size chip greater than 0 5 cm x 0 5 cm will do it will be easier to mount the coil diode and resistor on a lcm x 1cm chip YBCO films on sapphire are available from STAR Cryoelectronics 31Such as Radio Shack part number 276 1122 32Such as can be found in the surface mount chip resistor assortment pack sold as Radio Shack part number 271 313 33Such as Belden Beldsol Solderable Magnet Wire Types 8081 through 8087 34Such as a Kiethley Model 197 microvolt DVM Millivolt resolution may be acceptable but will limit the accuracy of the temperature measurements 35Any polystyrene cement model glue will work If none is available clear finger nail polish will work Duco Cement is a registered trademark of the Devcon Corporation Wood Dale IL 60191 U S A STAR Cryoelectronics LLC 77 Mr SQUID User s Guide e One binder clip e Aluminum foil e One wooden toothpick e 1cm piece of felt 1mm thick e Paper tape also called masking tape e A active dc constant current source capable of supplying 10 pA of current with a voltage compliance of at least 2 Volts e g the current source described in Section 7 1 3 7 5 1 Experimental Setup First take the magnet wire and wind a solenoid coil around the toothpick We want the coil
20. STEP 1 Disconnect all 8 inputs pins 11 14 of U6 from U4 and US STEP 2 Connect pins 5 11 of U6 to the circuit ground STEP 3 Connect pin 4 of U6 to the circuit 5 Volt power supply STEP 4 Connect a voltmeter from Test Point 3 TP3 to the circuit ground STEP 5 Adjust R2 until the voltage at TP3 is 0 000 Volts STEP 6 Reconnect all 8 inputs pins 4 11 of U6 to the correct pins of U4 and US Your circuit is should now be ready to function STAR Cryoelectronics LLC 91 Mr SQUID User s Guide The circuit should first be constructed with the Mr SQUID external coil disconnected from the circuit The Mr SQUID should be set up and running in the V mode with the amplitude of the flux of a few flux quantum The signal at Test Point 1 TP1 should look something like the one in Figure 7 15 In these scope photographs the x axis is the X output of the Mr SQUID box The signals at Test Point 1 will have a dc offset imposed on them so the oscilloscope will need to be ac coupled The signals at Test Point 2 may also have a de offset but we want to be able to see that offset so the scope will need to be de coupled while looking at Test Point 2 Test Point 1 is simply showing the V output of the Mr SQUID as a magnetic flux is swept Test Point 2 is also showing the V output of the Mr SQUID but magnified by a factor of 330 AND with an extra dc offset from the circuit s 10 kQ potentiometer One should then
21. This is illustrated in Figure 5 7 Thus the junctions serve as gates that allow magnetic flux to enter or leave the loop The voltage read with an oscilloscope or x y recorder is the average voltage across the SQUID Although the experimenter observes a non zero dc voltage hence the SQUID appears resistive just above J as shown in Figure 5 4 and the left side of Figure 5 8 the instantaneous voltage across the SQUID and the circulating current are actually oscillating at high frequencies in the microwave range in response to an applied magnetic field The phenomenon is not so surprising if you notice that it makes things easier for the SQUID Consider what happens to the screening current Rather than generating enough screening current to keep 0 51 flux quanta out now all the SQUID has to do is generate enough screening current to keep 0 49 flux quanta in which is of course a little easier that is lower in energy Of course the screening current has to change direction as shown in Figure 5 6 below bias 2 Figure 5 6 The screening current Z has reversed its direction If we consider the behavior of the screening current as more and more magnetic flux is applied we would obtain the plot shown in Figure 5 7 As you see the screening current changes sign really it changes direction when the applied flux reaches half of a flux quantum Then as the applied flux goes from half a flux quantum toward one flux quantum the s
22. active device of semiconductor electronics Junctions can be used in a variety of electronic circuits as switching devices as sensors as variable inductors as oscillators because of the ac Josephson effect and for other applications People have built Josephson electronic circuits that contain up to tens of thousands of junctions At the opposite extreme one of the most useful circuits made from Josephson junctions is the dc SQUID which contains only two junctions 5 7 The dc SQUID The de SQUID is actually a rather simple device The device operation is essentially the same regardless of whether the SQUID is constructed using low temperature superconductor LTS or high temperature superconductor HTS materials It consists of two Josephson junctions connected in parallel on a closed superconducting loop As we have said a fundamental property of superconducting rings is that they can enclose magnetic flux only in multiples of a universal constant called the flux quantum Because the flux quantum is very small this physical effect can be exploited to produce an extraordinarily sensitive magnetic detector known as the Superconducting QUantum Interference Device or SQUID SQUIDs actually function as magnetic flux to voltage transducers where the sensitivity is set by the magnetic flux quantum 2x10 5 Wb In practical terms the magnetic field of the earth passing through the area of a typical HTS SQUID sensor corresponds to over 100 flux quan
23. adjust the 10 KQ potentiometer so that the signal at Test Point 2 no longer shows any de offset In other words adjust the potentiometer until the sine wave at Test Point 2 has the same amplitude in the voltage direction as in the voltage direction while dc coupled to the scope In Figure 7 15 the tops of the V curve are clipped flattened because the amplification of U2 is a little larger than needed Your circuit may show more clipping or none at all Once you have obtained the above signals from your circuit you are ready to lock in the flux state of the Mr SQUID If this is not done properly you can cause the Mr SQUID to flux trap First turn off your flux locked loop circuit Second ground yourself to the Mr SQUID box by touching the BNC connectors labeled X or Y on the front of the Mr SQUID box Third carefully connect the circuit output to the BNC connector labeled EXT COIL on the back of your Mr SQUID box This BNC is a direct connection to the second gold coil on the Mr SQUID chip and so any small static discharges into the coil can create large magnetic fluxes in the SQUID Make sure the V output TP1 still looks correct If not you have caused your Mr SQUID to flux trap and will need to warm it up and recool it If you need to do this try recooling with your un powered flux locked loop circuit already attached to the EXT COIL connector TP1 TP2 Figure 7 15 Signal outputs of the 8 b
24. be connected to the vertical input or y axis While either display device is quite sufficient for Mr SQUID operation using both an x y chart recorder and an oscilloscope can be convenient for viewing and plotting the output of Mr SQUID Since there are a variety of display devices available in laboratories we cannot specify the optimal configuration of the controls here Therefore please refer to the manufacturer s instructions for proper operation of the display device you have chosen to use Figure 2 5 An operating Mr SQUID system using an oscilloscope display STAR Cryoelectronics LLC 8 Mr SQUID User s Guide At this point the Mr SQUID system is ready for operation Your set up should look more or less like that shown in Figure 2 5 above except perhaps for the replacement of the oscilloscope with an x y recorder The basic operation of Mr SQUID is outlined in the following sections If Mr SQUID represents your first experience with superconductive electronics we suggest that you follow the Getting Started instructions for New Users Section 3 This is in the form of a primer that discusses the phenomenon of superconductivity and includes a simple theory of SQUIDs It details the step by step demonstration of the basic SQUID experiments possible with Mr SQUID On the other hand if you are already familiar with SQUID operation or you have already used Mr SQUID and merely need to refresh your memory wi
25. connected from the X output on the front panel 5 reads the current being fed through the SQUID The cable connected to the Y output 6 reads the voltage across the SQUID Set the power switch 9 to the ON position On an oscilloscope there should be a small bright spot on the center of the screen On an x y recorder the pen should be stationary in the middle of the page You may have to adjust the offset controls on your display device to achieve this in either case 3 2 Varying the Current Bias The current bias control 3 varies the current being sent through the SQUID Slowly turn this knob in either direction The spot on the oscilloscope screen or the plotter pen will move in response to the changing current As you turn the knob back and forth you will trace out a curve representing the relationship between the current fed through the SQUID and the voltage across the SQUID This curve is called the V J curve for the SQUID 3 3 Varying the Amplitude of the Current Sweep Return the current bias control to the 12 o clock position and now slowly turn the amplitude control 4 in the clockwise direction This function sweeps the current through the SQUID back and forth between preset values thus automating the procedure you performed by hand using the current bias control A solid curve should now appear on the oscilloscope screen alternatively the pen on your plotter will repeatedly trace out the curve on the page STAR Cryoelectron
26. eds Walter de Gruyter amp Co Berlin 1977 ISBN 3 11 006878 8 page 88 of Superconductor Electronics J H Hinken Springer Verlag Berlin 1989 ISBN 3 540 51114 8 ISONY model SPP 50 2Paging systems in buildings often distribute their broadcasts by injecting their rf carrier into the building power lines This rf can interfere with the operation of your Mr SQUID 13Campus radio stations often distribute their broadcasts by injecting their rf carrier into the campus power lines to avoid certain FCC restrictions This rf can interfere with the operation of your Mr SQUID STAR Cryoelectronics LLC 51 Mr SQUID User s Guide A considerable amount of laboratory equipment also emits rf interference Almost any high voltage equipment thin film deposition equipment such as sputtering and e beam evaporators or electric welding equipment will also generate RFI Electric motors that run fans or other equipment particularly large electric motors also generate considerable RFI Any kind of rf or microwave test equipment will not only generate RFI but many for increased stability keep their internal oscillators generating rf power even when their front panel power switches are in the off position Unfortunately the only way to definitively determine if RFI is causing problems for your Mr SQUID is to operate the Mr SQUID in an environment know to be RFI clean Many low temperature physics laboratori
27. experience with the Mr SQUID system grows Registered owners will have access to updated versions of the Advanced Experiment Guide The Mr SQUID User s Guide is intended to be a complete reference for the Mr SQUID owner providing operating instructions background information and suggestions for additional experiments for the advanced user We invite your contributions and comments to the Guide STAR Cryoelectronics LLC 4 Mr SQUID User s Guide 2 SETTING UP MR SQUID 2 1 What You ll Need The first step in operating Mr SQUID is to be sure you have all of the necessary equipment Figure 2 1 shows the components that are provided with Mr SQUID They are as follows Electronic control box two 9 V batteries are included Probe with the SQUID sensor Cable to interconnect the electronics box and the probe and Liquid nitrogen dewar Figure 2 1 Mr SQUID system components Apart from the parts included in the Mr SQUID package there are several items that the user must supply in order to operate the system An output device either a 2 channel oscilloscope capable of x y display or an x y chart recorder There are advantages to having both on hand if possible BNC coaxial cables for connecting the electronics box to the output device These are standard items for any laboratory using electronic instruments Liquid nitrogen The dewar included with Mr SQUID holds about 1 liter of liquid ni
28. grain boundary junctions step edge junctions in which YBCO films develop grain boundaries as they grow over sharp steps in a substrate and bi crystal junctions in which grain boundaries in a substrate are replicated in an overlaying film Researchers at IBM first developed bi crystal grain boundary junctions In these devices a junction was created by growing YBCO films on Noise characteristics of single grain boundary junction DC SQUIDs in Y BazCu307 4 films R Gross P Chaudhari M Kawasaki M Ketchen A Gupta Physica C 170 315 1990 STAR Cryoelectronics LLC 44 Mr SQUID User s Guide top of a grain boundary in a specially prepared substrate The substrate was a bi crystal created by fusing together two crystals with different orientations Such a process cannot be extended to integrated circuits or to large scale manufacturing but at present it has resulted in the most sensitive YBCO SQUIDs ever produced and is the junction technology employed in the manufacture of Mr SQUID since early 1996 Fused crystal boundary
29. is 15 Hz making it suitable for oscilloscope use In the low speed position down the frequency of the triangle wave is 0 07 Hz making it suitable for x y recorder use 8 Battery Check Light Indicates whether the batteries for the electronics box are functional If the batteries are functional the LED will illuminate when the power switch 9 is pressed down in the BATT CHK position 9 Power A three position switch that selects between power on to the system up power off to the system center and a momentary contact position to test the system batteries down 4 2 Electronics Box Rear Panel The rear panel of the control box Figure 4 2 contains the input connector for the main cable 10 and the BNC female connector input to the external modulation coil 11 Battery replacement is through a panel in the bottom of the box STAR Cryoelectronics LLC 24 Mr SQUID User s Guide SQUID INPUT EXT COIL Figure 4 2 Rear panel of the Mr SQUID electronics box 4 3 Basic Operation The following discussion assumes that you have set up Mr SQUID as described in Section 2 To observe the V I curve of the SQUID cool down the probe without connecting or turning on the control box in order to minimize flux trapping effects Set the oscillator frequency control to suit your display device Typical sensitivities we suggest for the display device oscilloscope or x y recorder are approximately 0 2 V div for the cu
30. it is very often the case that only changes in field are of interest in which case no special measures are necessary 5 8 Details of dc SQUID operation So far we have discussed what it is that SQUIDs do namely SQUIDs convert magnetic flux which is hard to measure into voltage which is easy to measure Now we will describe how SQUIDs work As we have said a de SQUID is a superconducting loop with two Josephson junctions in it Suppose we pass a constant current known as a bias current through the SQUID If the SQUID is symmetrical and the junctions are identical the bias current will split equally half on each side A dc SQUID is generally represented schematically as shown in Figure 5 3 bias Figure 5 3 A schematic representation of the dc SQUID A supercurrent will flow through the SQUID as long as the total current flowing through it does not exceed the critical current of the Josephson junctions which as we discussed earlier have a lower critical current that the rest of the superconducting ring The critical current is the maximum zero resistance current which the SQUID can carry or the current at which a voltage across it develops You could measure the critical current of a SQUID by ramping the bias current up slowly from zero until a voltage appears then reading the current with an ammeter The value of current determined in this way is the critical current of the SQUID When the two junctions in the SQUID are identical t
31. laboratory SQUIDs and cannot be used to detect truly minute signals such as those generated by the human brain On the other hand Mr SQUID is designed to demonstrate all the principles behind SQUID applications In this user s guide we describe a number of experiments some simple others more complicated that allow you to explore the operation and the uses of SQUIDs The Basic Functions The Mr SQUID control box contains the necessary amplifiers current drivers and switches to allow you to observe and investigate two basic phenomena of SQUIDs and Josephson junctions without any additional experimental apparatus apart from an output device an oscilloscope or x y recorder and a supply of liquid nitrogen 1 Voltage current characteristics The Mr SQUID control box will allow you to observe the voltage current V I characteristics of the SQUID which consists of two Josephson junctions connected electrically in parallel Without liquid nitrogen cooling the V characteristic of the SQUID will be a straight line because the junctions behave like ordinary resistors Once the junctions are cooled the non linear shape you will see on the oscilloscope screen or x y plotter indicates the presence of a resistanceless current through the Josephson junctions The details of the shape are described later in this user s guide In this mode Mr SQUID allows you to observe directly the de Josephson effect the basis of many circuit a
32. locked loop can be read digitally by reading the 8 bits out of U4 and US or by monitoring the analog voltage at Test Point 3 TP3 42Radio Shack part number 276 038 43Tn the United States one example is Newark Electronics 312 784 5100 Newark Electronics is a registered trademark of the Newark Electronics Corporation 4801 N Ravenswood Ave Chicago IL 60640 and is not in any way affiliated with STAR Cryoelectronics or the Mr SQUID system 44Such as Radio Shack part numbers 276 169 276 174 270 175 STAR Cryoelectronics LLC 90 Mr SQUID User s Guide U1 U2 OP 27 U3 LM311 U4 U5 74LS169 4 bit U D counter From s U6 AD7524 8 bit DAC Rf aaa U7 LM1458 L 1k we 5 1kz 5V je All chip s use 15uf tantalum bypass caps between 5V pal the 5 and 5 volt power pins and the circuit ground R1 1kz eel ee 5V TTL Clock In from ig f Function V Generator se q 9 s i j zZz 6 orfu mye ad 6 oT m ht st oy 8252 hae lt lt a og a Sg ae P Pee ol 8252 ua FLL Analog output gong a 7 oe ee gt t 1 V 100uA 8252 825 DW ig 20k Si O 20k 5V Vv oe 5V oz 4 x B y as to Mr SQUID Light 7 10kz J external coil 4 7kz SV Emitting R2 5kz Diodes i Y 1 2k Figure 7 14 Schematic diagram of the 8 bit digital flux locked loop This circuit does require an adjustment to R2 connected to U6 in order to work correctly The adjustment procedure is as follows
33. microscopic objects Macroscopic objects are composed of enormous numbers of elementary particles whose complicated interactions and chaotic thermal motion completely masks the discrete nature of the microscopic world Superconductivity offers a unique opportunity to observe the quantization of a physical quantity in a macroscopic readily observable system The reason for this is that closed superconducting STAR Cryoelectronics LLC 28 Mr SQUID User s Guide circuits can only contain discrete units of magnetic flux known as fluxons More precisely the product of the magnetic field times the area of a closed superconducting loop must always be some multiple of h 2e where h is the aforementioned Planck s constant and 2e is the charge on an electron pair In other words a physically observable property of a macroscopic system must occur in units defined entirely by fundamental physical constants This is not only a profound observation to be made from a simple measurement it also has profound implications about the nature of superconductivity This fundamental flux unit is generally written as Do the flux quantum 5 5 Superconducting Rings The closed superconducting ring is a particularly convenient system to study for understanding the properties of superconductors It is also the basis of the SQUID Consider the following experiment We cool a ring of superconductor in a small magnetic field that corresponds to one flux quantum t
34. of SQUIDs and superconductivity not to teach solid state electronics Some of the experiments can be performed during the course of a single laboratory session while others may take more time We enthusiastically welcome feedback from users and particularly look forward to suggestions and descriptions for new experiments for the Mr SQUID system as well as improvements to the present experiments We would like to include them in later versions of the User s Guide and in supplements for current users Thank you in advance for your help Radio Shack and Tandy are registered trademarks of the Tandy Corporation Fort Worth TX 76102 and is not in any way affiliated with STAR Cryoelectronics or the Mr SQUID system STAR Cryoelectronics LLC 54 Mr SQUID User s Guide 7 1 Resistance vs Temperature of the YBCO SQUID Purpose This experiment will allow you to observe the superconducting transition of the YBCO film that forms the SQUID in Mr SQUID By tracking the resistance of the SQUID with the V I curve you can watch the YBCO undergo its superconducting transition The additional equipment needed for this experiment allows you to measure the temperature of the SQUID chip as it is cooled down to liquid nitrogen temperature Equipment For this experiment you will need e A glass encapsulated silicon diode 4 e 200 cm of insulated copper magnet wire of size 32 to 40 AWG 5 this corresponds to a diameter of 0 020 to 0 008 mm
35. of the previous experiment Also if you have not already measured the resistance of the external coil of your Mr SQUID while it is at 77 K do so now before connecting it to the flux locked loop STEP 2 On your voltage source change Rye to the lowest value on the resistor decade box STEP 3 Connect your oscilloscope to Test Point 2 of the flux locked loop circuit STEP 4 Turn the amplitude to zero completely counter clockwise on the Mr SQUID box We will not need the internal oscillator of the Mr SQUID electronic box for this experiment Now connect the voltage source to the Mr SQUID external coil At this point both the flux locked loop and the voltage source should be connected to the Mr SQUID external coil STEP 5 Using either an oscilloscope or a voltmeter measure the voltage at Test Point 2 of the flux locked loop circuit STEP 6 Connect a 9 Volt transistor battery to the input of your voltage divider circuit STEP 7 While measuring Test Point 2 of the flux locked loop circuit slowly increase R until you can just see a change at Test Point 2 STEP 8 Measure the voltage change V2 at Test Point 2 and measure the voltage of the 9 Volt battery that is energizing your double divider and record the value of Rye To calculate the value of the voltage at point B from the measurement at Test Point 2 it is illustrative to look at our circuit from the viewpoint of point B B Connection to 1 MQ resis
36. superconductor HTS thin film SQUID sensor chip normal metal coils for modulation and external coupling a cryogenic probe with a removable magnetic shield a cable to hook up the probe and a battery operated electronic control box containing all the circuits needed to operate the SQUID The probe is designed to be immersed in a liquid nitrogen bath in the enclosed dewar flask The user must supply the liquid nitrogen The only additional equipment required for the basic operation of Mr SQUID is either an oscilloscope or an x y recorder to display the output signals from the control box What s Inside the Probe At the heart of Mr SQUID is a small integrated circuit chip whose main components are a de SQUID and two modulation coils The SQUID is made of yttrium barium copper oxide Y BazCu307 sometimes called YBCO or 1 2 3 after the ratio of the metals in the compound that is fashioned into a ring containing two active devices called Josephson junctions The devices and structures on the chip are created using the same photolithographic steps that are used in the integrated circuits IC s that dominate today s conventional electronic devices What does Mr SQUID do Mr SQUID is an HTS de SQUID magnetometer and can therefore be used to detect small magnetic signals if they are properly coupled to the SQUID Because its modulation coils are not superconducting Mr SQUID does not have the sensitivity of high performance
37. times 330 It is not necessary for this amplifier to be inverting for this digital flux locked loop to function it was just easier to make a summing amplifier that inverts than one that does not U3 is a comparator that compares the output of U2 to ground If the output of U3 is greater than 0 volts then the output of U3 is 5 Volts a logical 1 for the digital circuits which follow If the output of U3 is less than 0 Volts then the output of U3 is 0 Volts a logical 0 for the digital circuits which follow U4 U5 and U6 are three 4 bit counters up down connected together to effectively form a 12 bit STAR Cryoelectronics LLC 95 Mr SQUID User s Guide up down counter An up down counter counts up if its data input is a 1 when its clock input is a 1 and counts down if its data input is a 0 when its clock input is a 1 The 12 bit output of the counter formed by U4 U5 and U6 is fed into U7 that is a 12 bit DAC The 12 LEDs allow you to see the bits output by U4 U5 and U7 that are input to the DAC The two 10 KQ potentiometers R2 and R3 connected to U7 are used to adjust the full scale voltage output of U7 The output of the DAC U7 is fed into the operational amplifier U8 to buffer its output The output of U8 is fed to the Mr SQUID external coil through a 10 KQ resistor The flux locked loop can be read digitally by reading the 12 bits out of U4 US and U6 or by monitoring the analog voltage at test point 3 TP3 This c
38. to see that offset so the scope will need to be de coupled while looking at Test Point 2 Test Point 1 is simply showing the V output of the Mr SQUID as a magnetic flux is swept Test Point 2 is also showing the V output of the Mr SQUID but magnified by a factor of 330 AND with an extra de offset from the circuit s 10 KQ potentiometer One should then adjust the 10 kQ potentiometer R1 so that the signal at Test Point 2 no longer shows any dc offset In other words adjust the potentiometer until the sine wave at Test Point 2 has the same amplitude in the voltage direction as in the voltage direction while dc coupled to the scope In Figure 7 18 the tops of the V curve are clipped flattened because the amplification of U2 is a little larger than needed Your circuit may show more clipping or none at all Once you have obtained the above signals from your circuit you are ready to lock in the flux state of the Mr SQUID If this is not done properly you can cause the Mr SQUID to flux trap First turn off your flux locked loop circuit Second ground yourself to the Mr SQUID box by touching the BNC connectors labeled X or Y on the front of the Mr SQUID box Third STAR Cryoelectronics LLC 96 Mr SQUID User s Guide carefully connect the circuit output to the BNC connector labeled EXT COIL on the back of your Mr SQUID box This BNC is a direct connection to the second gold coil on the Mr SQ
39. will be approximately linear with temperature and will depend only on the intrinsic gap of the semiconductor independent of the specific doping It also says that if one plots V T vs T one can take the high temperature region before the 5 2 In 7 term becomes significant and use it to extrapolate Vy to T 0 The zero intercept will give one the value of the semiconductor band gap E In other words all diodes made from a specific semiconductor such as silicon should display the same approximately linear behavior as a function of temperature under the same constant current conditions As a practical matter the above explanation breaks down at temperatures below about 30 K for silicon diodes Below that temperature a different mechanism takes over the diode behavior which still results in a linear VT down to almost 1 K but with a different slope Internal stresses in the silicon diode chip can also cause nonlinear V T relationships and so diodes sold specifically as cryogenic sensors are mounted in special packages to minimize the stresses from thermal contraction STAR Cryoelectronics LLC 61 Mr SQUID User s Guide 7 2 Building an Analog Flux Locked Loop Purpose and Background While the periodicity of the voltage modulation of a current biased SQUID is 1 flux quantum 2x10 Wb this is not the limiting resolution of magnetic flux measurement using a SQUID As mentioned in the SQUID Operation section of Section
40. 2 Varying the C rrent Blass ait caste ota ates ok Sealed Sate oe Sea anes a cae Fale tet nae nel 11 3 3 Varying the Amplitude of the Current Sweep ccccccccsseceeeceeeeeeseecaeceseeeeeeeeaeeesaeens 11 3 4 Calculatie the Current niesna aE a E E hive a 12 3 5 THe V ECUN Oea a a a R a A A eee eee eae 12 3 6 Observing V Characteristics using Mr SQUID wo eseeseesseseeseesseesesseessessesstesestessees 15 3 7 Modulating the Critical Current of the SQUID aonce cs case ease asieiienee oss 15 3 8 Additional SQUID Measurements jis sccsscceckessaassceadisessvasens adeadsnone ds antacashasteacisqaatiaspaaeeees 18 3 9 Summary of Basic EXPer iments lt iccs2ssiccavccts sxvsscedatteanicteeyliaincitends es iadaty dete iedeatocarenaecs 21 4 Getting Started with Mr SQUID Advanced Users i iuceeesa castes ante eects ocacesee d 23 4 1 Electronics Box Front Panel o iloc sc sacaacsaceascsqauasystecox cbse ouaken si sdedeueeacesucvascogsvaeeat esessae 23 42 Electronics Box Rear Panel is siscigess3icds casecavs suasvctess asthe ict shecsnes phatecdi casaleaveapeceangenne 24 4 3 Basic OPE ration aasgieren nir Oona a eis ase AE a Maen a iE 25 4 4 V Chatactetistics seiceraoeeente neaei e eet ei eE EE EETA Eas E EEEE 26 5 An Introduction to Superconductivity and SQUIDS ss sessssessesesseessessresressessrssresseeseesressee 27 5 1 A Capsule History of Superconductivity 0 ccccecccccceeseeeteceeeceeseeeseecsaeceeeeseeenseeeaeens 27 5 2 Superc
41. 3 Be sure to use at least 50 cm of fine copper wire no larger than 30 AWG between the DVM and the diode Turn on the constant current source and the DVM You should get a reading across the diode of between 0 3 and 0 4 Volts If you do not check the wiring for shorts Ifthe DVM reads several Volts check to see if you have the correct polarity wired between the diode and the current source STAR Cryoelectronics LLC 79 Mr SQUID User s Guide 10 pA Current Source Fos 100 cm fine copper wire Next connect the 0 10 Volt adjustable power supply to the resistor leads and connect the sine wave generator in series with the HTS chip coil leads and a 1000 Q resistor as shown below Set the sine wave generator to 1Hz frequency and set it to its minimum amplitude Coil mounted on HTS coated chip Sine Wave Generator Next empty the Mr SQUID dewar until there is only about 15 cm of liquid nitrogen left Place the Mr SQUID probe into the dewar as shown below Make sure to use the binder clip to keep the Mr SQUID probe from sliding down into the dewar You want to start with the Mr SQUID probe at the very top of the dewar At this point connect the Mr SQUID probe to the Mr SQUID electronics and connect the Mr SQUID electronics to the oscilloscope Turn on the Mr SQUID electronics and place the unit in the V J mode You should see a straight line The slope of this line is the resistance of the Mr SQUID
42. 5 one can using appropriate electronics measure changes far smaller than 1 flux quantum Low temperature SQUIDs can quite typically measure magnetic flux changes down to millionths of a flux quantum But in addition to requiring high sensitivity most experiments in which one would use a SQUID also require considerable dynamic range In other words one does not need merely to detect a small magnetic flux one may also need to measure a sizable magnetic flux with sub flux quantum accuracy The way one does this is to operate a SQUID in what is called a flux locked loop A flux locked loop functions in a straightforward way One biases the SQUID with a constant current so that the voltage across the SQUID will be periodic with the applied flux such as is done in the V setting on the Mr SQUID box One then amplifies this voltage response and uses the resultant signal to drive a coil near the SQUID The system is set up in such a way that the current flowing through the coil creates a magnetic flux of opposite polarity to the unknown flux to be measured If one sets up the system correctly the SQUID will be in a zero magnetic flux condition in fact it will be locked onto a zero flux condition Under the flux locked condition one only has to measure the current being used to generate the opposing flux in order to determine the magnitude of the unknown flux This scheme is called a flux locked loop How accurately one can create t
43. L with dynamic ranges of 256 and 4096 respectively Comparison of the two flux locked loop schematics will indicate how they can be extended to an arbitrary number of bits if an appropriate bit size digital to analog converter is used Equipment For both 8 bit and 12 bit versions of this experiment you will need e Some familiarity with reading electrical schematic drawings e Mr SQUID and liquid nitrogen e An oscilloscope e A solderless breadboard e Two low noise operational amplifier chips e g OP 27 e One voltage comparator chip e g LM311 e One 10 kQ ten turn potentiometer e One function generator capable of running up to 1 MHz and can put out a TTL compatible signal 0 5 Volts e A selection of resistors in the range of 1 KQ through 100 kQ e A selection of capacitors in the range of 0 001 uF through 15 uF e A selection of hook up wire and alligator clips Additional parts needed for the 8 bit version e Two 4 bit binary up down counter chips e g 74xx169 such as a 74LS169 37See for example Josephson integrated circuits HI A single chip SQUID magnetometer by Norio Fujimaki Fujitsu Sci Tech J 27 59 1991 which should be available at any major university physics or engineering library 38Such as Radio Shack part numbers 276 169 276 174 270 175 STAR Cryoelectronics LLC 88 Mr SQUID User s Guide e Eight light emitting diodes LEDs e One AD7524 8 bit digital to analog conver
44. O superconductor in Mr SQUID is approximately 90 K It is important to cool the SQUID into the superconducting state with a minimum of external magnetic fields present This will reduce the effects of a phenomenon known as magnetic flux trapping which will adversely affect the performance of the SQUID To cool the SQUID in the lowest ambient field it is best to shut off any nearby electrical devices such as radios or computers It is also advisable to leave the probe cable unconnected until after cooldown We will discuss the consequences of flux trapping later Figure 2 3 Mr SQUID inserted into liquid nitrogen dewar STEP 4 Connecting the probe After cooling the probe attach one end of the connection cable provided with Mr SQUID to the warm end of the probe and the other end to the SQUID Input connector 10 on the back of the electronic control box shown in Figure 2 4 below The cable can be connected in one orientation only STAR Cryoelectronics LLC 7 Mr SQUID User s Guide SQUID INPUT EXT COIL Figure 2 4 Rear panel of the Mr SQUID electronics box STEP 5 Connect the Output Device Connect the BNC coaxial cables to the output connectors labeled X 5 and Y 6 on the front panel of the control box The free end of the X cable should be attached to the horizontal input or x axis of your display device either a 2 channel oscilloscope or an x y recorder Likewise the free end of the Y cable should
45. One cannot change this resistor it arbitrarily however We would suggest that this be left to the student to determine how much they can change this resistor and what the trade offs are Third the digital flux locked loops clock frequency function generator can be increased to allow the counter and DAC to respond faster or slower Increasing the clock will allow the flux locked loop to respond the changing fluxes faster decreasing the clock will slow down its response This is analogous to changing C1 in Advanced Experiment 2 see Section 7 2 The bandwidth of the Mr SQUID electronics is about 2 8 kHz so increasing the clock speed past a certain point will not allow one to increase the ability of this circuit to cancel fluxes changing faster than this Other speed limitations may be encountered by hitting the limits of the digital chips used or the operational amplifiers used The counters U4 U5 and U6 used in our implementation cannot go faster than 20 MHz so they will not be a limitation the DAC U6 which was an AD563 cannot go faster than using a 700 kHz clock We would suggest that it be left to the student to see what the effects of varying the clock frequency has on the performance of the digital flux locked loop Advanced Experiment 3 Section 7 3 which uses the analog flux locked loop to create a voltmeter can be performed using your digital flux locked loop 50For you SQUID buffs Since the bandwidth of the Mr S
46. QUID is a system designed to be used in ordinary undergraduate laboratories However it is still a SQUID which is an extraordinarily sensitive detector of electromagnetic signals For this reason there are some locations in which it simply will never work properly without measures such as the Faraday cage mentioned above Your particular laboratory could possibly be such a location in the final analysis For this reason before you become convinced that there is an internal problem with your Mr SQUID make sure you operate it in a variety of locations What if it never looks right All Mr SQUID probes have been tested at STAR Cryoelectronics in unshielded laboratory space and have demonstrated acceptable characteristics It is possible that something may have gone wrong with the SQUID subsequent to its departure from our test lab but a chip or probe failure is unlikely to result in a linear V I curve of the sort usually associated with flux trapping i e displaying a superconducting transition below which the SQUID V I curve has a resistance of less than 1 Q Real chip failures generally yield a more catastrophic outcome If all else fails call us and describe your problem 6 6 Customer Service We are anxious to help you make the most of your Mr SQUID system You can best communicate with us by email at info starcryo com STAR Cryoelectronics LLC 52 Mr SQUID User s Guide When you do contact us please send a descri
47. QUID box is 2 8kHz this translates into a minimum DAC step flux noise of 65 u Hz We will examine the step size later in this experiment STAR Cryoelectronics LLC 98 Mr SQUID User s Guide 7 7 3 Additional Things to Explore with your Digital Flux locked Loop 1 Digitization error and noise In Figure 7 20 we show what the curve at test point 3 TP3 looks like when you increase the sensitivity on the oscilloscope The scope photos in Figure 7 20 were taken using the 8 bit flux locked loop while the loop is in its locked state The discreteness of the y axis display is an illustration of quantization error In other words the voltage at TP3 can vary between 5 Volts and 5 Volts 3 Volts and 3 Volts for the 12 bit FLL and must be described by a number between 0 and 255 by the 8 bit counter between 0 and 4096 for the 12 bit FLL This means the voltage at TP3 must be quantized in units of 10 Volts 256 0 039 Volts 6 Volts 4096 0 00146 Volts for the 12 bit FLL Since the external coil of the Mr SQUID unit is driven by the voltage at TP3 thought a 10 KQ resistor this means that the current through the Mr SQUID external coil is quantized in units of 0 039 Volts 10 KQ z 3 9 uA 0 00146 Volts 10 KQ 0 146 uA for the 12 bit FLL Now since all of our scope photographs use the x axis flux in the V mode of the Mr SQUID electronics box as their x axis we can look at the unlocked V curves in Figure
48. STAR Cryoelectronics Mr S YUID User s Guide Version 6 2 2 STAR Cryoelectronics LLC 25 Bisbee Court Suite A Santa Fe NM 87508 U S A Mr SQUID User s Guide Manual written by Randy W Simon Michael J Burns Mark S Colclough Greg Zaharchuk and Robin Cantor Advanced Experiments written by Michael J Burns Exp 1 5 and 7 and Greg Zaharchuk Exp 6 Mr SQUID is a registered trademark of STAR Cryoelectronics LLC Copyright 1996 2004 STAR Cryoelectronics LLC iii Mr SQUID User s Guide TABLE OF CONTENTS TS CHMTIC AN SS UO RG vines oy tains dade sacanacs 21 cass saucas vs eda gis ac aaactauceeta hcoianaoacdnsbne munca Saas y see ea eden vi Warranty SG teh ROO a ROR SO E NO E Ce RAR Ie Oe ae ORNS ASE CG CR AS vii Safety PTE CAUTIONS ninme a a E E E sites ch Rabi eke O Delica amend vii VP Tr due On senan inan Mia ees Dinsens Aes a a aes eg ated Saas iain ae ta 1 2 Setting Up Mr SQUID basciccssduies sks vqiedensasan au ela violas dkelyaaleaseawisasso tacstalenestaeduaatecacsaaoaass 5 2 1 What X ou l ING OU canter cebu ECE E AI AAEE e ai E A E E OT NEA 5 2 2 Assembling the Mr SQUID System c sceccsssssssssessssesecsesssssssssesussassstesscsessstesseseesneenss 6 3 Getting Started with Mr SQUID New USers csccsscsssssessscsessecesesesessasssssersussessnesessnceveneees 10 3 1 Setting Up the Output Devices uj aceccsnasszicatinanenipipncccum tet setataennodennatyatanm a eeaeae 10 3
49. This control is used to current bias the SQUID manually at a chosen fixed drive current 4 Amplitude control Sets the amplitude of the current triangle wave in either the V Z or the V mode In either mode use the amplitude control to set the width of the current sweep In the V I mode the current triangle wave is applied to the terminals of the SQUID In the V mode the current triangle wave is applied to the gold modulation coil 5 X Output A BNC female connector providing the x current output of the Mr SQUID box The voltage appearing at this terminal is developed across a 10 kQ resistor through which the current flows To determine the current divide the measured voltage by 10 KQ e Inthe V I mode the x output represents the bias current through the SQUID the sum of the triangle wave plus the fixed bias current set by the Current Bias control e Inthe V mode the x output represents the current through the modulation coil the sum of the triangle wave plus the fixed modulation current set by the Flux Bias control 6 Y Output A BNC female connector providing the y voltage output of the Mr SQUID box Voltages coming from the SQUID are amplified by a factor of 10 000 at this output i e 10 uV SQUID modulation voltage 100 mV at the y output 7 Oscillator Frequency Sets the frequency of the current triangle wave in both V J and V mode In the high speed position up the frequency of the triangle wave
50. UID chip and so any small static discharges into the coil can create large magnetic fluxes in the SQUID Make sure the V output TP1 still looks correct If not you have caused your Mr SQUID to flux trap and will need to warm it up and recool it If you need to do this try recooling with your un powered flux locked loop circuit already attached to the EXT COIL connector TPl TP2 Figure 7 18 Signal outputs of the 12 bit FLL in the unlocked mode at TP1 and TP2 Reconnect the power to your flux locked loop circuit Set the frequency of the function generator that is supplying the TTL to about 50 kHz to 200 kHz The signal at Test Point 2 should look like that shown in Figure 7 19 If it does not try adjusting the function generator frequency Test Point 2 ideally would be a flat line if your flux locked loop perfectly canceled the flux applied by the Mr SQUID box As can be seen below in our test circuit the line is pretty flat indicating that the cancellation is good From the slope of this line one can estimate how accurately the circuit is holding the flux constant In Figure 7 19 the very small slope of Test Point 2 indicates that the y axis shifts by less than 0 04 Volts when the applied flux covers 1 o By looking at the slope of TP2 near its zero crossing in Figure 7 18 above one can see that the slope dV d is 29 Volts p This means that the locked flux shifts by 1 4x10 Po when the applied flux covers 1 Bo
51. adjust or modify the instrument except for modifications as specified in this manual This could cause nullification of any warranty For service return the instrument to STAR Cryoelectronics or any authorized representative Do not operate this instrument in a volatile environment such as in the presence of any flammable gases or fumes The liquid nitrogen dewar provided with Mr SQUID is accompanied by instructions from the dewar manufacturer The user is responsible for the observance of the manufacturer s directions warnings and restrictions STAR Cryoelectronics LLC vil Mr SQUID User s Guide Congratulations You have just purchased the world s first high temperature superconductive electronic system product Mr SQUID originally developed by Conductus and now offered exclusively by STAR Cryoelectronics Contained within its cryogenic probe is an integrated circuit chip incorporating a high temperature superconducting quantum interference device SQUID This affordable instrument system will allow you to observe several of the unique features of superconductivity without the complications of liquid helium cooling and without specialized equipment or facilities In addition Mr SQUID will allow you to learn about the operation of SQUIDs by following a series of experiments that can be readily performed in undergraduate laboratories Mr SQUID is a First e Mr SQUID is the first electronic instrument on the
52. and the voltage across such a diode varies linearly with temperature The reason a diode can be used as a linear temperature sensor is explained in a section at the end of this experiment but this information is not required to perform the experiment 7 1 1 Diode sensor calibration Set up First trim the leads of the diode to be as short as possible then carefully solder on new leads using the copper magnet wire each one at least 50 cm long Be careful not to overheat the diode with the soldering iron After the leads are attached to the diode check the diode with an ohmmeter to verify continuity through its leads and that it still acts as a rectifier in one direction it should have a moderate resistance in the opposite direction the resistance should be extremely high Connect the silicon diode to the 10 pA de constant current source and DVM as shown in Figure 7 1 If you do not have a suitable constant current source available a procedure to make one is outlined at the end of this experimental section Be sure to use at least 50 cm of fine copper wire no larger than 30 AWG between the DVM and the diode Turn on the constant current source and the DVM You should get a reading across the diode of between 0 3 and 0 4 Volts If you do not check the wiring for shorts If the DVM reads several volts check to see if you have the correct polarity wired between the diode and the current source 10 pA Current Source 100 cm f
53. anies will screen STAR Cryoelectronics LLC 49 Mr SQUID User s Guide packages using x ray machines and these machines often generate magnetic fields There is no easy way to tell if the mu metal shield has become partly magnetized 6 4 Degaussing the Magnetic Shield If you suspect that your Mr SQUID magnetic shield may be partly magnetized there are products available that permit a simple procedure for demagnetizing it This procedure is also called degaussing We suggest that you use a Bulk Tape Eraser preferably one with an on off switch such as those sold by electronic dealers such as Radio Shack Please read and follow both the Safety Instructions and the Operating Instructions which come with the bulk tape eraser To degauss a Mr SQUID mu metal shield one should follow the instructions that come with the tape eraser but in this case the mu metal shield is degaussed rather than recording tape The instructions for degaussing the magnetic shield on Mr SQUID are as follows STEP 1 Remove the mu metal shield from the Mr SQUID probe by loosening the setscrew at the top of the shield Be sure the probe is at room temperature STEP 2 Plug in and turn on the bulk tape eraser STEP 3 While the tape eraser is on place the bottom of the eraser in contact with the mu metal shield to be degaussed Move the shield slowly in a circular motion over the entire area of the shield Do not turn off the tape eras
54. avefunction the amount of flux contained within in the ring can only assume certain discrete values This quantum mechanical property is the origin of flux quantization Thus we see that there is an intimate connection between flux quantization and the zero resistance property of superconductors There is one more aspect of superconductivity that we need to know a bit about in order to work with Mr SQUID the Josephson effect 5 6 Josephson Junctions The Josephson effect is yet another manifestation of what we call the long range quantum coherence of superconductors The simple picture of this effect is as follows o o gt Figure 5 2 Schematic diagram of two superconducting regions separated by a thin gap Two regions of superconductor are placed very close to one another as in Figure 5 2 The quantum mechanical phase on the left is 6 and the phase on the right is 62 In an ordinary material the phases at two different spots are unrelated In a single piece of superconductor the phases at two different places have a specific relationship to one another This arrangement assures a lower energy ground state that results in superconductivity In the picture above what will the phases do The surprising answer which also resulted in a Nobel Prize in Physics is STAR Cryoelectronics LLC 30 Mr SQUID User s Guide that if the two regions of superconductor are close enough together their phases will also be related In othe
55. between wave fronts that pass through the different slits By analogy the behavior of this double Josephson junction loop displays interference in the current voltage behavior as magnetic flux threads the loop hence the name Superconducting QUantum Interference Device SQUID ET 1 1 0 One does not need to measure a whole period in the SQUID modulation to perform a flux measurement One can measure quite accurately a small fraction of a period and detect changes in the flux threading the SQUID loop that are much smaller than a flux quantum Bp A SQUID biased to where 0OV O is maximized produces a considerable output voltage in response to a small input flux d thus acting as a magnetic flux to voltage converter One usually uses a SQUID in a flux locked mode where an external coil is used to generate a magnetic field in such a manner as to keep the total flux through the SQUID loop constant The current supplied to this coil is used to indicate the value of the unknown flux being canceled Thus the flux measurement is manifested as a current measurement that can be performed with extremely high sensitivity and accuracy and also has the additional advantage of large dynamic range in magnetic field measurements It is possible to use Mr SQUID in this way and this is detailed in the Advanced Experiments in Section 7 5 11 Practical SQUID Magnetometers Although in some applications it is convenient to expose the SQUID dire
56. ble before recording the temperature it will be very inaccurate Trouble avoidance tip Don t let the wires from the silicon diode extend far below the Mr SQUID magnetic shield If they do they might dip into the liquid nitrogen before the probe end does If this happens the thermal conductivity of the copper wires can cause the diode to indicate a temperature as much as 10 15 K lower than the superconducting thin film chip This is something to watch for particularly when below 120 K The data below of the V horizontal shift as a function of temperature were taken using a YBCO film on sapphire whose transition temperature was previously measured to be about 88 K Since we were using a excitation coil which induced currents just below J at 77 K the inductive tail is probably indicative of very minor thickness variations in the film demagnetization effects at the edges of the film or other inhomogeneities present in the film itself 0 4 o 0 3 S 0 2 0 1 0 75 80 85 90 Temperature K STAR Cryoelectronics LLC 82 Mr SQUID User s Guide 7 5 3 Additional exercises for this experiment 1 Calculate from the geometry of their coils and the values of the currents measured in step 3 above what size magnetic fields are being used to sense the superconducting state of the film 2 Repeat this experiment using increasing current levels in the coil Why are the curves different STAR Cryoelectronics LLC 83
57. can we understand flux quantization itself The answer lies in the long range coherence of the superconducting wavefunction As we said before the value of the wavefunction in one place in a superconductor is related to the value at any other place by a simple phase change The case of a superconducting ring places special restrictions on the superconducting wavefunction The wavefunction y at the point marked by the black dot on the ring in Figure 5 1 must be the same wavefunction obtained by traveling around the ring one full circuit it is the same spot The phase change for this trip must be 27 in order for the wavefunction to have a single value at a given point in space In ordinary wave language if the wave was at a crest at the starting point it must be at a crest 360 27 around the circle STAR Cryoelectronics LLC 29 Mr SQUID User s Guide Figure 5 1 A superconducting ring According to electromagnetic theory applying a magnetic field to a superconductor induces a change in the phase of the wavefunction For those of you who have studied quantum mechanics this comes from the relationship between phase and canonical momentum p eA where p is the mechanical momentum and A is the vector potential A given amount of magnetic field creates a specific phase change in the wavefunction Since the phase change going completely around the ring must be some multiple of 2z in order to maintain the single valuedness of the w
58. ch as a LM741 Radio Shack part number 276 007 21Such as Radio Shack part numbers 276 169 276 174 270 175 22Such as Radio Shack part number 276 565 23guch as Radio Shack part number 276 561 24 C T Sah R N Noyce and W Shockley Proc Inst Radio Engrs 45 1228 1957 STAR Cryoelectronics LLC 60 Mr SQUID User s Guide Eqn 7 1 I ae B where q is the charge of the carriers T is the absolute temperature kg is Boltzmann s constant and Vyis the voltage across the diode The current Z is given by A Eqn 7 2 I Ks i TE where A is the p n junction area T is the average carrier lifetime E is the electric field in the depletion region of the p n junction and n is the carrier density The value of n is given by 3 2 in E 3 2 E Eqn 7 3 n 2 ha exp Ce L exp 4 nh kT 4 mh 2k T where E is the conduction band energy E is the intrinsic energy gap in the semiconductor u is the carrier chemical potential and m is the effective mass of the carriers Combining these three equations and solving for V as a function of T and assuming we have a fixed forward bias current I through the diode we find E Eqn 7 4 V T In gt nT In eta q 2 q where 2mk TX A Eqn 7 5 a 1 Ks ka 4 T TE Note that the above equation for V 7 says that a p n semiconductor junction under constant forward bias current fixed Jy will display a voltage that
59. characteristics of a high T superconducting quantum interference device J Appl Phys 73 7929 1993 STAR Cryoelectronics LLC 20 Mr SQUID User s Guide 3 9 Summary of Basic Experiments By going through the previous set of experiments you should have been able to observe the fundamental properties of Josephson junctions and SQUIDs and calculate the values of these key parameters Critical current of the SQUID Ie Normal state resistance Ry Characteristic voltage of the SQUID Ry Maximum voltage modulation depth AV Inductance of the SQUID L and Modulation parameter z determined using two methods More advanced experiments with SQUIDs including those that use the external modulation coil can be found in Section 7 Advanced Experiments STAR Cryoelectronics LLC 21 Mr SQUID User s Guide Mr SQUID Data Sheet SQUID Serial Number Critical Current J Normal state Resistance Ry Q Characteristic Voltage Ry Modulation Depth AV SQUID Inductance L Bi from Modulation Depth Bi from Inductance STAR Cryoelectronics LLC 22 Mr SQUID User s Guide 4 GETTING STARTED WITH MR SQUID ADVANCED USERS This section is meant to give a quick explanation of the procedures for operating Mr SQUID and the features of the Mr SQUID control box and assumes a previous knowledge of superconductivity and SQUIDs The same information is provided in far greater detail in S
60. common difficulty encountered with Mr SQUID and for that matter with all Josephson electronic circuits is the effect of magnetic flux being trapped in the SQUID loop or in the junctions themselves Trapped flux can greatly diminish the critical currents of the junctions In the extreme but unfortunately quite likely case the critical current in the SQUID may vanish entirely resulting in a linear V J curve The cause of this problem is the extraordinary sensitivity of the SQUID and of Josephson junctions to applied magnetic fields There are many sources of external magnetic fields in the operating environment of Mr SQUID The most obvious one is the field of the earth itself which is approximately 0 5 gauss in magnitude If this entire field found its way into the SQUID it would correspond to several hundred flux quanta in the loop In addition electrical devices of all sorts emanate magnetic fields that can affect Mr SQUID It is for this reason that the end of the Mr SQUID probe that includes the chip is enclosed in a mu metal shield If this shielding were perfect then external fields would not affect the SQUID at all Bringing a small magnet close to the Mr SQUID dewar while the SQUID is operating should convince you that the shielding is not perfect In any event it is important to cool down the SQUID into the superconducting state with the least amount of magnetic field present This means leaving off any electronics tha
61. concepts briefly and without theoretical rigor This user s guide is not intended to be a textbook on quantum mechanics or on superconductivity Fortunately many such books exist and we refer you to some in the References in Section 10 What this guide will try to do is give you some idea of the underlying physical principles behind Mr SQUID 5 3 The Superconducting State A fundamental aspect of physical systems is that they naturally seek a state of lowest energy An example of this is that a ball will roll to the lowest spot on an uneven surface the lowest potential energy An external source of energy such as kicking the ball is required to raise it to a higher spot energy level Similarly systems of particles such as the electrons in a metal will occupy a lowest energy state known as the ground state unless they are excited by some external source of energy In certain materials it is possible for electrons to achieve a ground STAR Cryoelectronics LLC 27 Mr SQUID User s Guide state with lower energy than otherwise available by entering the superconducting state What is this state The Nobel Prize in Physics was awarded for the development of the theory that describes this state Simply put the superconducting ground state is one in which electrons pair up with one another such that each resultant pair has the same net momentum which is zero if no current is flowing In this ground state all the electrons are desc
62. correspond to the n 1 steps So for our data above e v _ 4 52x10 Hertz a h 2V 2 9 25x10 Volts Eqn 7 16 2 44x 10 Hertz Volt The official value of e h is 2 4179671x10 4 Hertz Volt which means our measurement was good to about 0 8 This relatively high level of accuracy using such a simple measurement is the reason the ac Josephson Effect is used by the National Institute of Standards However for us to claim that we made this measurement to this level of accuracy would be somewhat misleading The reason is that if you look at the scope picture of the Shapiro steps above the steps are not perfectly flat and show some rounding This might be due to small fluctuations in the microwave generator frequency or they might also be due to thermal noise in the SQUID Remember although 77 K may seem cold to us it is rather hot compared to the superconducting transition temperature of your SQUID 77 K T 0 85 So there is some uncertainty in the placement of the steps The voltages at which the steps appear could be stated to be at 9 25 0 3 uV To calculate the uncertainty in a function f x from the uncertainty of x we would use Eqn 7 17 0 Zro 0 This means the 0 3 uV uncertainty in the voltage step Oy would result in an uncertainty Oe n for e h of Eqn 7 18 where oy 0 3 uV There are many good books on error analysis and error propagation Two that we recommend are Introduc
63. creening current decreases When the applied flux reaches exactly one flux quantum the screening current goes 3An article which describes this is Ryh nen et al SQUID Magnetometers for Low Frequency Applications Journal of Low Temperature Physics 76 287 1989 STAR Cryoelectronics LLC 34 Mr SQUID User s Guide to zero At that point the magnetic flux inside the loop and the magnetic flux applied to the loop are equal so there s no need for a screening current If you increase the applied magnetic flux a little more a small screening current starts to flow in the positive direction and the cycle begins again The screening current is periodic in the applied flux with a period equal to one flux quantum Do 3 2 5P 3o 7Po 2 2 2 2 Figure 5 7 Relationship between screening current and applied magnetic flux Since you already know these two facts e The screening current of a SQUID is periodic in the applied flux and e The critical current of a SQUID depends on the screening current it makes sense that a SQUID s critical current is also periodic in the applied magnetic flux The critical current goes through maxima when the applied magnetic flux is an integer multiple of the flux quantum because that s when the screening current is zero It goes through minima when the applied magnetic flux is an integer of the flux quantum plus one half because that s when the screening current is largest Because
64. ctly to the magnetic field of interest more often the magnetic signal is conveyed to the SQUID by a flux transformer A flux transformer is a closed superconducting circuit consisting of two coils in series We emphasize that a SQUID flux transformer is superconducting because that means it can be used to couple static fields 0 as well as the alternating gt 0 fields that a non superconducting transformer can couple One coil the input coil is magnetically coupled to the SQUID and is usually fabricated along with it the second or pick up coil is exposed to the field to be measured This second coil acts as a magnetic antenna that couples external signals into the SQUID It isa basic principle of superconductivity that the flux inside a closed superconducting circuit cannot change Consequently a change in field that causes the flux in the pick up coil to change also causes a change in the flux in the input coil The SQUID senses this latter flux change The area of the pick up coil is usually much greater than the area of the SQUID The prime function of the transformer is to convert the high magnetic flux sensitivity of the SQUID itself into a high magnetic field sensitivity STAR Cryoelectronics LLC 39 Mr SQUID User s Guide Another advantage of using a flux transformer is that the input coil which can be made as a wire or a thin film structure can be configured to suit the measurement at hand In particular it can be
65. culating current in the SQUID can shield the applied flux and is a factor in determining the flux to voltage transfer ratio of the SQUID In Section 3of the User s Guide two procedures for determining this parameter for the SQUID in the Mr SQUID system are outlined In addition to these theoretical parameters there are some restrictions that are determined by the superconducting technology used in the SQUID In the case of the YBCO grain boundary junctions used in Mr SQUID the most important restriction arises from the fact that as well as allowing Cooper pairs to pass the junctions also allow a large current of single electrons to pass This current behaves like the current that would flow through an intentionally added parallel resistor One consequence is that the condition on Be is always satisfied the junctions are not hysteretic A less welcome consequence is that the product J Ry is a constant determined by the nature of the grain boundary and the temperature The size of J Ry is important because along with Bz it determines the voltage that the SQUID generates in response to a change in flux It has been shown see the reference by Tesche and Clarke that at the optimum bias current the change in SQUID voltage when the applied flux changes from zero to 2 is approximated by the expression4 Eqn 5 5 AV Extensive calculations and experiments have shown that a value of Bz 1 is a good choice for low noise operati
66. d engineers exploit to create the world s most sensitive magnetic field detectors This flux vs voltage curve will appear on your oscilloscope or x y recorder page during your experiments with Mr SQUID Although the model of SQUIDs we just discussed is not rigorous it is true as far as it goes and it will give you a feeling for how SQUIDs work without delving into the deeper aspects of quantum mechanics The main weakness of the model is that it doesn t really convey the phenomenon of quantum interference A SQUID is a Superconducting QUantum Interference Device The curve showing how the critical current of the SQUID varies with applied flux is an interference pattern analogous to an optical interference pattern If you shine coherent light through two slits on a screen you see maxima and minima of intensity bright and dark spots as you move from left to right because the two sources of light interfere with each other If you pass a current through a dc SQUID you see maxima and minima of critical current as you raise or lower the applied flux because the macroscopic quantum wave functions at the two junctions interfere with each other The analogy is very close 5 9 SQUID Parameters With a little device modeling we can quantify some of the SQUID behavior discussed in the previous section In a real dc SQUID the non ideal characteristics of the Josephson junctions play a significant role in the behavior of the device The shunt r
67. d levels of various sources Today s dc SQUIDs are made up of rings of thin film superconductor interrupted in two places by Josephson junctions Additional thin film layers make up the flux transformer and in some cases the pick up coil Progress in Josephson junction technology based on niobium low temperature superconductors has led to SQUIDs with unprecedented levels of performance SQUID performance is limited by intrinsic flux noise within the device that sets a lower limit on STAR Cryoelectronics LLC 40 Mr SQUID User s Guide the external magnetic signals that can be detected with a SQUID magnetometer The noise levels in the best niobium SQUIDs are low enough to permit the detection of tiny magnetic signals associated with the electrical currents of nerve impulses in the human brain These signal levels are compared to a variety of other sources of magnetic fields in the chart shown in Figure 5 10 The price that must be paid for this sensitivity is that niobium SQUIDs require cryogenic cooling down to temperatures of a few Kelvin in order to function This cooling is generally provided by immersion in liquid helium at 4 2 K 269 C The chart above indicates the magnetic field levels that are characteristic of a variety of sources The ability of a magnetometer to sense these fields is limited by the noise levels within the device The table below lists the estimated field noise in femtotesla 10 T per root Hertz for seve
68. d resistively should be compared with the value predicted by theory 600 500 4 400 4 300 _ 200 100 4 Critical current UA 0 10 20 30 40 50 60 70 80 Temperature K STAR Cryoelectronics LLC 87 Mr SQUID User s Guide 7 7 Building an 8 bit or 12 bit Digital Flux Locked Loop Purpose and Background While analog flux locked loops as described in Advanced Experiment 2 are by far the most common all commercial SQUID systems use analog flux locked loops flux locked loops that are intrinsically digital in nature can also be built Digital flux locked loops have the advantage of being more amenable to use in systems such as magnetoencephalography brain scanning which require tens or even hundreds of SQUIDs They have the disadvantage of being limited in dynamic range to about 18 bits due to the fact that digital to analog converters of sufficient speed are typically limited to this range The dynamic range of the flux locked loop is the ratio between the smallest signal and the largest signal the flux locked loop can measure correctly For 18 bits this is a ratio of largest to smallest signal of 2 262144 By contrast a quality analog flux locked loop can have a dynamic range on the order of 10 10 There are excellent review articles on digital flux locked loops for those interested in the state of the art gt 7 In this experiment we will show you how to build an 8 bit and a 12 bit digital flux locked loop FL
69. derably larger The normal state resistivity does not change that much since it reflects the properties of YBCO in the normal i e not superconducting state You should also now be able to calculate the reduced temperature t T T using the value of T as determined by Advanced Experiment 1 see Section 7 1 If not STAR Cryoelectronics LLC 85 Mr SQUID User s Guide by taking two sets of measurements of Ie at 77 K and at the new lower temperature you can theoretically estimate the critical temperature What kind of dependency do the standard superconducting properties exhibit with respect to the reduced temperature t No one yet completely understands the precise mechanism responsible for high temperature superconductivity nor is there a clear model of why certain crystalline grain boundaries such as those forming the Josephson junctions in your Mr SQUID act the way they do In many ways these grain boundary Josephson junctions appear similar to a common junction in low temperature superconductors called an S N S junction so called because it is made by inserting a thin layer of normal N metal in between two superconductors F Grain boundary ae Grain boundary Figure 7 13 Two methods of forming the Josephson junctions in a dc SQUID Left S N S Josephson junctions Right Grain boundary Josephson junctions The SQUID on the left in Figure 7 13 shows S N S Josephson junctions a standard method used for most
70. ductor has the same property it ceases to be resistanceless as soon as the current it is carrying exceeds a maximum value called the critical current A Josephson junction is a weak link between two regions of superconductor and this weak link carries far less resistanceless current than the superconductor on either side The maximum supercurrent that can flow through a Josephson junction is called the critical current of the junction At this point you might want to adjust the flux bias control 2 on the control box This control feeds current into a small gold coil placed above the SQUID and this current applies a magnetic field upon the loop the SQUID As explained in Section 5 a magnetic field will modulate the critical current in the SQUID in a very specific manner By turning the flux bias control knob the critical current in the junction will change visibly on the oscilloscope screen or on your plotter page At this point try to adjust the flux bias current such that the flat region of the V curve is widest The response to these changes may be quite sensitive it may take some practice to tune the critical current to its maximum value This procedure may be especially useful if some small amount of magnetic field was already present in the SQUID loop A zero applied field will yield the largest critical current through the junction STAR Cryoelectronics LLC 13 Mr SQUID User s Guide Z Slope Ry 2 A 4x Junction
71. e slope of the V I curve out at the ends where it is essentially a straight line To obtain a resistance you must convert the x axis value into amperes from volts and take into account the amplification of the y axis signal This is all very simple since the conversion factor for each axis is the same value of 10 000 Remember that the de SQUID contains two junctions in parallel so that the measured resistance corresponds to half the resistance of a single junction assuming they are identical Thus simply taking the slope numbers in volts off your oscilloscope or x y recorder will give you one half the normal state resistance in ohms The product of the critical current and the normal state resistance J Rw is a voltage that is an important parameter for the operation of a SQUID Make a note of it now for use later Note that Ry for one of the junctions has the same value for the SQUID which has two junctions in parallel For the junctions in Mr SQUID operating in liquid nitrogen you will probably obtain a value between 10 and 100 microvolts This value sets the maximum voltage change in the SQUID by an individual magnetic flux quantum and is discussed later in this section STAR Cryoelectronics LLC 14 Mr SQUID User s Guide As you observe the properties of the Josephson junctions in Mr SQUID realize that such an experiment just a few years ago required the use of liquid helium and several pieces of sophisticated electronic in
72. e capacitor one general purpose operational amplifier2 and two 9 volt batteries The schematic diagram is shown in Figure 7 5 This circuit can be assembled using a solderless breadboard although we recommend that it be built on a solderable breadboard and housed in a metal or plastic box The specific selection of the resistor labeled Recurrent is determined by the specific zener diode used 100 Q C Vzener 10 pA Rcurrent Vzener Rcurrent De Output Figure 7 5 Schematic diagram of the constant current source The circuit design requires that the ratio of the zener voltage to Recurrent be equal to 10 pA This means that for a 2 5 volt zener diode Reyrrent 250 KQ for a 5 1 Volt zener 2 Recurrent 510 KQ for a 6 2 Volt zener Recurrent 620 KQ and so on The capacitor C is present to suppress any high frequency noise or oscillations and can have any value between 100 pF and 100 nF If you build the circuit and it oscillates you should increase C higher than 100 nF until the oscillations cease If you decide to make a soldered version of this current source and house it permanently in a box we strongly recommend that you add a power switch 7 1 4 Why does a silicon diode work as a linear temperature sensor Here is how a diode can act as a temperature sensor the current through a forward biased p n semiconductor junction diode is determined by an expression first worked out by Sah Noyce and Shockley 4 20Su
73. e characteristics of single grain boundary junction DC SQUIDs in Y BazCu307 films R Gross P Chaudhari M Kawasaki M Ketchen A Gupta Physica C 170 315 1990 The first SQUID made using the basic junction technology similar to that used in your Mr SQUID Extension of the bi epitaxial Josephson junction process to various substrates K Char M S Colclough L P Lee and G Zaharchuk App Phys Lett 59 2177 2179 1991 A detailed description of the technology used in making the older pre June 1995 Mr SQUID chips STAR Cryoelectronics LLC 112 Mr SQUID User s Guide STAR Cryoelectronics LLC 113
74. e coil This has the advantage of requiring only one coil on the SQUID but it means that the flux locked loop current will be equal to the current drawn from the unknown voltage and hence will be of limited sensitivity Equipment For this experiment you will need e Mr SQUID and liquid nitrogen e An oscilloscope e The flux locked loop from the previous experiment e A solderless breadboard can be the same as the flux locked loop board e One 9 Volt transistor battery e A selection of resistors in the range of 1 KQ through 100 KQ e An decade resistor box capable of resistance values from below 100 Q to above 100 KQ e A selection of hook up wire and alligator clips Optional e A low frequency sine wave generator capable of frequencies below 2 5 kHz We first must construct a voltage source for controllably producing extremely small voltages We will do this as follows On a spare section of the solderless breadboard construct the double divider shown below Use the decade resistor box for Rset Such as Radio Shack part numbers 276 169 276 174 270 175 STAR Cryoelectronics LLC 66 Mr SQUID User s Guide Connection to Flux Locked Loop Mr SQUID External Coil Figure 7 9 Schematic diagram of the voltage source The equivalent circuit is shown below in Figure 7 10 The low output impedance of U2a in the flux locked loop circuit looks like a ground to point B hence Vin Rset 1350 kQ
75. e electronics in general and on SQUIDs in particular is in the professional scientific literature However there are a number of texts and popularizations available that can serve as sources of information beyond what is provided in this User s Guide Also included are some technical review articles and papers that discuss SQUID operation and applications Popularization Superconductors Conquering technology s new frontier Randy Simon and Andrew Smith Plenum Publishing New York 1988 A non mathematical presentation of the history physics and applications of superconductivity up to and including the discovery of high temperature superconductivity Texts Foundations of Applied Superconductivity Terry Orlando and Kevin Delin Addison Wesley Publishing Co Reading MA 1991 The new standard text on the principles of superconducting applications both thin film and bulk written in the post high T era and incorporating the consequences of the new materials Introduction to Superconductivity Michael Tinkham McGraw Hill Inc New York 1975 A classic text on the science of superconductivity geared to upper division undergraduates and graduate students Written before the high T discovery Superconductivity of Metals and Alloys P G de Gennes Addison Wesley Publishing Co Reading MA 1966 1989 THE classic monograph on superconductivity Reissued in 1989 with corrections by de Gennes Geared to upper div
76. e of the SQUID washer Ls is the inductance of the long slit in the washer Lx is the small kinetic inductance of the washer arising from the inertia of the electrons and L is the inductance of the Josephson junction bridges which also includes a small kinetic inductance contribution For a square washer with outer side length D and a square hole with inner side length d such that d D lt 1 Ln 1 24 uod Using d 24 um for the Mr SQUID washer Ly 37 7 pH For the washer the slit inductance per unit length is 0 38 pH um it would be slightly less if the modulation coils were superconducting rather than normal metal The slit in the Mr SQUID washer is 33 um from the inner hole to the outer edge of the washer Then La 12 5 pH The kinetic inductance of the washer is more difficult to determine precisely but is estimated to be about 2 pH The inductance of the Josephson junction bridges is estimated to be about 8 pH which includes the kinetic inductance contribution the inductance per unit length of the bridges is much higher than 0 38 pH um because of the narrow width of the bridges Thus the total inductance is approximately L 60 pH In general for an N turn coil integrated on top of the Mr SQUID washer the mutual inductance is given by Eqn 3 3 M N L L 0 5 L L For Mr SQUID the single turn modulation coil actually goes around only three quarters of the washer see Figure 3 6 Then using N 0 75 a
77. e playing a large role in the behavior of high T SQUIDs The lack of agreement between Eqn 3 1 and Eqn 3 2 is in large part due to the fact that the Mr SQUID is at a relatively high temperature where thermal energies kp are no longer small compared to the energy of a flux quantum L The relationship between the observed voltage modulation and 8 at a nonzero temperature T changes Eqn 3 2 to 4I_R Jk TL Eqn 3 5 B fiss TAV 0 Figure 3 9 illustrates the differences between the 8 values calculated using Eqn 3 1 Eqn 3 2 and Eqn 3 5 10 8 e c 6 o Lu o 54 gM 2 leak e o 0 o ae Be B from eq 3 2 Fook o o B from eq 3 5 0 oe 0 2 4 6 8 10 B from Eqn 3 2 and Eqn 3 5 Figure 3 9 Values of B 2 L p versus measurements of B based upon Ry AV for 44 Mr SQUID probes As one can see from Figure 3 9 the method of calculating 8 that takes thermal effects into account agrees quite well with the inductive Bz measurements On the following page we include a data sheet for your SQUID You may wish to use it or better still a photocopy to enter your measurements on Mr SQUID An interesting and important issue for SQUID applications is how the SQUID sensor varies with age You can track this with Mr SQUID by filling out a copy of the data sheet each time you use the system 2 K Enpuku Y Shimomura and T Kisu Effect of thermal noise on the
78. ection 3 The Mr SQUID probe contains a planar washer de SQUID fabricated using thin film YBCO technology The Josephson junctions are made with the bicrystal grain boundary junction process described at the end of Section 5 Flux is coupled to the SQUID via two separate single turn gold coils situated above the SQUID on top of a thin film dielectric layer Input to the modulation coil is made directly through the main cable in the system the flux biasing current is supplied by the Mr SQUID control box Input to the external coil is at the discretion of the user Terminals are available both at room temperature through a BNC connector on the back of the control box and at low temperature through terminals at the bottom of the probe The probe is equipped with a removable metal magnetic shield to attenuate external magnetic fields The SQUID chip itself is encased in an epoxy capsule that protects it from water vapor and ensures that it is cooled and warmed relatively slowly The Mr SQUID control box is designed to provide all the electronics necessary to observe the basic functions of a dc SQUID system Included is a low noise amplifier section for the output voltage of the SQUID current driver circuits for biasing the SQUID and driving the modulation coil and the switching required for the various functions The current triangle waves are available at two different frequencies to optimize them for both oscilloscope and x y recorder presentat
79. ed although the Mr SQUID User s Guide is not intended as a substitute for a textbook on SQUID operation and applications Several such textbooks are listed in the References Section 10 of this Guide Section 2 Setting Up Mr SQUID provides a detailed description of the components of the Mr SQUID system and instructions on how to set up the system for operation All users should familiarize themselves with the information contained in this section Section 3 Getting Started with Mr SQUID New Users is a step by step guide to the main functions of Mr SQUID It will show you how to observe both the V I and V characteristics of the SQUID Very little knowledge is assumed on the part of the user apart from the operation of either an oscilloscope or x y recorder Some knowledge of superconductivity and SQUIDs would be helpful but is not essential If you are entirely new to these subjects you may want to read Section 5 of this Guide An Introduction to Superconductivity and SQUIDs before proceeding Section 5 covers these topics in some detail and ranges in level from very elementary to rather sophisticated Depending on your own background portions of this section may either be too simple or too advanced to be useful We suggest you use it as a starting point for your inquiries into the scientific topics related to SQUIDs Section 4 Getting Started with Mr SQUID Advanced Users provides a quick start exposure to the M
80. ed Experiment 3 Section 7 3 which uses an analog flux locked loop to create a voltmeter can be performed using your digital flux locked loop 7 7 2 The 12 bit Flux Locked Loop A 12 bit Flux Locked Loop circuit that can be used with your Mr SQUID is shown in Figure 7 17 The circuit will allow you to measure magnetic fluxes imposed on Mr SQUID down to about less than 0 01 o In the ideal case your Mr SQUID system can be used to measure flux as small as about 0 001 p a limit set by the electronics in the control box This experiment falls somewhat short of limiting performance because the circuit illustrated was designed for simplicity rather than performance It can easily be built by students with little or no training in electronics The integrated circuits were chosen to be readily available although the 12 bit DACs can be expensive In the illustrations that follow the integrated circuits are OP07 and LF441 operational amplifiers LM311 comparators 74LS169 4 bit up down counters and AD563 digital to analog converters available from most electronics parts stores or electronic supply houses We suggest that you start by assembling the circuits on a solderless breadboard 8 This will allow you to make changes easily 47In the United States one example is Newark Electronics 312 784 5100 Newark Electronics is a registered trademark of the Newark Electronics Corporation 4801 N Ravenswood Ave Chicago IL 60640 and
81. ed disk of superconductor This effectively demonstrates the ability of the superconductor to screen out magnetic fields one aspect of a property known as the Meissner Effect By attaching wires to a superconducting sample one can just as easily demonstrate the zero resistance property of superconductors that gives them their name A standard experiment is to monitor the electrical resistance of the sample as the temperature is lowered from room temperature When the superconducting transition temperature Te is reached the resistance plummets abruptly to zero STAR Cryoelectronics LLC 2 Mr SQUID User s Guide ia F The quantum mechanical coherence effects in superconductors which are of great significance both for our theoretical understanding of the phenomenon of superconductivity and for electronic device applications are more difficult to demonstrate Until now there was no simple way to do it with liquid nitrogen cooling Mr SQUID is the first commercially available system for the convenient investigation of the quantum effects of superconductors and is a particularly effective system for demonstrating these effects in undergraduate laboratory facilities A Guide to the Guide The User s Guide to Mr SQUID is designed for users with a wide range of expertise in superconductivity quantum physics electronics and related topics For people new to these subjects a great deal of background information is provid
82. encies a generator with some frequency tuning will make this experiment easier to perform Mr SQUID Probe MW Generator 1 10 GHz A word of caution Microwave radiation can be dangerous even at relatively low levels especially in the frequency range of this experiment 1 10 GHz For example microwave ovens operate at 2 45 GHz where H20 is very strongly absorbing The maximum safe level as specified by the U S Government for rf and MW radiation is 10mW cm2 However this is higher than the maximum safe levels specified by many countries some of which have 28 For example Pethig states on page 235 that in the USA and UK permissible microwave exposure levels are a maximum power density of 10mW cm and exposures should not exceed 1mW cm for a continuous period of less than 0 1 hour In the Former Soviet Union Pethig states the limit as 0 01mW cm for one working day and wearing protective equipment is required for exposures not to exceed 1mW cm for 20 minutes or 0 1mW cm for 2 hours STAR Cryoelectronics LLC 72 Mr SQUID User s Guide specified maximum safe levels as low as 0 01mW cm Read the instructions for your microwave generating equipment and follow ALL safety instructions Set up your Mr SQUID unit and cool it down with liquid nitrogen Turn it on in the V I mode This is the only mode we will be using in this experiment You will need to have a fairly clean V I curve as illustrated below free
83. er s Guide 7 3 Using a Flux Locked Loop as a Sensitive Voltmeter Purpose and Discussion Once you have a working flux locked loop the obvious question to ask is What else can I do with it besides measure flux A powerful application of the flux locked loop technology is configuring a SQUID to be a picovoltmeter One picovolt is 10 Volts As a result of the resistive metal coils on the SQUID chip Mr SQUID cannot be made sensitive enough to measure picovolts but it can be used to measure microvolt 10 to nanovolt 10 signals The principles behind the measurement however are the same Therefore it is instructive to perform this SQUID voltmeter experiment Using a SQUID in a flux locked loop as a sensitive voltmeter is in theory very simple The unknown voltage is applied to one of the SQUID coils Current then flows through the coil creating a magnetic flux in the SQUID The flux locked loop circuit creates an opposing magnetic flux that cancels the flux from the current driven by the unknown voltage The current of the flux locked loop in then measured In general one constructs the coils in such a way that the flux locked loop coil in order to create a given flux requires many times more current than the unknown voltage coil requires This larger current is then easier to measure In the following Mr SQUID experiment we are going to have the flux locked loop and the unknown voltage inject their currents into the sam
84. er yet STEP 4 Make circular passes around the shield for approximately 10 20 seconds then slowly withdraw the eraser until the unit is about three feet away from the shield This slow withdrawal creates a decaying degaussing field that results in the shield having no net magnetic moment STEP 5 Turn off the bulk tape eraser This procedure should effectively eliminate any magnetization of the Mr SQUID magnetic shield and may in some instances restore the critical current in the SQUID 6 5 RF Interference SQUIDs are the most sensitive detectors of magnetic fields ever made being sensitive to magnetic fluxes below a millionth of a gauss centimeter squared Josephson junctions a de SQUID contains two of them have extremely fast switching times between their superconducting and normal states lt 10 sec The critical current of your Mr SQUID is on the order of 10 uA at 77 K What are the consequences of these three statements If the sum of the currents induced through your Mr SQUID from dc up through 100 GHz exceeds about 7An example is Radio Shack part number 44 233 Its cost is approximately 35 00 8 The saturation induction of the shield is 8000 gauss at room temperature STAR Cryoelectronics LLC 50 Mr SQUID User s Guide 10 pA your Mr SQUID will display a linear V I curve As a matter of fact this hypersensitivity of SQUIDs and Josephson junctions to rf microwaves and millimeter waves has been pro
85. erting In other words its output is the sum of the outputs from Ula and U1b times 10 and while it is taking the sum U2a also integrates or averages this sum for a period of time equal to the product of C1 in Farads times 100 kQ 26Radio Shack part number 276 038 27Such as Radio Shack part numbers 276 169 276 174 270 175 STAR Cryoelectronics LLC 63 Mr SQUID User s Guide The circuit should first be constructed with a value for C1 of 0 01uF and the Mr SQUID external coil should be disconnected from the circuit The Mr SQUID should be set up and running in the V mode with the amplitude of the flux about 0 5 flux quantum The signals at Test Point 1 TP1 and Test Point 2 TP2 should look something like those in Figure 7 7 In these scope photographs the x axis is the x output of the Mr SQUID box The signals at Test Point 1 will have a dc offset imposed on them so the oscilloscope will need to be ac coupled The signals at Test Point 2 may also have a dc offset but we want to be able to see that offset so the scope will need to be de coupled while looking at Test Point 2 Test Point 1 is simply showing the V output of the Mr SQUID as a magnetic flux is swept Test Point 2 is also showing the V output of the Mr SQUID but magnified by a factor of 10 AND with an extra de offset from the circuit s 10kQ potentiometer
86. es have RFI shielded rooms as do many electrical engineering departments However if you do not have access to an RFI shielded room the first thing to do is to determine if any RFI sources are nearby When looking for possible sources of RFI try to cover everything within 50 meters or so Walls even brick and concrete will often not attenuate RFI very much Remember to not only look in the surrounding area but also on several floors above and below the room in which you are attempting to run your Mr SQUID After you have identified possible RFI sources you should try switching them off one by one while watching the V I or V curve of your Mr SQUID This will allow you to identify which of the possible sources are causing the largest problems Basically just keep turning things off until the RFI goes away Some sources of RFI either cannot be turned off or are not under your control In this case you will need to consider operating your Mr SQUID at another location For example if there are TV or radio broadcast towers nearby try operating your Mr SQUID in a room such that the bulk of the building is between your Mr SQUID and the broadcast tower Another solution is to place the Mr SQUID system in a closed metal box a Faraday cage to screen out the RFI In the past SQUID systems were primarily operated in controlled environments in which detrimental external influences such as RFI were carefully kept away Mr S
87. esistance of the junctions which is intentionally added to tunnel junctions but occurs intrinsically with weak links prevents unwanted hysteresis in the V I characteristics of the device The loop with the junctions and resistors has a total inductance L and has a total magnetic flux through it of The details of the junction construction determine the effective R s and C s and the details of the loop construction determine the effective L A schematic of a dc SQUID is shown above Once the parameters are known a great deal can be predicted about the resultant SQUID performance STAR Cryoelectronics LLC 36 Mr SQUID User s Guide bias Em E Figure 5 9 A more complete model of a de SQUID The theory of de SQUIDs and rules that help with their design and the predicting of their performance are well established see the references at the end of the Guide The following discussion is of an advanced nature and is provided only for users interested in the details of SQUID design The basic parameters of a SQUID as shown in Figure 5 9 are the critical currents of the junctions the junction capacitances C the shunt resistances R and the SQUID inductance L It is a fair approximation to ignore differences between the parameters of the two junctions in a dc SQUID We begin by specifying the values of these parameters that are needed to produce a practical SQUID Several considerations must be addressed In order to produce a
88. etic Shield Conetic alloy tube 0 625 in 15 9 mm diameter 3 5 in 88 9 mm long Black baked enamel finish textured outside smooth inside 7500 Gauss saturation induction Initial permeability 30 000 at 295 K approx 4 500 at 77 K STAR Cryoelectronics LLC 109 Mr SQUID User s Guide Equivalent to Magnetic Shield Corp P N 06P35 9 4 RF Filter Module DB 9 M F EMI filtered connector adapter Each line contains a 0 8 MHz 4 000 pF low pass pi filter Equivalent to Spectrum Control Inc 5 P N SCI 56 705 005 LI 9 5 Cable DB 9 M M 6 ft 1 8 m long Equivalent to Radio Shack gt 4 P N 26 116 9 6 Dewar Aluminum encased silvered glass vacuum flask Volume 1000 mL ID 2 75 in 70 mm Height 13 3 in 337 mm Includes foam cap with slot and hole for supporting the Mr SQUID probe Equivalent to Pope Scientific Corp 55 P N 8645 0099 The above specifications are effective 5 10 02 and subject to change without prior notice 52Magnetic Shield Corp 740 North Thomas Drive Bensenville IL 60106 U S A tel 708 766 7800 53Spectrum Controls Inc 2185 West Eighth Street Erie PA 16505 U S A tel 814 455 0966 54Equivalent to Radio Shack part number 26 116 55Pope Scientific Corp N90 W14337 Commerce Drive P O Box 495 Menomonee Falls WI 53051 U S A tel 414 251 9300 STAR Cryoelectronics LLC 110 Mr SQUID User s Guide 10 REFERENCES Most of the available information on superconductiv
89. for the Mr SQUID dewar drill a hole in the rubber stopper that is slightly smaller than the outer diameter O D of the tubing you plan to use Often cooling the rubber down using liquid nitrogen makes it easier to drill Insert the tubing so that approximately 1 extends through the hole and make sure that it is fairly secure i e not easy to pull out Fill the dewar about half full with liquid nitrogen If you have not yet calibrated your silicon diode temperature sensor you should do so now Also it should be attached to the back of the Mr SQUID probe with masking tape Both of these procedures are described in Advanced Experiment Section 7 1 At this time you should record the superconducting parameters of the SQUID at 77 K if you have not already done so Now we are ready to pump on the liquid nitrogen to reduce its boiling temperature Stick the rubber stopper into the top of the Mr SQUID dewar with the stopper wide side towards the Mr SQUID dewar as shown in Figure 7 12 Do not use a stopper that enters the Mr SQUID dewar Do not immerse the tubing into the liquid nitrogen inside the dewar 36As for example part number 59580 524 from VWR Scientific Phone 800 257 8407 International orders 415 468 7150 STAR Cryoelectronics LLC 84 Mr SQUID User s Guide a Tube to Vacuum Pump on Upside down Size 14 Rubber Stopper lt t _ Liquid Nitrogen Level Figure 7 12 Configuration
90. functioning SQUID the first requirement is that the Josephson coupling between the two sides of the junction should not be destroyed by thermal fluctuations This can be quantified by an expression of the form I Eqn 5 1 lt 9 gt 5k T 21 where kg is Boltzman s constant kg 1 38 x 10 23 Joule K This determines a desirable minimum value for J The second requirement is that thermal fluctuations in the flux in the SQUID should not exceed a fraction of a flux quantum This can be quantified in the following form 2 p Eqn 5 2 T gt 5k T which puts an upper limit on the inductance of the SQUID The unavoidable capacitance of any junction tends to make its current voltage characteristic hysteretic This complication can be avoided by making the shunt resistance small enough This condition can be met by limiting the value of a parameter known as the McCumber parameter Be given by STAR Cryoelectronics LLC 37 Mr SQUID User s Guide 27l R C _ lt Eqn 5 3 Be 1 For Be lt 0 7 the junctions are non hysteretic and this fixes the maximum resistance that can be used for a given capacitance and critical current This capacitance is usually determined for a particular junction technology once the critical current has been set The final design parameter is the modulation parameter defined by the expression Sor P Eqn 5 4 B This parameter determines the maximum extent to which cir
91. g of this experiment DO NOT READJUST THE KNOB LABELED FLUX BIAS while getting this new version of the flux locked loop circuit functioning Next turn down the AMPLITUDE knob on your Mr SQUID unit DO NOT READJUST THE KNOB LABELED FLUX BIAS Watch the pattern of the LEDs in your digital flux locked loop Write the pattern down using a 1 if a given LED is on a 0 if a given LED is off If a LED is flickering you might wish to denote it with a instead of a 1 or 0 Also measure voltage at test point 3 TP3 Do you get the same pattern as before Can you figure out why Did you get the same voltage at test point 3 TP3 Why Once you have added the inverter to the MSB do you notice any difference in the performance of the loop Why STAR Cryoelectronics LLC 103 Mr SQUID User s Guide 7 7 4 Troubleshooting your digital flux locked loop This flux locked loop circuit is fairly robust however the circuits are rather complex for a lab course that does not assume prior knowledge of anything more complex than a LRC circuit We will assume that nothing catastrophic occurred when the digital flux locked loop was powered up i e no chips blew up or resistors started burning If so please talk to your lab instructor immediately If your digital flux locked loop does not work but nothing obviously is smoking or burning up here are a few things to check and the order to check them in We will assume that you used the same c
92. h to adjust at this stage Below we show a zoology of symptoms displayed at TP3 when the digital flux locked loop is not quite working along with a suggestion to lock it in TP3 shows lines with large vertical zigzags This usually means that R1 has drifted out of adjustment the above scope photo is a multiple exposure so it shows several sweeps of the x STAR Cryoelectronics LLC 105 Mr SQUID User s Guide axis Try monitoring TP2 and readjusting R1 This can often happen if the flux locked loop circuit has only recently been powered up and the R1 adjustment was performed before the components had thermally stabilized One might wish to wait a while after adjusting R1 and check it again for drifts 2V 500mV TP3 shows lines with short horizontal zigzags This usually means that the TTL clock is too fast the above scope photo is a multiple exposure so it shows several sweeps of the x axis Try turning down the function generator frequency This usually means you would be properly locked except you are exceeding the maximum clock speed of the DAC used in your flux locked loop Try turning down the function generator frequency used to provide the TTL clock input to the counters Typically 10 kHz is reasonable for the 8 bit version and 200 kHz is reasonable for the 12 bit version This usually means that the TTL clock is too slow the above scope photo is a multiple exposure so it shows several sweeps of the
93. he Mr SQUID probe is a thin film washer of YBCO superconductor broken in two places by Josephson junctions The YBCO is patterned into a washer in order to take advantage of the Meissner Effect which is the ability of a superconductor to expel magnetic flux from its interior Because most of the magnetic flux generated by either of the Mr SQUID modulation coils see Figure 3 6 is forced into the center hole of the SQUID the inductive coupling of each coil to the SQUID is similar even though their physical sizes are different This is not exactly true because the coils do not make completely closed loops This flux focusing can be used to allow multi turn spiral coils to be fabricated over a SQUID washer yet have each turn contribute the same amount of flux gt Figure 5 11 a Magnetic flux penetrating the body of the SQUID while in the normal state above T b Flux focusing produced by the Meissner Effect when the SQUID is in the superconducting state below Te The HTS Josephson junctions made to date appear to fall into two categories S N S junctions and grain boundary junctions Some of the best results particularly in the context of SQUID performance have been obtained for grain boundary junctions In these devices the Josephson effect occurs because of the existence of a crystallographic grain boundary in a thin film that allows two grains to couple only weakly together Examples of these are naturally occurring
94. he characteristic voltage I Ry also shows a similar temperature dependency Eqn 7 21 I Ry Op 1 ty Since we have made two measurements at different temperatures 77 K and the lower temperature in the pumped liquid nitrogen we can solve either of the above equations to determine the constant of proportionality either O or Oz and the critical temperature 7 of the SQUID remember that t 7 T If you did Advanced Experiment 1 you should compare this calculated result to the value of T that you measured directly For example a typical measurement of J at 77 K for one SQUID was 7 uA After pumping on the liquid nitrogen and measuring the temperature using the extrapolation of a calibrated silicon diode as 66 K we measured a new critical current of 34 uA for this same SQUID By using Eqn 7 20 with these two data points we were able to determine to be 622 uA and T to be 86 1 K actually because Eqn 7 20 is a quadratic equation there are two solutions one however will predict that T is lower than 77 K so this one is eliminated Note that the proportionality constant amp represents an estimation of the critical current at a reduced temperature of 0 i e absolute zero 0 K Although equation Eqn 7 20 is really only valid for temperatures near T it is interesting to note that the 0 K value compares favorably with similar SQUIDs measured in liquid helium at 4 2 K Also if you did Advanced Experiment 1 the Te measure
95. he loop is symmetrical and the applied field is zero both junctions will develop a voltage at the same time So the critical current of the SQUID is simply twice the critical current of one of its junctions If the critical current of each junction is 5 microamps for example then the critical current of the SQUID is 10 microamps STAR Cryoelectronics LLC 32 Mr SQUID User s Guide The voltage current characteristic or V I curve of a SQUID looks very much like the V I curve of a bulk superconductor except the value of the critical current is smaller A typical V I characteristic for Mr SQUID is shown in Figure 5 4 Figure 5 4 A typical Mr SQUID V I characteristic Now imagine what happens if a magnetic field is applied to the SQUID First let s bias the SQUID with a current well below its critical current Then if we apply a tiny magnetic field to the SQUID the magnetic field wants to change the superconducting wave function But the superconducting wavefunction doesn t want to change as discussed earlier it must maintain an integral number of wavefunction cycles around the loop So the superconducting loop does what you would expect it opposes the applied magnetic field by generating a screening current I that flows around the loop see Figure 5 5 The screening current creates a magnetic field equal but opposite to the applied field effectively canceling out the net flux in the ring V bias 2 wai
96. he opposing flux is limited by factors like the noise of the SQUID and the noise of the electronics Ideally one can match the opposing fluxes to within a very small fraction of a flux quantum In the experiment outlined below you will use the external field coil on the Mr SQUID chip to set up a flux locked loop Equipment e For this experiment you will need e Mr SQUID and liquid nitrogen e An oscilloscope e A solderless breadboard gt e Three general purpose operational amplifier chips e g 741 e Two 9 Volt transistor batteries e One 10 KQ potentiometer e A selection of resistors in the range of 1 kQ through 100 kQ e A selection of capacitors in the range of 0 001 uF through 1 uF e A selection of hook up wire and alligator clips Advanced experiment 7 is building a digital flux locked loop 25Such as Radio Shack part numbers 276 169 276 174 270 175 STAR Cryoelectronics LLC 62 Mr SQUID User s Guide A simple flux locked loop circuit that can be used with your Mr SQUID is shown in Figure 7 6 This circuit will allow you to measure magnetic fluxes imposed on Mr SQUID down to about 0 1 o In the ideal case your Mr SQUID system can be used to measure fluxes as small as about 0 001 a limit set by the electronics in the control box This experiment falls far short of limiting performance because the circuit illustrated was designed for simplicity rather than performance It can eas
97. he recooling with your un powered flux locked loop circuit already attached to the EXT COIL connector Reconnect the power to your flux locked loop circuit The signals at Test Point 1 and Test Point 2 should look like those shown in Figure 7 8 Test Point 1 ideally would be a flat line if your STAR Cryoelectronics LLC 64 Mr SQUID User s Guide flux locked loop perfectly canceled the flux applied by the Mr SQUID box As can be seen below in our test circuit the line is slightly sloped indicating that the cancellation was not perfect From the slope of this line one can estimate how accurately the circuit is holding the flux constant In Figure 7 8 the slope of Test Point 1 indicates that the locked flux shifts by 0 07 Po when the applied flux covers 1 Po One can improve this by increasing the gain of U2a By looking at Test Point 2 we can determine the applied flux that the flux locked loop is canceling out The voltage at Test Point 2 is across the 1350 Q resistor and this prototype Mr SQUID external coil which was 74 Q at 77 K for the SQUID used in this illustration NOTE 1 We are assuming the inductance of the Mr SQUID coil is small enough at 15 Hz for us to ignore 2 This prototype Mr SQUID external coil had a mutual inductance of 100 pH 3 Typical production Mr SQUID chips have coil resistances of 15 30 Q and mutual inductances of 75 pH This means that the y axis for the Test Point 2 signal below is
98. hin the superconductor but knowing the function in one place determines it in another Physicists call such a wavefunction a many body wavefunction Strictly speaking electrons are indistinguishable particles there is no way to keep track of an individual electron in the population and it in fact has no meaning to speak of one The pairs of electrons that comprise the superconducting state are constantly forming breaking and reforming such that the wavefunction that describes the superconducting state remains the same As we will see it is the existence of this coherent wavefunction that accounts for the phenomena associated with superconductivity 5 4 The Quantum of Flux Quantum mechanics is the modern theory of physical world in which matter and energy at their most fundamental levels occur in discrete chunks called quanta rather than being continuously divisible We are familiar with this concept with respect to electrical charge for example To our knowledge all electrical charge excluding quarks for the moment occurs in units of 1 6x10 9 coulombs the charge on a single electron Therefore nothing in nature has 1 5 times this charge for example Electromagnetic energy is quantized in units called photons whose magnitude is set by the product of the frequency of the radiation times a fundamental constant called Planck s constant written simply as h In general quantization is only readily apparent when we are dealing with
99. hreading the ring We now have a superconducting ring threaded by a single flux quantum Suppose we now turn off the applied field According to Faraday s Law of Induction the moment that we change the field lines that thread the ring a current flows in the ring The current induced tries to oppose the change in magnetic field by generating a field to replace the field we removed In an ordinary material that current would rapidly decay away In the superconductor something entirely different happens If the induced current decreased just a little bit in the ring then the flux threading the ring would be a little less than a flux quantum This is not allowed The next allowable value of flux would be zero flux Therefore the current would have to abruptly cease rather than decay away Because the superconducting state is composed of an enormous number of electrons that are paired up and occupying the same quantum state a current reduction of the sort needed would require all the electrons to jump into another state simultaneously This is an extraordinarily unlikely event Practically speaking it will never happen As a result the current induced in a superconducting ring will flow indefinitely People have actually tried this experiment for years on end As long as the ring is kept cold the current flows without resistance Thus the concept of flux quantization gives us an insight into why superconductors pass current without any resistance How
100. ics LLC 11 Mr SQUID User s Guide If you now turn the current bias control the center point of the curve being traced on the screen or page will move The current bias control sets a single value of current being passed through the SQUID and the amplitude control sweeps the current back and forth about that set value 3 4 Calculating the Current Your output device acts like a voltmeter The sensitivity settings on it determine how much voltage corresponds to a division on the screen or on the page of graph paper The current output on the Mr SQUID box 5 actually represents the voltage across a 10 000 resistor in the electronics box According to Ohm s Law J V R the current flowing through the resistor is therefore equal to the voltage across it divided by 10 000 Q The typical voltage levels from the SQUID are small enough that we have provided amplification in the Mr SQUID control box Thus to calculate the actual voltages across the SQUID the measured value on the oscilloscope or x y plotter should also be divided by 10 000 3 5 The V I Curve If the settings on the Mr SQUID box and your output device are correct and if the SQUID is behaving properly you will see a curve that looks more or less like this on the screen or page Figure 3 3 Typical Mr SQUID V I characteristic It is important that there is a flat region in the center of the curve as shown above although its width may vary from device to de
101. ility of such surveying techniques As in the case of the magnetic anomaly detection applications remote magnetic field measurement is a critical issue for geophysical applications and therefore HTS SQUIDs represent a significant advance in practicality Another area of investigation has been non destructive evaluation NDE using SQUIDs Once again there are a variety of proposed techniques and implementations both active and passive Of special interest is the testing of submerged or otherwise inaccessible pipes the evaluation of structural members such as bridge components the location of buried toxic waste drums and the testing of welds in structures such as aircraft wings Initial studies indicate that SQUIDs may be effective in all these areas but considerable modeling and testing remains to be done to demonstrate the viability of the method In summary there is a great variety of SQUID applications either under investigation or commercially available What has kept the majority of them out of the marketplace is a combination of the difficulties imposed by cryogenic requirements and the lack of sufficient demonstration of their utility As high temperature superconductor based SQUIDs alleviate the former problem the opportunities to eliminate the latter problem will only increase The Mr SQUID system before you represents the first step in bringing HTS SQUID technology into the marketplace 5 13 A Brief History of SQUIDs The quan
102. ily be built by students with little or no training in electronics The integrated circuits were chosen to be inexpensive and readily available In the illustrations that follow the integrated circuits were LM1458 dual op amps available from most electronics parts stores We suggest that you start by assembling the above circuit on a solderless breadboard This will allow you to make changes easily You should also use two 9 Volt batteries to power your circuit DO NOT USE A 120 VAC DC POWER SUPPLY to power this circuit Too much 60 Hz generated by the power supply may strongly interfere with the Mr SQUID signal Test Point 1 Y output of Mr u gt SQUID Box I C1 in V R2 mode 9 V 1350 10k Spa a S OB Test Point 2 Mr SQUID 1s R1 External 10k Coil U1 U2 are LM1458 9 V Figure 7 6 Schematic diagram of the analog flux locked loop circuit Notes Circuit details for electronics buffs The first pair of op amps Ula and U1b are configured as unity gain buffers to isolate the Mr SQUID electronics and the output of the 10 kQ potentiometer voltage divider from the rest of the circuit and each other In other words the Ula and U1b op amps put out a voltage equal to their inputs but they draw no current from the Mr SQUID box or the 10 KQ potentiometer U2a is configured as a summing amplifier with a long time constant with a gain of 10 By a gain of 10 we mean that it has a gain of 10 AND is inv
103. in the photograph is the external modulation coil that allows you to couple other sources of current to the SQUID The labels internal and external refer to the accessibility of the coils to the Mr SQUID user Electrical connections to the external coil are made through the BNC connector on the back of your Mr SQUID electronics box The internal coil is used by the Mr SQUID electronics to apply flux to the SQUID and is not directly accessible to the user If you slowly turn the flux bias control knob you will see the change in the critical current and the changing V I curve that occurs as the magnetic flux threading the loop of the SQUID is varied Another way to see the sensitivity of the SQUID to external fields is to rotate a small horseshoe magnet slowly in the vicinity of the dewar If you experiment carefully with the flux bias control you will see that the critical current of the SQUID oscillates between a maximum value the flat region of the V I curve is at its widest and a minimum value at which point the V I curve may be more or less linear The Mr SQUID control box allows you to view the periodic behavior of the SQUID ina convenient automated way To obtain the V plot the bias current is set so that the SQUID voltage is most sensitive to changes in applied magnetic field This occurs at the knee of the V I curve the area highlighted in Figure 3 7 below STAR Cryoelectronics LLC 15 Mr
104. ine copper wire Figure 7 1 Diode setup Temperature Calibration The next step is to calibrate the temperature response of the silicon diode The diode voltage will increase linearly with decreasing temperature Using an ordinary thermometer determine the temperature of the laboratory in the vicinity of the diode the value in Kelvin should be in the vicinity of 293 K for most rooms and record the diode voltage at this temperature This is our first calibration point for the sensor Next fill the Mr SQUID dewar with liquid nitrogen without the Mr SQUID probe in it Slowly lower the diode into the liquid nitrogen Once the diode is at the bottom of the dewar push an additional 20 cm of the diodes wires into the liquid nitrogen be careful to avoid skin contact with the liquid nitrogen The voltage across the diode should increase to 0 9 to 1 volts It may take several minutes for the diode voltage to reach a stable value This is our second calibration point at 77 K Strictly speaking we need only two calibration points for a linear sensor However if your lab has facilities to create a dry ice and acetone bath you should place your diode in that bath to get a STAR Cryoelectronics LLC 56 Mr SQUID User s Guide 195 K calibration point Caution These calibrations are for the diode not the Mr SQUID probe Do not expose the Mr SQUID probe to acetone On a piece of linear graph paper plot the diode voltage a
105. ion the remote fielding and demanding environment for the system are major barriers to the use of liquid helium cooled SQUIDs Nitrogen cooling offers a far more viable alternative if HTS SQUID performance can meet the requirements of this application A number of applications have been investigated in the area of geophysics These range from prospecting for oil and minerals to earthquake prediction There are a variety of different techniques that have been explored that use of SQUIDs Active systems introduce pulsed magnetic signals into the earth and then detect the response by means of the SQUID One version of this technique is essentially a type of NMR that determines the properties of the different strata that make up the ground in a test site Currently conventional i e non SQUID magnetometers are used for bore hole logging an important technique for locating oil An important passive geophysical technique that utilizes SQUIDs is known as magnetotellurics In this technique the properties of an area of ground actually the impedance tensor of the ground are determined by comparing the signals at a reference SQUID to those at a test SQUID that is moved from point to point During the early 1980 s several companies practiced this technique on a commercial basis However the subsequent drop in the cost of oil and the removal of incentives to develop alternative energy sources such as geothermal energy ended the commercial viab
106. ion of the data The box is battery operated to minimize levels of 60 Hz in the circuits the SQUID modulation voltage is of the order of 10 uV 4 1 Electronics Box Front Panel The front panel controls and connectors on the Mr SQUID control box are referenced by the numbers shown in Figure 4 1 below FLUX CURRENT BIAS BIAS AMPLITUDE OUTPUTS 0000 oc Mr SQUID 0 conpgetus Figure 4 1 Front panel of the Mr SQUID electronics box 1 Function switch Selects between V I mode and V mode e In V I mode a triangle wave current is made available directly to the input of the SQUID STAR Cryoelectronics LLC 23 Mr SQUID User s Guide e In V mode a triangle wave current is made available to the normal metal modulation coil that is inductively coupled to the SQUID 2 Flux Bias control Applies a fixed de current to the modulation coil In the 12 o clock position this current is approximately zero Turning the knob in either direction applies a fixed current and thus an applied magnetic field This control is used to modulate the critical current of the SQUID manually by the application of an external magnetic flux by varying the current in the modulation coil 3 Current Bias control Applies a fixed dc current to the SQUID In the 12 o clock position this current is approximately zero Turning the knob in either direction applies a fixed current to the SQUID in either of two directions
107. ircuit does require adjustments to R2 and R3 connected to U7 in order to work correctly The adjustment procedure is as follows STEP 1 Disconnect all 12 inputs pins 13 24 of U7 from U4 U5 and U6 STEP 2 Connect all 12 inputs pins 13 24 of U7 to the circuit ground STEP 3 Connect a voltmeter from Test Point 3 TP3 to the circuit ground STEP 4 Adjust R2 until the voltage at TP3 is 3 000 Volts STEP 5 Connect all 12 inputs pins 13 24 of U7 to the circuit 5 Volt power supply STEP 6 Adjust R3 until the voltage at TP3 is 3 000 Volts STEP 7 Repeat steps 2 through 6 until TP3 reads 3 000 Volts when pins 13 24 of U7 are grounded and TP3 reads 3 000 Volts when pins 13 24 of U7 are connected to the 5 Volt power supply STEP 8 Reconnect all 12 inputs pins 13 24 of U7 to the correct pins of U4 U5 and U6 Your circuit is should now be ready to function The circuit should first be constructed with the Mr SQUID external coil disconnected from the circuit The Mr SQUID should be set up and running in the V mode with the amplitude of the flux of a few flux quantum The signal at Test Point 1 TP1 should look something like the one in Figure 7 18 In these scope photographs the x axis is the X output of the Mr SQUID box The signals at Test Point 1 will have a dc offset imposed on them so the oscilloscope will need to be ac coupled The signals at Test Point 2 may also have a dc offset but we want to be able
108. is not in any way affiliated with STAR Cryoelectronics or the Mr SQUID system 48Such as Radio Shack part numbers 276 169 276 174 270 175 STAR Cryoelectronics LLC 94 Mr SQUID User s Guide Th U1 U2 OP 27 U3 LM311 ur Sou P U4 U5 U6 74LS169 4 bit U D counter 5V U7 AD563 12 bit DAC sev agv LAM pa eth U8 LF441 HA D VA All chip s use 15yf tantalum bypass caps between iS kam 5V V sy the 5 5 and 15 volt power pins and circuit ground TTL Clock In m we E Pee T Hat LO soes u g e w 1 Us 6 otf KRN spy e TT PP sv s ola A fll ao MSB 5V 6 l HIT LBV ie Let v 8252 825 aa E 825 oy b ae T a i O a co SSE eee an a A ys i Si il Se ig a 8252 8252 Pal EEC to Mr SQUID 21 20 19 18 17 16 15 14 10k ag external coil 8252 FLL Analog Output 1 1 V 100pA TP3 10k Figure 7 17 Schematic diagram of the 12 bit digital flux locked loop Circuit details for electronics buffs The first op amp U1 is configured as unity gain buffer to isolate the output of the 10 KQ potentiometer voltage divider R1 from the rest of the circuit In other words the U1 op amp put out a voltage equal to its input but it draws no current from the 10 KQ potentiometer U2 is configured as a summing amplifier with a gain of 330 By a gain of 330 we mean that it has a gain of 330 AND is inverting In other words its output is the sum of the outputs from U1 and the Mr SQUID box
109. ision undergraduates and graduate students A must for serious researchers Written before the high T discovery Introduction to Superconductivity A C Rose Innes and E H Rhoderick International Series in Solid State Physics Vol 6 Pergamon Press Oxford 1978 Written at more accessible level this text focuses on explaining the experimental effects of superconductors Written before the high T discovery Principles of Superconductive Devices and Circuits Theodore Van Duzer and Charles Turner Elsevier North Holland Inc New York 1981 The standard text on superconductive electronics with an emphasis on the physics of the electronic devices Written before the high T discovery A Seminar on Superconductivity Ch 21 from The Feynman Lectures on Physics Vol III Richard P Feynman Robert B Leighton and Matthew Sands Addison Wesley Publishing Co Reading MA 1965 An early treatment of the quantum nature of superconductivity including the original data and interpretation of some of the first devices to show quantum interference Written before the high T discovery STAR Cryoelectronics LLC 111 Mr SQUID User s Guide Articles and Technical Papers General Audience Superconductivity Kevin A Delin and Terry P Orlando The Electrical Engineering Handbook R C Dorf ed pp 1114 1123 CRC Press Cleveland OH 1993 This is a short overview of superconductivity at an undergradua
110. it Record this value This is the ac noise in the circuit STEP 5 Turn the amplitude of the sine wave generator to its minimum value and set R to its minimum value Set the frequency of the sine wave generator to below 2 5 kHz STEP 6 Turn on the sine wave generator and slowly turn up its amplitude to about 9 V STEP 7 While measuring Test Point 2 of the flux locked loop circuit slowly increase Rye until you can just see a change at Test Point 2on the ac voltmeter STEP 8 Measure the voltage change V2 at Test Point 2 and measure the voltage of the 9 Volt battery that is energizing your double divider and record the value of Rye See what changes you can make to the flux locked loop circuit to increase the sensitivity of your Mr SQUID ac voltmeter Note that you can create a larger voltage at Test Point 2 for a given voltage at point B by substituting a larger resistor for the 1350 Q resistor If you do this what other change to the flux locked loop circuit must you make How sensitive can you make this ac voltmeter Which is more sensitive the ac or the dc voltmeter Why STAR Cryoelectronics LLC 69 Mr SQUID User s Guide 7 4 The ac Josephson Effect Microwave Induced Shapiro Steps at 77K and Determining h e Purpose and Discussion The following discussion of the ac Josephson effect contains a fair amount of mathematical rigor in order to quantitatively explain the origin of the microwave induced step
111. it FLL in the unlocked mode at TP1 and TP2 STAR Cryoelectronics LLC 92 Mr SQUID User s Guide Reconnect the power to your flux locked loop circuit Set the frequency of the function generator that is supplying the TTL to about 5 kHz 15 kHz The signal at Test Point 2 should look like that shown in Figure 7 16 If it does not try adjusting the function generator frequency gt Test Point 2 ideally would be a flat line if your flux locked loop perfectly canceled the flux applied by the Mr SQUID box As can be seen below in our test circuit the line is pretty flat indicating that the cancellation is good From the slope of this line one can estimate how accurately the circuit is holding the flux constant In Figure 7 16 the very small slope of Test Point 2 indicates that the y axis shifts by less than 0 04 Volts when the applied flux covers 1 Bo By looking at the slope of TP2 near its zero crossing in Figure 7 15 above one can see that the slope dV d is 29 Volts o This means that the locked flux shifts by 1 4x10 Po when the applied flux covers 1 Bo By looking at Test Point 3 we can determine the applied flux that the flux locked loop is canceling out If one looks closely one may be able to see the steps in the DAC output The voltage at Test Point 3 is across the 10 KQ resistor and the Mr SQUID external coil whose resistance is negligible compared to 10 KQ This means that the y axis for the Test Point 3 signal bel
112. ks like it is working then the next thing to look at is the wiring of the counter chips U4 and U5 for the 8 bit version U4 U5 and U6 for the 12 bit version A Check the wiring including whether the 5 Volt power is connected to the proper pins on the integrated circuit U3 Check the wiring including whether the 5 Volt power and ground are connected to the proper pins on the integrated circuit sU4 and U5 and U6 for the 12 bit version B Check that the TTL clock signal from the function generator is really 0 to 5 Volts and that the function generator is properly powered up and set to a frequency between 5 kHz and 15 kHz for the 8 bit flux locked loop and 50 kHz to 200 kHz for the 12 bit version C Are some of the LEDs blinking or flickering If not recheck the wiring and go back to step 4 A 6 Can you perform the proper adjustments to R2 in the 8 bit version or R2 and R3 in the 12 bit version If not recheck the wiring including whether the 5 Volt power and ground are connected to the proper pins on integrated circuit U6 and U7 in the 8 bit version If you are making the 12 bit version recheck the wiring including whether the 5 Volt power 15 Volt power and ground are connected to the proper pins on integrated circuits U7 and U8 Make sure you recheck all of the wiring 7 Does everything appear to work when the Mr SQUID EXT COIL is not connected yet does not work when it is connected Fortunately there is not muc
113. low temperature superconductors primarily with niobium Te 9 2 K as the superconductor S and aluminum or copper as the normal metal N The right side shows the grain boundary Josephson junctions such as those in your Mr SQUID It is interesting to note that grain boundaries act as Josephson junctions only in the high temperature copper oxide based superconductors where the superconductivity is much more sensitive to the crystalline quality and orientation than in low temperature metal based superconductors Also no true S N S structures have been made yet in the high temperature superconductors for various reasons including their complex crystal structures and compatibility with metallic oxides though considerable progress is currently being made in this area Nevertheless there appear to be many similarities in the electrical properties of classical low temperature S N S Josephson junctions and high temperature grain boundary Josephson junctions including the temperature dependence of many of the critical parameters Previous measurements of the temperature dependency of grain boundary Josephson junctions have shown that the critical current J is proportional to the term 1 i e Eqn 7 20 12a STAR Cryoelectronics LLC 86 Mr SQUID User s Guide Also the resistance of the junction is only very weakly temperature dependent so that the normal state resistance Ry of the junctions is almost a constant so that t
114. lsesanchat EE ER AEE A ERE aS 109 94 RF Filter Modlen iniae vias ave aude a Tiaa 110 9 5 CG E A E E T AE EE E E 110 9 6 Dewar eiin a ea AE ae alc eS ken Ma ea EET an EAEE aaa aE 110 10 Reference Sion nueia ws ca aca a e a cote a aes al aa ON 111 STAR Cryoelectronics LLC v Mr SQUID User s Guide Revision Record STAR Cryoelectronics Release Copyright 2000 2002 by STAR Cryoelectronics LLC Santa Fe NM 87508 Updated contact information Updated specifications Updated specifications Updated specifications All rights reserved No part of this manual may be reproduced stored in a retrieval system or transmitted in any form or by any means electronic mechanical photocopying recording or otherwise without prior written permission of STAR Cryoelectronics STAR Cryoelectronics reserves the right to change the functions features or specifications of its products at any time without notice TECHNICAL SUPPORT If you have any questions or comments about this product or other products from STAR Cryoelectronics please contact STAR Cryoelectronics 25 Bisbee Court Suite A Santa Fe NM 87508 U S A http www starcryo com Technical Support 505 424 6454 505 424 8225 info starcryo com STAR Cryoelectronics LLC vi Mr SQUID User s Guide WARRANTY STAR Cryoelectronics Limited Warranty STAR Cryoelectronics warrants this product for a period of
115. made Practical superconducting wire for use in moving machines and magnets also became available in the 1960 s For the next twenty years the field of superconductivity slowly progressed toward practical applications and to more profound understanding of the underlying phenomena A great revolution in superconductivity came in 1986 when the era of high temperature superconductivity began The existence of superconductivity at liquid nitrogen temperatures has opened the door to applications that are simpler and more convenient than were ever possible before Nevertheless the product you have in your hands today was made possible by many aspects of the 80 years of discovery that preceded it 5 2 Superconductivity A Quantum Mechanical Phenomenon There are certain materials actually many thousands of them by now that exhibit a remarkable transition in their ability to pass electrical currents when they are cooled down to a sufficiently low temperature their electrical resistance vanishes completely How this behavior comes about was a mystery that occupied the minds of theoretical physicists for nearly half a century after it was first observed The answer turned out to be tied to the quantum mechanical nature of solids in particular to the tendency of electrons to become paired These Cooper pairs behave cooperatively in certain materials and form a single quantum mechanical state In the following discussions we can only explain these
116. market that incorporates high temperature superconductor HTS thin film devices e Mr SQUID is the first commercial use of liquid nitrogen cooled SQUID technology e Mr SQUID is the first instrument for the demonstration of the quantum effects of superconductors designed for undergraduate laboratories About This Manual Mr SQUID is designed to assist in the education of young scientists in training Every effort has been made to try to make this manual as readable and accurate as possible All of the experiments were performed multiple times before their manual sections were written Considerable effort has been made to make this product and manual as valuable and easy to use as possible Just as in performing cutting edge research however difficulties performing the experiments in this manual can arise and the apparatus may become uncooperative We encourage you to contact us if you encounter problems that appear to be insurmountable or to make suggestions or to point out errors so that we may improve this product and this manual The best way to contact us is by email at info starcryo com Other means of contacting us about this product are described in the troubleshooting section of this manual STAR Cryoelectronics LLC viii Mr SQUID User s Guide 1 INTRODUCTION What is Mr SQUID Mr SQUID is a de Superconducting QUantum Interference Device SQUID magnetometer system incorporating a high temperature
117. measure the horizontal shifts in the V curve STEP 2 Slowly increase the amplitude of the sine wave generator connected to the coil until you see the V curve start rocking horizontally back and forth about once a second This means our coil is generating a field that induces currents in our film greater than the films critical current Now decrease the amplitude of the sine wave generator until you lose sight of the V rocking motion STAR Cryoelectronics LLC 81 Mr SQUID User s Guide STEP 3 Record the value of the current in the coil by measuring the voltage across the 1000 Q resistor using the second DVM Write this in your lab notebook STEP 4 Wait until the voltage on the diode stabilizes This can take as long as 10 minutes STEP 5 Record the diode voltage in your lab notebook STEP 6 Record the amplitude that you see of any rocking motion of the V curve along the horizontal axis STEP 7 Carefully raise by a small amount the voltage supplied to the chip resistor mounted on the back of your superconducting film Steps 4 7 are to be repeated until the film temperature has been raised to about 90 K The accuracy of the measurements and the number of data points you record is largely a function of your patience If you want to spend less time raise the chip resistor current in larger steps You will get fewer temperature readings this way However if you do not wait until the diode voltage at each point is sta
118. ng the frequency until you see a symmetric pattern of steps in the V I curve Below is an illustration of the Mr SQUID V I curve from step 1 after tuning to 4 520 GHz which shows two steps one at about 1 9 divisions and one at about 1 9 divisions Dielectric and Electrical Properties of Biological Materials by Ronald Pethig John Wiley and Sons Chichester 1979 ISBN 0 471 99728 5 STAR Cryoelectronics LLC 73 Mr SQUID User s Guide Trouble avoidance tip If you cannot see any steps in the V I after tuning the frequency up all the way go back and repeat step 1 at a slightly higher frequency then repeat step 2 Due to the spurious electromagnetic modes which form in the Mr SQUID dewar due to the silver coating inside the glass dewar getting the microwaves to couple properly can be somewhat of a black art 7 4 2 Procedure for using an x band microwave horn STEP 1 Cool the Mr SQUID unit down using the Styrofoam container rather than the glass and metal dewar which came with you Mr SQUID dewar Note Styrofoam is quite often used to hold liquid nitrogen for short duration uses such as cooling absorption pumps However use a container with thick enough walls at least 3 cm so that moisture does not condense on the outside during the course of this experiment STEP 2 Once you have a clean V I curve place the microwave unit on the table and point the horn towards the Mr SQUID unit Move the unit
119. of flux trapping and RF interference If you cannot get a good clean curve see Section 6 Troubleshooting and Getting Help 7 4 1 Procedure for using a coaxial cable microwave generator STEP 1 Once you have a clean V I curve reset the microwave generator to its lowest frequency setting or 1GHz whichever is higher Slowly increase the amplitude on the microwave generator At some point you should see the V I curve flatten out with a complete disappearance of the supercurrent You may or may not see steps in the V Z curve before this point The reason is that the Mr SQUID dewar co axial cable combination acts as a complicated resonator with many modes Many of these modes may couple with the SQUID junctions enough to exceed their critical currents but do not couple with the junctions correctly to display the ac Josephson Effect If you have reached the maximum amplitude of your MW generator but have not suppressed the critical current by at least 70 try moving the coaxial cable closer to the cold end of your Mr SQUID probe STEP 2 Once you have suppressed the critical current back the amplitude back down until part one half to one third of the original supercurrent has returned At this point slowly change the frequency Watch the V Z curve while you are doing this Again due to the various electromagnetic modes that can arise inside the Mr SQUID dewar not all frequencies will properly couple into the SQUID Keep slowly varyi
120. of the rubber stopper to pump on the Mr SQUID dewar If the liquid level is too high simply pour some of the liquid away Next attach the free end of the tubing to your vacuum source Only about 10 minutes is required to come to thermal equilibrium at the lower temperature Turn off the vacuum source and carefully remove the stopper from the top of the dewar Depending on the strength of your vacuum and the pumping time your liquid nitrogen might be beginning to freeze and may appear slushy If this is the case allow it to warm until it is a liquid before continuing The hold time for the new temperature is quite long at least 10 minutes due to the high heat capacity of liquid nitrogen If your measurements take longer than this keep a careful note of the temperature reading of the silicon diode and when you see it start to increase repeat the pumping procedure outlined above Immerse the Mr SQUID probe into the dewar Using the two calibrated points of the silicon diode room temperature and 77 K extrapolate the temperature of the liquid nitrogen It should be between 65 K the freezing point and about 71 K depending on the end pressure of your pumping source Measure the SQUID and record the properties along with the temperature on the data sheet that follows this experiment Compare the superconducting properties of the SQUID at 77 K to those at the lower temperature The critical current and the modulation depth should be consi
121. omponents illustrated in Figure 7 14 and Figure 7 17 and that you did not stick a wrong resistor value in somewhere Unfortunately this troubleshooting guide cannot cover every possible problem If at the end you cannot get your digital flux locked loop to function yet your Mr SQUID unit is operating correctly we would suggest that you ask for help from your instructor or someone else knowledgeable about simple circuits 1 Do you have the proper power supplies hooked up to you circuit and are they turned properly on Are the power cords for the power supplies connected correctly 2 With the loop disconnected completely from your Mr SQUID can you get your Mr SQUID to give a proper V I and V curve If no go the main troubleshooting chapter of this manual Section 6 3 When the Mr SQUID y output is connected to Test Point 1 TP1 of your circuit while the Mr SQUID box is in the V mode yet the external coil output of your circuit is not connected to the EXT COIL of the Mr SQUID box does TP1 look correct yet TP2 look like a flat line In other words does TP1 look like Figure 7 15 or Figure 7 18 but TP2 look flat A First check the scale setting on your scope when looking at TP2 It should be set 500x less sensitive B Check the wiring including whether 5 Volt power is connected to the proper pins on the integrated circuits U1 and U2 C Turn R1 clockwise until it will not turn anymore Then adjust R1 counte
122. on In the Mr SQUID experiments it is possible to calculate Bz using the measured values of J and L and Eqn 3 1 Then one may compare the predicted voltage modulation using Eqn 5 5 and Eqn 3 5 with the value determined experimentally 5 10 SQUID Operation If a bias current less than the junction critical current is injected through the loop then as a consequence of the dc Josephson effect there will be no voltage across the loop If the bias 4 This equation is obtained by solving Eqn 3 2 for AV If thermal effects are to be considered as in the case of a high T SQUID then Eqn 3 5 is used STAR Cryoelectronics LLC 38 Mr SQUID User s Guide current is raised above this critical current then a voltage develops across the loop The critical current is also a function of the magnetic flux through the loop and may be expressed as g cos P where o h 2e 2 07x10 Wb the magnetic flux quantum and this leads to the V characteristic shown in Figure 5 8 The total measured current is Itotal Neakage where Ijeakage is the leakage current through resistors of Figure 5 9 So if the magnetic flux through the loop is changed the critical current is changed and the non linear voltage current behavior of the loop is altered Note that this equation is identical in form to the equation describing quantum interference of light diffracted by two slits which displays an interference pattern
123. on before recombining at the right side The Mr SQUID control box allows you to perform this experiment quite easily If you have set up the system according to the instructions in the previous section you are ready to try this voltage current experiment 3 1 Setting Up the Output Device Once again we assume that you are familiar with the operation of your oscilloscope or x y recorder For initial settings try an x sensitivity of 0 2 volts per division or whatever value is closest to this on your instrument and a y sensitivity of around 50 millivolts per division You may want to adjust these values as needed later Now refer to the diagram of the Mr SQUID control box Figure 3 2 below STAR Cryoelectronics LLC 10 Mr SQUID User s Guide FLUX CURRENT BIAS BIAS AMPLITUDE OUTPUTS e000 osc Mr SQUID FO conng tus Figure 3 2 Front panel of the Mr SQUID electronics box STEP 1 If you are using an oscilloscope set the oscillator frequency toggle switch 7 to the OSC high speed position If you are using an x y recorder use the X Y low speed position STEP 2 Before turning on the power make sure the amplitude control 4 is at its minimum fully counter clockwise position and set the flux bias control 2 and the current bias control 3 to their 12 o clock straight up positions STEP 3 Make sure the function switch 1 is in the V I position In this position the BNC cable
124. onducting Transition Temperature of an HTS Film Purpose SQUIDs by virtue of being the world s most sensitive detectors of magnetic fields are commonly used in instruments designed to measure the magnetic properties of materials Knowing the magnetic behavior of a material is often of direct technological importance as in the case of metals and oxides used for magnetic recording The magnetic behavior of a material is often an indicator of its electronic properties as in the case of the Meissner effect in superconductivity In this experiment we will measure the ability of a superconducting film to expel magnetic flux as it undergoes a superconducting transition Equipment For this experiment you will need e A HTS thin film grown on sapphire at least 0 5cm x 0 5 cm in size e Mr SQUID and liquid nitrogen e An oscilloscope or X Y recorder e One glass encapsulated silicon diode e One 100 Q surface mount thin film chip resistor e 500 cm of copper wire of size 36 to 40 AWG insulated magnet wire this corresponds to diameters of 0 013 to 0 08 mm e A digital volt meter DVM with sub millivolt resolution 34 e A second digital volt meter DVM may be a hand held unit e A 0 10 Volt adjustable power supply e A decade resistor box with resistance values from below 100 Q to above 100 kQ e A low frequency sine wave generator capable of frequencies below 2 5 kHz e A soldering iron and electronics grade solder e
125. onductivity A Quantum Mechanical Phenomenon ceceeseeseereeeeeeeeeeeee 27 5 3 The S perconducting State ax sires tell saat eek ttc ta od sale Pala a leh 27 5 4 TOUTING oo ea hata eo A ates E EEE a tote ean 28 5 5 S percondu cting RINgS 55 c5c cis deascaeydoatecansady tealosedaceentesmaydansccinsets E A donoouaeetecss 29 5 6 Josephson AUN CHONG karnen e e a E ET ERO AAE 30 3A Med SOU r eee arr e a n A E PT 31 5 8 Details of de SQUID operation sessesseseesseesseseesseessessreseesseesesresstesesersstessessrssressesse 32 STAR Cryoelectronics LLC iv Mr SQUID User s Guide 5 9 SO WT Parameters sce aeedkinccibes ater cds a e a N s etait nest 36 5 10 SSOUID HOM SrAN OMe scutes ae aie Saha E E EA A eto tok ES 38 5 11 Practical SQUID Magnetometers g1 ssscst Sh dveaassesscendshcanchoa teeth iaeceasstelicaplavsantuaedeaparaeiees 39 512 SQULD Appl Catt On sx ieasssisccaxthseis pd ana a a iea aiaeei 41 513 A Bret History OF SQUIDS prisene ytter eaa aE O biden nar EO R E AA 42 5 14 The SQUID in Mr SQUID trated een lo eae he 44 6 Troubleshooting and Getting Help cece csccceseceseceeeceeseecsseceseeeeeeesseecsaeeeeeeeeeeeseeenaeens 46 6 1 Problems tt VF MOU ee icosadcstysacistneaattd data iaio a E ated EE EAE 47 6 2 Problems in V Mode Assuming Everything Works in V I Mode ccceeseeeteees 48 6 3 Magnetic Flux Trapping in SQUIDS ssssessesessseessesesssressessrssessessrssresseesessresseeseesressee 49 6
126. ons as well as for observations of the properties of materials Until Mr SQUID the only superconducting property that was easy to demonstrate was magnetic flux expulsion using a levitated magnet Now with Mr SQUID other aspects of superconductivity can be observed in any laboratory Demonstrating the Hallmarks of Superconductivity Superconductivity is a unique property of certain materials that gives them remarkable advantages as electric conductors magnetic shields sensors and as elements of advanced integrated circuits The three primary hallmarks of this phenomenon are 1 Zero resistance to the flow of dc electrical current 2 The ability to screen out magnetic fields perfect diamagnetism 3 Quantum mechanical coherence effects magnetic flux quantization and the Josephson effects Until 1987 none of these effects could be observed without a liquid helium cooled cryostat and in general fairly elaborate instrumentation This was because all known superconductors became superconducting only at temperatures below 23 K 250 C and more typically below 10 K In 1987 the startling discovery of superconductivity in a class of copper oxide based compounds raised the operating temperature of superconductors to 90 K and beyond Suddenly superconducting experiments cooled by liquid nitrogen at 77 K 196 C were possible The first and easiest demonstration of superconductivity consisted of floating a small magnet above a cool
127. oop experiment first get your loop running as before Then before altering your circuit turn down the AMPLITUDE knob on your Mr SQUID unit Watch the pattern of the LEDs in your digital flux locked loop Write the pattern down using a 1 if a given LED is on a 0 if a given LED is off If a LED is flickering you might wish to denote it with a instead of a 1 or 0 You might also want to adjust the knob labeled FLUX BIAS to achieve an interesting pattern of LEDs although doing so is not important Also measure voltage at test point 3 TP3 Once you have done this DO NOT READJUST THE KNOB LABELED FLUX BIAS One can alter the circuits shown in Figure 7 14 and Figure 7 17 to explicitly perform the MSB conversion by using an inverter to invert the most significant bit An inverter simply changes a logical 1 into a logical 0 and a logical 0 into a logical 1 The schematic symbol for an inverter and its implementation using a CD4009 CD4049 or 74xx05 e g 74LS05 chip is shown in Figure 7 21 CD4009 or CD4049 DM74LS04 in J gt out Figure 7 21 STAR Cryoelectronics LLC 101 Mr SQUID User s Guide The alteration for the 8 bit flux locked loop circuit is to place an inverter pin 11 of US as shown in Figure 7 22 The alteration for the 12 bit flux locked loop circuit is to place an inverter pin 11 of U4 as shown in Figure 7 23 U1 U2 OP 27 U3 LM311 U4 U5 74LS169 4 bit U D counter
128. opment production final assembly and test of product shipping and sales and marketing activities STAR Cryoelectronics was formed as a limited liability company in the State of New Mexico in April 1999 For further information about STAR Cryoelectronics and the advanced SQUID products offered by STAR Cryoelectronics please visit the company web site http www starcryo com STAR Cryoelectronics LLC 108 Mr SQUID User s Guide 9 TECHNICAL SPECIFICATIONS 9 1 Electronics Box Steel construction with internal battery compartment Size WxHxD 6 x 2 6 x 7 5 in 153 x 66 x 190 mm Weight 2 65 Ib 1200 g Power 9 VDC 48 mA supplied by two 9 V alkaline transistor batteries Outputs X current 1 V corresponds to 100 uA through SQUID or mod coil Y voltage 1 V corresponds to 100 uV across SQUID Sweep Oscilloscope high speed setting 15 Hz X Y recorder low speed setting 0 07 Hz Amplifier Voltage gain x10 000 Frequency response 0 to 2 8 kHz Voltage noise floor lt 1 8 nV JHz for f gt 10 Hz Total output noise voltage lt l mV 9 2 Probe Ver 8 Length 17 5 inch 445 mm Connector DB 9 receptacle with integral pi filter SQUID type Bicrystal grain boundary Josephson junction de SQUID SQUID inductance nom 100 pH Internal coil 2 external coil 1 mutual inductance to SQUID nom 28 41 pH SQUID critical current gt 5 pA Voltage swing gt 2 uV SQUID field sensitivity 0 5 uT o 9 3 Magn
129. or the amplitude control 4 Instead of controlling the sweep of the drive current through the SQUID it now controls the amplitude of the current through the modulation coil which is linearly related to the magnetic field applied to the SQUID To view as many V periods as possible turn the amplitude control 4 in the clockwise direction Depending on the particular SQUID and coil in your probe you should be able to see at least four or five periods of oscillation as shown in Figure 3 8 AV T Figure 3 8 A typical Mr SQUID V characteristic The maximum AV may range from 10 to 30 uV or higher The voltage change that occurs due to the influence of the magnetic field appears now on the vertical axis of your display device The voltage amplification provided by the Mr SQUID box is unchanged from before To determine the actual voltage across the SQUID you must divide by 10 000 However since the SQUID modulation signals are smaller than the junction voltages you examined earlier you will need to increase the sensitivity of the vertical scale on your display device The maximum peak to peak voltage swing of the SQUID modulation in Mr SQUID AV typically is between 10 and 30 uV or 100 to 300 mV output from the front panel of the Mr SQUID control box Depending on the setting of the amplitude control you may wish to change the x sensitivity to more conveniently view the oscillations of the SQUID In addition it may be nece
130. ords the U1 op amp puts out a voltage equal to its input but it draws no current from the 10 kQ potentiometer U2 is configured as a summing amplifier with a gain of 330 By a gain of 330 we mean that it has a gain of 330 AND is inverting In other words its output is the sum of the outputs from U1 and the Mr SQUID box times 330 It is not necessary for this amplifier to be inverting for this digital flux locked loop to function it was just easier to make a summing amplifier that inverts than one that does not U3 is a comparator that compares the output of U2 to ground If the output of U3 is greater than 0 Volts then the output of U3 is 5 Volts a logical 1 for the digital circuits which follow If the output of U3 is less than 0 Volts then the output of U3 is 0 Volts a logical 0 for the digital circuits which follow U4 and U5 are two 4 bit counters up down connected together to effectively form an 8 bit up down counter An up down counter counts up if its data input is a 1 when its clock input is a 1 and counts down if its data input is a 0 when its clock input is a 1 The 8 bit output of the counter formed by U4 and US is fed into U6 that is an 8 bit DAC The 8 LEDs allow you to see the bits output by U4 and U5 that are input to the DAC The output of the DAC U6 is fed into the dual operational amplifier U7a and U7b to buffer its output The output of U7b is fed to the Mr SQUID external coil through a 10 KQ resistor The flux
131. oscilloscope The slope of this line is the resistance of the Mr SQUID At room temperature this should be several hundred Ohms STAR Cryoelectronics LLC 58 Mr SQUID User s Guide As shown in Figure 7 3 the chip end of the probe is to be suspended well above the liquid nitrogen level in the dewar The paper binder clip is a handy way to hold the probe in a fixed position with respect to the foam cap on the dewar Start with the end of the probe just under the level of the foam and follow the procedure below to record the temperature and resistance of the SQUID 7 1 2 The Resistance vs Temperature measurement procedure STEP 1 Wait until the voltage on the diode stabilizes This can take as long as 10 minutes STEP 2 Record the diode voltage in your lab notebook STEP 3 Record the slope of the V I curve near the origin V 0 point in your lab notebook STEP 4 Carefully loosen the binder clip while holding the Mr SQUID probe and lower the probe about 2 mm further down into the dewar This procedure is repeated until the probe has been lowered all the way into the nitrogen and has reached 77 K The diode voltage should correspond to liquid nitrogen temperature at that point The accuracy of the measurements and the number of data points you record is determined by your patience If you want to spend less time lower the probe in larger steps You will get fewer temperature readings this way However if you do not wait un
132. ow is 50 pA per division For this Mr SQUID external coil this translates into a flux of about 2 Wy per division TP2 TP3 Figure 7 16 Signal outputs of the 8 bit FLL in the locked mode at TP1 and TP2 A few words are in order concerning improvements to this elementary 8 bit flux locked loop circuit First this circuit is not significantly different from a real digital flux locked loop TP 1 of Figure 7 15 would indicate that the coupling of our Mr SQUID coil was 44 1A p The voltages that can appear at Test Point 3 TP3 are about 5 Volts that drive the external coil through a 10 kQ resistor So the maximum flux that the loop as constructed in Figure 7 14 can cancel out and hence measure is 11 o The 8 bit DAC step size is 1 part in 2 256 which for a total span of 22 o gives a DAC flux step size of 0 086 o 46 Second changing the value 45There is a trouble shooting section at the end of this experiment 46For you SQUID buffs Since the bandwidth of the Mr SQUID box is 2 8kHz this translates into a minimum DAC step flux noise of 1625 u Hz We will examine the step size later in this experiment STAR Cryoelectronics LLC 93 Mr SQUID User s Guide of the 10 KQ resistor between TP3 and the Mr SQUID external coil will allow one to trade off resolution for maximum flux cancellation One cannot change this resistor it arbitrarily however We would suggest that this be left to the studen
133. pled to an inductor in parallel with a capacitor and the circuit is excited by an external oscillator at its resonant frequency typically 30 MHz The amplitude of the rf signal across the tank circuit turns out to be periodic in the flux applied to the SQUID the period of course is o so that by monitoring this amplitude with suitable electronics one can measure small changes in magnetic flux in much the same way as for the dc SQUID At the time a major advantage of the rf SQUID over the de SQUID was the fact that it required only a single Josephson junction The rf SQUID with a point contact junction became commercially available in the early 1970 s by S H E now BTi and has had a long history of successful use It is undoubtedly true that until very recently more physics experiments were carried out with the rf SQUID than with the dc SQUID for the simple reason that only the former was commercially available The next major step in the development of SQUIDs was the introduction of the thin film dc SQUID in 1976 This device built on a cylindrical quartz tube and involving Nb NbO PbIn tunnel junctions offered a major advance in resolution This improvement was due partly to the use of ideal junctions and partly to the optimal coupling of the SQUID to the room temperature electronics via a cooled resonant circuit Shortly afterwards a comprehensive theory for the white noise in the dc SQUID demonstrated that smaller is better
134. posed for use in ultra sensitive receivers with several GHz bandwidth 9 Your Mr SQUID system was constructed to minimize pick up of power line 60 Hz interference radio frequency interference RFI and microwave interference MWI The rf interference filter module connected to the top of the probe is designed to eliminate the effects of these signals Even so it is still possible that external signal sources in your operating environment may affect the performance of Mr SQUID Above are V I traces for a Mr SQUID in the absence and in the presence of rf interference of about 30 MHz The critical current is totally suppressed when the RFI is present The RFI was produced simply by pushing the talk button on a cordless telephone located a distance of about 1 foot from an operating Mr SQUID with the RFI filter module removed from the top of the probe Other sources of RFI that are commonly encountered are computers microwave ovens garage door openers pagers CB radios campus police radios radio stations 3 and TV stations These latter sources can be a problem at considerable distances since most commercial stations broadcast hundreds of thousands of watts of rf power Lower rf levels may only perturb the V I curve yet suppress the V curve If this is the case usually the flat part of the V I curve will also have a small non zero slope 0See for examples pages 323 394 in SQUID H D Hahlbohm and H Lubbig
135. pplications of superconductivity 2 Voltage flux characteristics The Mr SQUID control box also will allow you to observe the voltage flux V characteristics of the SQUID As we will explain in detail later applying an external magnetic field to a dc SQUID causes the voltage across the STAR Cryoelectronics LLC 1 Mr SQUID User s Guide SQUID to change periodically as the field is varied The periodicity of the voltage modulation is governed by a fundamental quantity known as the magnetic flux quantum or fluxon Briefly the voltage undergoes a complete cycle of modulation each time a quantum of flux passes through the superconducting loop that comprises the SQUID Since magnetic flux is the product of magnetic field times area the magnetic field period of these voltage oscillations is determined by the geometry of the SQUID This is a fundamental property of superconducting rings and SQUIDs that Mr SQUID allows you to investigate The Mr SQUID control box allows you to apply an external magnetic field to the SQUID and to vary that field in a way that is convenient for display on an oscilloscope or x y recorder Obtaining the V J and V curves are the essential elements of SQUID operation and are the starting point for working with Mr SQUID Later in the user s guide in Section 7 we will outline a series of more advanced experiments using Mr SQUID that demonstrate how SQUIDs can be used for a variety of applicati
136. ption of the problem the serial number of your probe and electronics box and descriptions of your V J and V curves values of J Ry and AV You can also reach us weekdays between 8 00 a m and 6 00 p m Mountain Time at 505 661 6481 or by fax at 505 661 4287 When you do contact us please send a description of the problem the serial number of your probe and electronics box and descriptions of your V I and V curves values of Ie Ry and AV STAR Cryoelectronics LLC 53 Mr SQUID User s Guide 7 ADVANCED EXPERIMENTS This section of the User s Guide details a series of more advanced experiments using Mr SQUID that go beyond the basic functions of the SQUID system Unlike the basic functions these experiments require various additional pieces of equipment and often some assembly of simple electronic circuits Where possible the circuits used in the experiments can be built from readily available electronic components which can be obtained from local electronic parts suppliers such as Radio Shack Outside of the United States Radio Shack affiliated stores often go under the parent company name as Tandy Electronics The effort and experimental skills required to perform these experiments goes beyond the level of the basic operation of the system but they are well within the scope of an advanced undergraduate laboratory course The intent of these experiments is to demonstrate the operation and applications
137. r SQUID system for users who are already familiar with SQUID operation Later on other users may want to use this section as a reference on various functions of the Mr SQUID system STAR Cryoelectronics LLC 3 Mr SQUID User s Guide Section 5 An Introduction to Superconductivity and SQUIDs contains background material describing the phenomenon of superconductivity with an emphasis on explaining how Mr SQUID works In it you will find discussions of superconducting rings phase coherence the Josephson effects magnetic flux quantization and basic SQUID operation as well as a history of SQUIDs and a brief description of the methods used to make the SQUID in your Mr SQUID system Section 6 Troubleshooting and Getting Help is provided to help you deal with some common problems encountered in SQUID operation It also provides information on how to contact STAR Cryoelectronics with problems that you cannot solve yourself Section 7 Advanced Experiments contains information on advanced experiments that are possible using Mr SQUID in conjunction with other instruments and materials some background about STAR Cryoelectronics the developer and manufacturer of Mr SQUID technical specifications and schematics for Mr SQUID and a reference section that lists some useful books on superconductivity and SQUID operation We anticipate that the Advanced Experiments in Section 7 will be periodically updated as worldwide
138. r clockwise slowly while watching TP2 on the scope There should be a narrow range where TP2 looks somewhat like that shown in Figure 7 15 or Figure 7 18 Remember your Mr SQUID may show more or less flattening of the V curve 4 When the Mr SQUID Y output is connected to test point 1 TP1 of your circuit while the Mr SQUID box is in the V mode yet the external coil output of your circuit is not connected to the EXT COIL of the Mr SQUID box does TP1 look correct yet TP2 look much less than about 2 Volts peak to peak If so you can increase the gain of the amplifier U2 by changing the 330 kQ feedback resistor to something larger As shown in Figure 7 14 and Figure 7 17 the gain of this stage is 330 330 kQ 10 KQ Increasing the 330 KQ to a larger value will increase the size of the signal at TP2 To calculate the size resistor needed to bring your signal up measure the present peak to peak value at TP2 in Volts and let s call this Vp Tp2 o14 And let s say we wish to bring it up to a peak to peak value of Vpp TP2 new The new resistor needed to increase this to about Vpp TP2 new Volts peak to peak is 330Vpp TP2 new Vpp TP2 014 KQ For example if the value at TP2 was 2 Volts STAR Cryoelectronics LLC 104 Mr SQUID User s Guide peak to peak and we wanted to bring it up to say 8 Volts peak to peak then we would change the 330 kQ resistor on U2 to a 1 32 MQ resistor 5 If everything up through TP2 loo
139. r the unwanted nitrogen onto the floor making sure to avoid people s feet etc Place the Mr SQUID probe into the dewar as shown in Figure 7 3 You can use the binder clip in conjunction with the foam dewar cap that was shipped with your Mr SQUID If you are performing this diode calibration for the magnetic shielding experiment Experiment 5 you may now return to that section STAR Cryoelectronics LLC 57 Mr SQUID User s Guide unit If you no longer have the foam cap a suitable replacement can be fashioned out of Styrofoam or cardboard with a small hole large enough to fit the probe stick as shown in Figure 7 3 The binder clip is used to keep the Mr SQUID probe from sliding down into the dewar You want to start with the Mr SQUID probe at the very top of the dewar Mr SQUID Probe Binder Clip a Diode Sensor Wires lt t __ Liquid Nitrogen Level Figure 7 3 Position of the Mr SQUID probe inside the liquid nitrogen dewar At this point connect the Mr SQUID probe to the Mr SQUID electronics box using the cable provided with the system and connect the Mr SQUID electronics box to the oscilloscope with BNC co axial connectors Turn on the Mr SQUID electronics and set the unit to the V I mode Turn on the current source for the silicon diode and verify that it is indicating that it is near room temperature according to your calibration curve You should see a straight line on the
140. r words they will act like a superconductor Functionally speaking electrical currents can flow between the two regions with zero resistance Such currents are called Josephson currents and physical systems composed of two regions of superconductor that exhibit this property are called Josephson junctions Strictly speaking the resistanceless currents that flow in a Josephson junction are a manifestation of the dc Josephson effect a second property of junctions by which the current oscillates at high frequencies is called the ac Josephson effect A discussion of the ac Josephson effect and a description of an experiment to observe it may be found in Section 7 Any weak coupling between two regions of superconductor such as tiny constrictions microscopic point contacts weakly conducting layers or certain crystallographic grain boundaries exhibit the Josephson effect All of these structures can be called Josephson junctions and are more typically called weak links The Josephson junctions in Mr SQUID are grain boundary weak link junctions The term weak link comes from the fact that Josephson junctions generally have a much lower critical current which is the maximum current that can be carried before resistance begins to appear than that of the two superconducting regions that it connects Josephson junctions are the essential active devices of superconductive electronics much as the transistor is the essential
141. ral SQUID magnetometers together with that for a fluxgate magnetometer which is a commonly used non superconducting instrument for measuring magnetic fields Field Noise in fT Hz Sensor At 1 Hz At 100 Hz Flux Gate room temperature 30 000 30 000 77K YBCO de SQUID Magnetometer lt 100 lt 40 4 2 K Nb de SQUID Magnetometer lt 5 lt 4 5 12 SQUID Applications Liquid helium cooled SQUIDs have been commercial products for two decades In the early stages the primary uses for these devices were in laboratory instrumentation Generally speaking technically trained users such as physicists and electrical engineers used commercial SQUIDs as highly sensitive magnetic field detectors voltmeters or null detectors for experiments that were already being conducted at cryogenic temperatures During the past decade however complete instruments have become available that incorporate helium temperature SQUIDs that require less expertise on the part of the user The prime example of this type of application is the SQUID susceptometer that is widely used by many laboratory scientists Ironically this instrument has found its greatest application in the study of material properties of high temperature superconductors Other examples include rock magnetometers that analyze the magnetic properties of mineral samples These SQUID based instruments feature liquid helium dewars with hold times greater than one year Clearly for at least some fixed installation
142. ribed by the same wavefunction What does this mean In quantum mechanics also called wave mechanics physical entities such as electrons are described mathematically by wavefunctions Like ordinary waves in water or electromagnetic waves such as light waves quantum mechanical wavefunctions are described by an amplitude the height of the wave and a phase whether it is at a crest or a trough or somewhere in between When you are describing waves of any kind these two parameters are all that is necessary to specify what part of the wave you are discussing and how large it is Moving waves oscillate both in time and in space If we sit at one point in space the wavefront will move up and down in time If we look at one moment in time the wavefront undulates in space The quantum mechanical wavefunction is a mathematical entity that describes the behavior of physical systems such as electrons and light waves A unique property of quantum mechanics is the interchangeability of particles and waves in describing physical systems Generally there will be a unique wavefunction required to describe each particle in a physical system In the usual or normal state the wavefunctions describing the electrons in a material are unrelated to one another In a superconductor on the other hand a single wavefunction describes the entire population of superconducting electron pairs That wave function may differ in phase from one place to another wit
143. rrent x axis and 50 mV div for the voltage y axis You may wish to adjust these initial settings as you go along Zero the flux bias and current bias controls set them at 12 o clock and turn up the sweep amplitude The V I curve should appear on your output device The current bias control can be used to symmetrize the trace if necessary In addition the flux bias control should be adjusted to maximize the critical current A typical Mr SQUID V I curve looks like this Figure 4 3 A typical Mr SQUID V I characteristic If the critical current is far less apparent than in Figure 4 3 the likely cause is flux trapping Try thermally cycling the probe with the control box off to restore the maximum critical current Under some circumstances several attempts may be necessary We discuss this problem in some detail in Section 6 Troubleshooting and Getting Help STAR Cryoelectronics LLC 25 Mr SQUID User s Guide Mr SQUID displays a V I curve for convenience in switching over to the V curve If you prefer to view the more traditional V curve with the current on the vertical axis feel free to exchange the x and y cables The junctions in Mr SQUID may generally be represented by the RSJ model with considerable noise rounding at 77 K The critical current of Mr SQUID typically is between 5 and 150 uA The Ry product for these junctions and SQUIDs is a few tens of microvolts at 77 K 4 4 V Characteristic
144. s To obtain the V characteristics for Mr SQUID turn down the amplitude control and use the current bias control to bias the SQUID just above the critical current at the knee of the V I curve This will be the most sensitive point in the curve You can now manually modulate the SQUID with the flux bias control The point on the oscilloscope screen or plotter pen will oscillate up and down in response to changing the flux bias Now switch the function control to the V position The amplitude control will sweep the current through the modulation coil which is linearly related to the magnetic field applied to the SQUID and the familiar V curve should appear on your output device The modulation depth is smaller than the voltages you were measuring before so increase the y sensitivity of your oscilloscope or plotter at this time Also if your output device can be AC coupled using this mode to view the vertical axis may be helpful You may also want to tweak the current bias control to maximize the modulation depth Adjusting the flux bias control will allow you to select a region of the V curve for observation A typical Mr SQUID voltage flux characteristic appears in Figure 4 4 Depending upon the particulars of the individual SQUID and coil in your probe you should be able to see at least four or five oscillations on your output device AV 4 Figure 4 4 A typical Mr SQUID V characteristic You may wish to calc
145. s liquid helium does not impose great hardships Special purpose SQUID instruments for users other than laboratory scientists have been slower to reach the marketplace The main example in this category is the multi channel SQUID based system for biomedical applications Several companies worldwide market systems of this kind which sell for as much as 3 million The two main applications are to magnetoencephalography MEG and magnetocardiology MKG in which the magnetometers measure magnetic signals generated in the brain and heart respectively The SQUID system is contactless and may yield additional or complementary information to the conventional electroencephalogram EEG or electrocardiogram EKG There are a number of applications beyond MEG and MKG that STAR Cryoelectronics LLC 41 Mr SQUID User s Guide make use of SQUIDs The combination of SQUIDs and superconducting magnets can be used as a magneto ferritometer which is a specialized instrument used to monitor iron levels in the liver This is an important diagnostic tool for identifying a condition known as hemochromatosis which can be extremely serious if not detected In addition to the commercial marketplace there has been considerable development effort on a variety of SQUID applications for the military The U S Navy has sponsored research for many years on SQUIDs for submarine and mine detection in both airborne and ocean going platforms For this applicat
146. s a function of temperature using your two or three data points Draw the best fit line to the data you may wish to perform a least squares fit if you are familiar with the technique in order to produce a calibration curve that scales diode voltage with temperature At this point your diode is calibrated sufficiently to perform Mr SQUID experiments Mounting the diode Next we need to attach the diode to the Mr SQUID probe in order to measure the SQUID chip temperature Since we do not want the diode to be permanently mounted on the probe we will use masking tape to hold the diode on the backside of the probe as shown in Figure 7 2 We want the wires to trail downward under the magnetic shield and out the bottom of the probe Be sure to wait until you diode is at room temperature and is dry before taping it to your Mr SQUID probe Also try to avoid getting tape onto any part of the chip front side of the Mr SQUID probe Place the Mr SQUID magnetic shield on the Mr SQUID probe so that the diode wires come out of the bottom Stuff a small amount of cotton into the bottom of the magnetic shield to block the opening This will improve the temperature uniformity of the region inside the magnetic shield Mr SQUID chip Diode lt housing Figure 7 2 Attaching the diode sensor to the Mr SQUID probe Next empty the Mr SQUID dewar until there is only 10 12 cm of liquid nitrogen left at the bottom you can pou
147. s a rough approximation along with the inductance values given above M 37 pH The horizontal axis of the V curve measures the current through the modulation coil and this is linearly related to the magnetic flux in the SQUID The current gain in the Mr SQUID control box is 10 000 V A i e 1 Volt 10 Amperes The period of the modulation of the magnetic flux in the Mr SQUID loop is the flux quantum p 2 07x107 Wb in MKS units By measuring the amount of current AJ in the coil that is required to produce a change of one fluxon through the hole of the SQUID you can determine the mutual inductance M of the SQUID using the following formula P Eqn 3 4 M Al You can find the value of Bz for the SQUID in your Mr SQUID probe using Eqn 3 1 your measurement of and L 60 pH From the measured values of J and AV you can calculate Bz using Eqn 3 2 Compare these two values Do they agree The fact that the values calculated using Eqn 3 1 and Eqn 3 2 do not agree was a mystery for a number of years after the 1986 discovery of high T materials as these equations worked quite well for SQUIDs made using traditional low 7 materials This lack of agreement was resolved 1 Priciples of Superconductive Devices and Circuits T Van Duzer and C W Turner Elsevier New York 1981 pp 114 116 STAR Cryoelectronics LLC 19 Mr SQUID User s Guide in 1993 with the recognition that thermal effects wer
148. s in the V I curve of a Josephson junction The current density J of a Josephson junction with a fixed dc voltage V across it oscillates according to the equation Eqn 7 10 J th J i510 2 j where e is the charge on an electron 1 602x10 coulomb amp 0 is the superconducting phase across the junction at time f 0 and h is Planck s constant 6 62x10 J s This is called the ac Josephson Effect This means that the current in the junction oscillates with a frequency of 2mn 4neV h A 1 uV dc voltage across a Josephson junction will cause the current to oscillate at v 4 83593420x10 Hz Note that this formula contains neither materials parameters nor extrinsic quantities such as temperature This formula holds for a niobium Josephson junction at 0 01 K as well as the high T grain boundary Josephson junctions in your Mr SQUID unit The frequency v depends only on the ratio of twice the electronic charge to Planck s constant In fact the National Institute of Standards NIST uses the ac Josephson Effect to set the standard for the official value of the Volt As a practical matter one cannot dc voltage bias a Josephson junction to a few microvolts set a radio receiver next to it and tune in to the radio frequency rf radiation emitted by the junction The main reason is that the impedance of free space is 370 Q while the junction is usually much less than 1 Q For this reason the rf will stay in the j
149. s used to counteract any change in external magnetic field By measuring the amount of feedback current it is possible to detect magnetic fields corresponding to a tiny fraction of the characteristic field required to produce a quantum of flux on the SQUID This experiment is detailed in Section 7 Advanced Experiments 3 8 Additional SQUID Measurements Now that you can measure a variety of properties of the SQUID in the Mr SQUID probe you can determine a key parameter of the device namely the By parameter This is defined by 21 Eqn 3 1 q B where L is the inductance of the SQUID loop Earlier we mentioned that the maximum modulation voltage depth AV as measured from the V curve is related to the Ry product that can be determined from the V I curve As we will discuss in Section 5 this relationship can be expressed simply in terms of the Bz parameter _ 4 Ry i Eqn 3 2 q B TAV The above expression provides a simple way to determine the 8 parameter empirically i e without knowing the inductance L of the SQUID This expression is strictly correct only if the STAR Cryoelectronics LLC 18 Mr SQUID User s Guide critical currents of the two junctions are equal and only if thermal noise effects are negligible Both of these are approximations for the junctions in your Mr SQUID The inductance of the Mr SQUID chip may be written as the sum of four terms L L L Lq L where L is the inductanc
150. ss controlled manner by waving a small permanent magnet near the probe Another way to see the effect of an additional applied field is to rotate the entire dewar This rotates the SQUID with respect to the earth s magnetic field and causes a shift Actually the magnetic shield on the probe screens out most of the earth s field but the amount of field that gets by the shield is quite enough to move the V pattern noticeably on the screen Later on you may want to warm up the probe to room temperature to remove the magnetic shield from the bottom of the probe This may be done by loosening the small setscrew that supports the shield Set both the shield and the screw aside in a safe place so that they can be reinstalled later If you now cool down the probe and set up the V measurement you will find that the SQUID is tremendously more sensitive to its environment In fact you may have a great deal of difficulty in getting a good V I curve without flux trapping see the discussion in Section 6 Assuming you succeed in observing the V curve without the magnetic shield which may be impossible in many environments you will find that almost any magnetic disturbance anywhere near the dewar will be visible on an oscilloscope screen Try swiveling a metal chair for example The most sensitive mode of operating a SQUID is to flux locked the SQUID using closed loop feedback electronics In the flux locked loop FFL mode a feedback current i
151. ssary to use the position knob on your output device to center the curve If your oscilloscope can be operated in an AC coupled mode on the vertical channel you can use this mode for more convenient viewing of the V curve never use the AC mode to look at the V I curve or it will be completely distorted on the oscilloscope screen You should see a curve that resembles the one shown in Figure 3 8 Depending on the particular device and on the settings on the control box you may see many more periods than shown here At this point you can try to maximize the signal by fine tuning the current bias control 3 to the most sensitive part of the V I curve just keep your eye on the V curve as you tweak the current bias control until you get the maximum modulation There will be some setting of the current bias control that gives the largest modulation amplitude STAR Cryoelectronics LLC 17 Mr SQUID User s Guide Notice the effect that the flux bias control 2 has on the V curve It allows you to set the central value of applied flux about which the amplitude control sweep varies In other words this control allows you to apply a static magnetic field to the SQUID on top of the oscillating field applied with the amplitude control Turning the flux bias control will therefore allow you to move left and right along the V curve and thereby explore more of it than the amplitude sweep permits You can accomplish the same thing in a le
152. strumentation In this era of high temperature superconductivity Josephson electronics is becoming a far more accessible technology 3 6 Observing V Characteristics using Mr SQUID Up to this point we have been looking at the properties of Josephson junctions Now we will turn our attention to the properties of the de SQUID itself The de SQUID has the remarkable property that there is a periodic relationship between the output voltage of the SQUID and applied magnetic flux This relationship comes from the flux quantization property of superconducting rings that is discussed in detail in Section 5 The Mr SQUID control box will allow you to observe this periodic relationship in the form of V characteristics on your oscilloscope screen or x y plotter page You have already observed the effects of a magnetic field on the V Z characteristics of the SQUID by adjusting the flux bias control current The V characteristics are basically an automatically plotted version of this behavior The physics underlying the V curve is discussed in Section 5 3 7 Modulating the Critical Current of the SQUID As we saw before in the V I operating mode one can apply a magnetic field to the SQUID using the flux bias control This dial controls a current that is applied to the internal modulation coil simply a 3 4 turn gold or silver coil that creates a magnetic field inside the loop of the SQUID as shown in Figure 3 6 The second coil shown
153. t are nearby or connected to the system This includes the Mr SQUID control box itself as well as your display device Nearby computers can often cause trouble if they are on In addition it takes some time for the SQUID to reach liquid nitrogen temperature Make sure you have waited long enough perhaps a couple of minutes before turning on the power If after taking these precautions the critical current is still miniscule or non existent warm up the probe again it only needs to go above the critical temperature of the YBCO at 90 K and cool it back down perhaps rotating it to alter its orientation with respect to any local fields If after several cooldowns the V Z curve still shows the superconducting transition i e the slope of the V I curve indicates several hundred Ohms and suddenly switches to a few tenths of an Ohm one last thing to check is whether the black magnetic shield has itself become magnetized Remember the 0 5 gauss field of the earth forced through the SQUID will result in over a hundred trapped flux quanta so even residual magnetizing of the shield at levels too small to measure by normal means can strongly affect the SQUID This can happen if the shield has been dented has been in extended contact with magnetized tools such as screwdrivers has been rubbed by a magnet or even has been rubbed by ordinary steel or iron It is also possible for the shield to become magnetized during shipping since many shipping comp
154. t pattern of the binary counters 7 7 1 The 8 bit Flux Locked Loop An 8 bit Flux Locked Loop circuit which can be used with your Mr SQUID is shown in Figure 7 14 All unconnected pins on chips U4 and US pins 3 4 5 6 and 9 on U4 and pins 3 4 5 6 9 and 15 on U5 should remain unconnected on your circuit board The circuit will allow you to measure magnetic fluxes imposed on Mr SQUID down to about less than 0 01 o In the ideal case your Mr SQUID system can be used to measure fluxes as small as about 0 001 a limit set by the electronics in the control box This experiment falls somewhat short of limiting performance because the circuit illustrated was designed for simplicity rather than performance It can easily be built by students with little or no training in electronics The integrated circuits were chosen to be readily available In the illustrations that follow the integrated circuits are OPO07 operational amplifiers LM311 comparators 74LS169 4 bit up down counters AD7524 digital to analog converters and LM1458 dual op amps available from most electronics parts stores or electronic supply houses We suggest that you start by assembling the circuits on a solderless breadboard 4 This will allow you to make changes easily Circuit details for electronics buffs The first op amp U1 is configured as unity gain buffer to isolate the output of the 10 kQ potentiometer voltage divider R1 from the rest of the circuit In other w
155. t to determine how much they can change this resistor and what the trade offs are Third the digital flux locked loops clock frequency function generator can be increased to allow the counter and DAC to respond faster or slower Increasing the clock will allow the flux locked loop to respond the changing fluxes faster decreasing the clock will slow down its response This is analogous to changing C1 in Advanced Experiment 2 see Section 7 2 The bandwidth of the Mr SQUID electronics is about 2 8 kHz so increasing the clock speed past a certain point will not allow one to increase the ability of this circuit to cancel fluxes changing faster than this Other speed limitations may be encountered by hitting the limits of the digital chips used or the operational amplifiers used The counters U4 and US both of which were 74LS169 used in our implementation cannot go faster than 20 MHz so they will not be a limitation the DAC U6 which was an AD7524 cannot go faster than using a 1 to 2 MHz clock We would suggest that it be left to the student to see what the effects of varying the clock frequency has on the performance of the digital flux locked loop There are additional exercises for you to explore with your digital flux locked loop after the section describing the 12 bit digital flux locked loop You do not need to build the 12 bit version to do these additional exercises Most are illustrated with the 8 bit flux locked loop Advanc
156. ta This is why the small fraction of the earth s field that is not attenuated by the magnetic shield on the Mr SQUID probe is sufficient to shift the V curve by several flux quanta The previous comment is based on the fact that the output voltage of a SQUID is a periodic function of applied magnetic flux going through one complete cycle for every flux quantum applied While it would be possible to obtain quite a sensitive measure of a magnetic signal simply by counting flux quanta practical SQUID systems involve control electronics that interpolates between whole numbers of flux quanta and greatly enhances their ultimate sensitivity SQUID sensitivity is finally limited by the intrinsic noise in the device which in STAR Cryoelectronics LLC 31 Mr SQUID User s Guide 4 2 K niobium dc SQUIDs for example typically approaches a millionth of a flux quantum corresponding to a few billionths of the earth s field passing through a 100 um diameter SQUID The inherent periodicity of the SQUID implies that it cannot distinguish between zero applied field and any other field that generates an integral number of flux quanta This allows the dynamic range of the SQUID to be extended almost indefinitely by re zeroing the SQUID ina controlled way It also means that in order to measure the absolute value of an applied field it is necessary to reset the SQUID in a known field or to rotate the SQUID with respect to the field Nevertheless
157. te level SQUIDs brains and gravity waves John Clarke Physics Today March 1986 pp 36 44 Written just before the advent of the high T cuprate superconductors this is an accessible account of low 7 de SQUIDs and some of their applications Principles and applications of SQUIDs John Clarke Proc IEEE 77 pp 1208 1223 1989 A more comprehensive account of both low and high T SQUIDs The impact of high temperature superconductivity on SQUID magnetometers John Clarke and Roger H Koch Science 242 pp 217 223 1988 Discusses some early high Te SQUIDs and compares their performance with that of other kinds of magnetometers Advanced Topics DC SQUID Noise and optimization Claudia D Tesche and John Clarke Journal of Low Temperature Physics 29 pp 301 331 1977 This technical paper sets out the results of an extensive computer simulation of the operation of the de SQUID SQUID magnetometers for low frequency applications Tapani Ryh nen Heikki Seppa Risto Ilmoniemi and Jukka Knuutila Journal of Low Temperature Physics 76 pp 287 386 1989 A long review describing many kinds of SQUIDs and their applications Radio frequency SQUID operation using a ceramic high temperature superconductor M S Colclough C E Gough M Keene C M Muirhead N Thomas J S Abell and S Sutton Nature 328 47 48 1987 The first SQUID magnetometer made with a high T superconductor Nois
158. ter chip e One dual operational amplifier e g LM1458 e A 5 Volt power supply or batteries configured to provide 5 Volts and 5 Volts Additional parts needed for the 12 bit version e Three 4 bit binary up down counter chips e g 74xx169 such as a 74LS169 e One ADS563 12 bit digital to analog converter chip e One FET operational amplifier chips e g LF44 e Two 10 turn 10 kQ potentiometers e 12 light emitting diodes LEDs e A 5 volt power supply or batteries configured to provide 5 Volts and 5 Volts e A 15 Volt power supply Additional parts needed for the optional section e One Inverter chip e g DC4009 CD4049 or 74xx04 type A digital flux locked loop functions is a straightforward way The output of the SQUID signal is fed into a comparator configured to detect the zero crossings of the SQUID modulation voltage The output of the comparator is a 1 if the SQUID modulation voltage Vmoa is greater than zero and is a 0 if the SQUID modulation voltage is less than zero This output is fed into a binary up down counter What the counter does is to look at the output of the comparator 1 if Vinod 0 0 if Vinod lt 0 every digital clock cycle typically 100 s of kHz to a few MHz and count up if there is a 1 and count down if there is a 0 The output of the counter is fed into a digital to analog converter whose output is buffered to provide a bipolar output fed into the SQUID ex
159. ternal coil that opposed any externally applied flux So when the SQUID voltage increases a tiny bit because an external field is applied the comparator should output 1 s the counter should count up the DAC output increase the current through the external coil which opposes the external field increases canceling the external field When the SQUID voltage decreases a tiny bit because an external field is reduced the comparator should output 0 s the counter should count down the DAC output decrease the current through the external coil which opposes the external field decreases its canceling the external field One wishes the step size change in the least significant bit or LSB of the DAC into the SQUID s external coil to represent a shift in the V curve which is less than the noise of the SQUID otherwise one will introduce what is called a quantization error One does this by setting up the circuit to have a change in the LSB represent a current into the SQUID external coil and hence a change in flux AQ which is less than the fuzziness of the V curve in the horizontal axis One can read the 39Such as Radio Shack part number 276 044 40This part may be somewhat expensive 4lSuch as Radio Shack part number 276 044 STAR Cryoelectronics LLC 89 Mr SQUID User s Guide flux locked loop output in an analog fashion by monitoring the output voltage of the DAC or ina digital fashion by reading the bi
160. th the details of its operation you can use the Getting Started instructions for Advanced Users Section 4 These two versions cover the same material but are quite different in approach STAR Cryoelectronics LLC 9 Mr SQUID User s Guide 3 GETTING STARTED WITH MR SQUID NEW USERS The directions that follow assume that you have some familiarity with the basics of superconductivity including zero resistance flux quantization and the Josephson effect If not you may wish to read some of Section 5 An Introduction to Superconductivity and SQUIDs before going any further The Mr SQUID chip contains a de SQUID made with thin film YBCO superconductor The de SQUID is a simple circuit that can be schematically represented like this Figure 3 1 Schematic representation of a dc SQUID The dc SQUID is simply a ring of superconductor containing two Josephson junctions which are marked by the X s labeled J and Jz in the circuit diagram above The Josephson junctions can be thought of as weakened areas of the superconductor which nevertheless still allow a certain amount of resistanceless current to flow The simplest experiment to perform with this circuit is to pass current 7 from left to right across the ring and to measure the voltage V that appears across the ring If the two junctions in the SQUID are identical in the absence of any magnetic field the current will divide evenly and half of it will pass through each juncti
161. the 10 kQ resistor between TP3 and the Mr SQUID external coil Over what value range can you change this resistor and still have your loop work Why 2 Inverting the Most Significant Bit MSB In the schematic shown above for the digital flux locked loops one aspect which some may notice is that the counters and the DACs while both binary chips are not using the same binary number system For example in the 8 bit version the counters count from zero STAR Cryoelectronics LLC 100 Mr SQUID User s Guide 0000 0000 up to 255 1111 1111 If the counter is at zero and counts down once it will also be at 255 1111 1111 Similarly in the 12 bit version the counters count from zero 0000 0000 0000 up to 4096 1111 1111 1111 Ifthe counter is at zero and counts down once it will also be at 4096 1111 1111 1111 The 8 bit DAC on the other hand outputs 5 Volts when its inputs are at 0000 0000 and the 12 bit DAC outputs 3 Volts when its inputs are at 0000 0000 0000 Likewise the 8 bit DAC outputs 5 Volts when its inputs are at 1111 1111 and the 12 bit DAC outputs 3 Volts when its inputs are at 1111 1111 1111 The 8 bit DAC outputs 0 Volts when its inputs are at 1000 0000 and the 12 bit DAC outputs 0 Volts when its inputs are at 1000 0000 0000 The counters output 2 s compliment binary while the DAC interprets its inputs as offset binary For this optional part of the digital flux locked l
162. the critical current of the SQUID is periodic in the way you just saw the V I curve of a SQUID oscillates periodically between two extremes as shown in Figure 5 8 Figure 5 8 Periodic dependence of the SQUID voltage on applied flux STAR Cryoelectronics LLC 35 Mr SQUID User s Guide First look at the left plot in Figure 5 8 The rightmost V I curve is what you see when the applied magnetic flux is a multiple of one flux quantum The V I curve on the left is what you see when the applied magnetic flux is a multiple of one flux quantum plus one half As you increase the magnetic flux continuously from zero the SQUID V I curve oscillates continuously between these two extremes with a period of one flux quantum You will see this oscillation on your oscilloscope when you experiment with Mr SQUID To make a magnetometer or magnetic field detector we operate the SQUID with a constant bias current slightly greater than the critical current so the SQUID is always resistive Under these conditions there is a periodic relationship between the voltage across the SQUID and the applied magnetic flux with a period of one flux quantum Note that at fixed bias current the voltage across the SQUID is a maximum when the critical current is a minimum and vice versa The relationship between the input flux and the output voltage across the SQUID looks like the right side of the diagram on the previous page This is the phenomenon scientists an
163. til the diode voltage at each point is stable before recording the temperature it will be very inaccurate Trouble avoidance tip Don t let the wires from the silicon diode extend far below the Mr SQUID magnetic shield If they do they might dip into the liquid nitrogen before the probe end does If this happens the thermal conductivity of the copper wires can cause the diode to indicate a temperature as much as 10 15 K lower than the Mr SQUID chip This is something to watch for particularly when below 120 K The following data was taken using a glass encapsulated switching diode as the diode sensor Data can be taken all the way down from room temperature but in Figure 7 4 we only show the region around the transition temperature of the YBCO film which will generally be near 90 K Resistance Q 75 85 95 105 Temperature K Figure 7 4 Resistance vs temperature data for a Mr SQUID probe STAR Cryoelectronics LLC 59 Mr SQUID User s Guide This concludes the instructions for the R vs T experiment for Mr SQUID The following optional help section will tell you how to build a simple dc constant current source suitable for use in this experiment and some of the other advanced experiments and also will explain the physics behind the operation of diode temperature sensors 7 1 3 Building a simple constant current supply A simple constant current supply can be build using a zener diode two resistors on
164. tion to the Theory of Error by Yardley Beers Addison Wesley Menlo Park California 1962 ISBN 0 201 00470 4 and An Introduction to Error Analysis by John R Taylor University Science Books Mill Valley California 1982 ISBN 0 935702 10 5 STAR Cryoelectronics LLC 75 Mr SQUID User s Guide Then 4 52x10 Hz oona 1 58x10 3 Hz V LOX Eqn 7 19 6 V which means we really have about a 6 uncertainty in our measurement So our value for e h is 2 44 0 16 x10 Hz V as compared to the official value of 2 4179671x10 Hz V One can increase the accuracy of this measurement by cooling the SQUID to reduce the thermal rounding of the steps by stabilizing the microwave source so that its frequency does not fluctuate and shielding the SQUID from RF interferences other than the microwave source which can also cause rounding of the steps By doing all these things the ratio of value for e h has been determined to a large number of decimal places Since ultra stable frequency sources are relatively easy to build e g atomic clocks the U S National Institute of Standards NIST uses such time references along with the ac Josephson Effect to set the standard for the official value of the volt 2 W H Parker B N Taykor and D N Langenburg Phys Rev Letters 18 287 1967 STAR Cryoelectronics LLC 76 Mr SQUID User s Guide 7 5 Inductive Measurement of the Superc
165. tions despite the large impedance mismatch between the junctions and free space Equipment For this experiment you will need e Mr SQUID and liquid nitrogen e An oscilloscope or x y recorder preferably both e A microwave source of known frequency capable of operating somewhere between 1 GHz 10 GHz If you are using an x band microwave unit with a horn antenna e A Styrofoam container large enough to use in place of the Mr SQUID dewar STAR Cryoelectronics LLC 71 Mr SQUID User s Guide Illustrated below is a procedure to couple microwaves MW from a generator into the Mr SQUID dewar For the illustration that follows we used an HP8616A function generator that can produce microwaves with frequencies in the range of 1 6 GHz to 4 5 GHz Any microwave source that you can couple into the Mr SQUID dewar should work including the x band microwave units with horn antennas found in many undergraduate labs A co axial cable is connected to the generator The other end of the co axial cable is devoid of a connector Instead approximately 2 3 cm of the coax cable s shield was removed to expose a 2 3 cm length of the center conductor which acts as an antennae If you do not have access to a microwave function generator a microwave generator with a horn antennae may be used and pointed down into the dewar Due to possible resonances and spurious microwave modes developing inside your Mr SQUID dewar at specific frequ
166. to have 10 to 20 turns be as small as possible and leave about 50 cm of wire on each side free to be used as electrical leads Record in your lab notebook the number of turns the diameter and height of your coil You can hold the wire in place by coating the coil with a thin coating of polystyrene cement After the cement has dried carefully cut off the toothpick where it protrudes from the coil Next carefully solder magnet wire leads each at least 50 cm long to the 100 Q chip resistor Check the continuity of the resistor through its leads Trim the leads to the diode to be as short as possible and then carefully solder on leads each at least 50 cm long Be careful not to overheat the diode with the soldering iron After the leads are attached to the diode check the diode with an ohmmeter to verify continuity through its leads and that it still acts as a rectifier Take the diode and your current source and perform the calibration as described in Section 7 1 3 Next using the polystyrene cement attach the diode and chip resistor to the HTS coated sapphire chip on the side opposite the film Attach the coil with its longitudinal axis perpendicular to the plane of the sapphire substrate to the HTS coated sapphire chip on the side opposite the film An illustration is shown below BACK side of Chip Resistor Sapphire HTS film is on opposite side Diode Coil STAR Cryoelectronics LLC 78 Mr SQUID User s Guide
167. to a distance such that you have suppressed the critical current of the Mr SQUID STEP 3 Once you have suppressed the critical current move the microwave unit away until part one half to one third of the original supercurrent has returned STEP 4 Ideally you will have a nice set of Shapiro steps in your V curve If no steps are visible you will need to play with the relative positioning of your Mr SQUID unit and the microwave unit You may need to have the microwave beam graze the Mr SQUID unit or be aimed at the probe stick rather than directly at the SQUID chip Getting the microwaves to couple properly can be somewhat of a black art 7 4 3 Determining e h To determine the value of e h we need to measure the voltages at which the steps occur This can usually be done to greater accuracy by having the V I curve traced on an x y recorder rather than on an oscilloscope From the trace shown above we would place the steps at 9 25 uV and at 9 25 uV NOTE The vertical scale on the scope display is 50 mV per major division which STAR Cryoelectronics LLC 74 Mr SQUID User s Guide with the 10 gain of the Mr SQUID electronics box means the scale of the display is really 5 uV per major division Since h h Eqn 7 14 Vee 4re 2e then v Eqn 7 15 alee h 2V As can be seen by comparing the oscilloscope trace immediately above with the Shapiro step illustration earlier our steps
168. tor Connection to output of FLL U2a TP2 Mr SQUID Vv External Coil Figure 7 11 Circuit as seen from point B The voltage at Test Point 2 can be related to that at point B according to V 1350 R Equation 7 1 V Bl coit coil STAR Cryoelectronics LLC 68 Mr SQUID User s Guide From the value of V2 and using the equation above calculate the voltage at point B Vz in the equation above Compare this with the value for Vg you would expect from the equations above governing the double divider See what changes you can make to the flux locked loop circuit to increase the sensitivity of your Mr SQUID voltmeter Note that you can create a larger voltage at Test Point 2 for a given voltage at point B by substituting a larger resistor for the 1350 Q resistor If you do this what other change to the flux locked loop circuit must you make How sensitive can you make this de voltmeter 7 3 2 Building an ac voltmeter For this experiment a low frequency sine wave generator is required STEP 1 If you have not already done so build the dc voltmeter described above STEP 2 On your voltage source change Rser to the lowest value on the resistor decade box STEP 3 Disconnect the 9 Volt battery from the double divider and connect the sine wave generator Be sure the sine wave generator is off STEP 4 Using an ac voltmeter measure the voltage at Test Point 2 of the flux locked loop circu
169. trogen which should last for several hours There are hazards associated with the use of liquid nitrogen and with vacuum vessels used to contain it STAR Cryoelectronics LLC 5 Mr SQUID User s Guide DIRECT SKIN EXPOSURE TO LIQUID NITROGEN CAN CAUSE SEVERE BURNS Personnel experienced in the use of cryogenic liquids should be on hand for all experiments involving the use of liquid nitrogen and appropriate cautions must be taken A special caution when removing the Mr SQUID probe from the nitrogen dewar be careful not to handle the cold end until it warms up completely the frost will disappear when it has warmed completely 2 2 Assembling the Mr SQUID System In this section we explain how to assemble the various parts of Mr SQUID The set up instructions refer to the various controls and connectors on the Mr SQUID electronics box with the numbers shown in Figure 2 2 below STEP 1 Battery check The first step is to check the batteries by pressing the power switch 9 downward to the BATT CHK position Ifthe batteries are functional the red LED 8 will light otherwise you should open the battery compartment through the underside of the electronics box and replace the batteries with two 9 Volt batteries To maximize the lifetime of the batteries make sure the power switch is in the OFF position any time that Mr SQUID is not in use FLUX CURRENT BIAS BIAS AMPLITUDE OUTPUTS 0000 osc
170. ts include biomedical imaging non destructive testing of materials geophysical exploration and laboratory instrumentation STAR Cryoelectronics manufactures and offers Mr SQUID under license from Conductus Inc The cryogenic sensors from STAR Cryoelectronics are based on superconductors and typically operate in liquid nitrogen or in liquid helium The basic sensor element is a Superconducting Quantum Interference Device SQUID which is the most sensitive detector of magnetic flux known Aside from precision measurements of minute magnetic fields or field gradients a SQUID may be used to measure any physical quantity that can be converted to a magnetic field such as electrical currents or voltages magnetic susceptibility physical displacement etc In addition to the extensive sensor product line STAR Cryoelectronics also offers a line of advanced PC based sensor control electronics sold under the trade name pcSQUID The state of the art control electronics are easy to use and offer the user unsurpassed flexibility and performance STAR Cryoelectronics pcSQUID and Mr SQUID products are CE certified STAR Cryoelectronics staff and contract consultants include four members of the former Conductus SQUID Technology Group Production sales and customer service are handled through the company s headquarters in Santa Fe NM The company s commercial facilities include about 4 000 square feet of space for research and design devel
171. tum interference between two Josephson tunnel junctions was first reported by Jaklevic Lambe Silver and Mercereau in early 1964 roughly a year after the first observation of STAR Cryoelectronics LLC 42 Mr SQUID User s Guide Josephson tunneling by Anderson and Rowell In both of these experiments the authors used tunnel junctions consisting of two thin superconducting films separated by an oxide layer roughly 20 A thick However at the time tunnel junctions were difficult to make reproducibly and usually did not cycle reliably between room temperature and liquid helium temperatures For this reason virtually all the device development over the ensuing decade involved devices made from bulk superconductors rather than thin films Much progress was made with SQUIDs involving point contact junctions consisting of sharpened niobium screws often adjustable from the top of the cryostat pressed against a block of niobium Another device the SLUG Superconducting Low inductance Undulating Galvanometer consisted of a bead of tin lead solder frozen around a length of niobium wire Supercurrents flowed between the solder and the wire at a few discrete points only and the critical current of the device was modulated by a current passed along the wire A major change occurred in the late 1960 s however with the advent of the rf SQUID a closed superconducting loop interrupted by a single Josephson junction The rf SQUID is inductively cou
172. twelve 12 months from date of original shipment to the customer Any part found to be defective in material or workmanship during the warranty period will be repaired or replaced without charge to the owner Prior to returning the instrument for repair authorization must be obtained from STAR Cryoelectronics or an authorized STAR Cryoelectronics service agent All repairs will be warranted for only the unexpired portion of the original warranty plus the time between receipt of the instrument at STAR Cryoelectronics and its return to the owner This warranty is limited to STAR Cryoelectronics products that are purchased directly from STAR Cryoelectronics its OEM suppliers or its authorized sales representatives It does not apply to damage caused by accident misuse fire flood or acts of God or from failure to properly install operate or maintain the product in accordance with the printed instructions provided This warranty is in lieu of any other warranties expressed or implied including merchantability or fitness for purpose which are expressly excluded The owner agrees that STAR Cryoelectronics liability with respect to this product shall be as set forth in this warranty and incidental or consequential damages are expressly excluded SAFETY PRECAUTIONS Do remove product covers or panels except for modifications as specified in this manual Do not operate without all covers and panels in place Do not attempt to repair
173. ulate Bz for your SQUID at this point using techniques outlined in Section 3 A form for recording this and other data is provided in that section as well A variety of other experiments designed around the Mr SQUID system including those that use the external coil are discussed in Section 7 Advanced Experiments STAR Cryoelectronics LLC 26 Mr SQUID User s Guide 5 AN INTRODUCTION TO SUPERCONDUCTIVITY AND SQUIDS 5 1 A Capsule History of Superconductivity Superconductivity was first discovered in 1911 in a sample of mercury metal that lost its resistance just four degrees above absolute zero The phenomenon of superconductivity has been the subject of both scientific research and application development ever since The ability to perform experiments at temperatures close to absolute zero was rare in the first half of this century and superconductivity research proceeded in relatively few laboratories The first experiments only revealed the zero resistance property of superconductors and more than twenty years passed before the ability of superconductors to expel magnetic flux the Meissner Effect was first observed Magnetic flux quantization the key to SQUID operation was predicted theoretically only in 1950 and was finally observed in 1961 The Josephson effects were predicted and experimentally verified a few years after that SQUIDs were first studied in the mid 1960 s soon after the first Josephson junctions were
174. unction rather than radiate away into free space The ac Josephson Effect is usually observed by placing the dc voltage biased junction in an applied oscillating electric field In this case V V t which alters the ac Josephson Effect equation to Eqn 7 11 Ta sin 30 ee 0 If V t Vo Va cos at then Eqn 7 12 MOST isO ae E Jino 0 Given that sin X sin q bA J X sin ng where J is the nth order Bessel function of the first n 0o kind the current density becomes STAR Cryoelectronics LLC 70 Mr SQUID User s Guide ca K 4neV _ 4teV Eqn 7 13 J J gt C1 1 a Js 50 7 J n 0o a which indicates that when V nha 4me with n an integer there will be a discontinuous shift in the de current with no change in the dc voltage across the junction If one is sweeping out a V I curve while applying an ac electric field to the Josephson junction one will see a curve similar to the one that appears below Such constant voltage steps i e discontinuous shift in the dc current in the V I curve are called Shapiro steps V 0 There are a number of ways to impress an ac voltage on Josephson junctions The easiest way is to simply send microwaves v gt 1 GHz into the cryogenic container holding the Josephson junction Due to the high sensitivity of the Josephson junctions even at very modest rf power levels a significant amount of radiation will couple into the junc
175. vice If what you see looks like a straight line as in Figure 3 4 below then either you don t have enough liquid nitrogen in the dewar you have not let the probe get cold or there may be trapped magnetic flux in the SQUID The latter is a very common occurrence because the SQUID is very sensitive to external magnetic fields Refer to the discussion on trapped flux in Section 6 3 Magnetic Flux Trapping in SQUIDs if this appears to be the problem Assuming you see the proper curve how can we understand its shape STAR Cryoelectronics LLC 12 Mr SQUID User s Guide Figure 3 4 A linear V I characteristic What you are looking at is the V Z characteristic of two Josephson junctions connected in parallel with one another Assuming they are identical junctions in practice they are at least very similar the V Z characteristic you see is the same as for a single junction The most important feature of the curve is the flat spot in the middle called the critical current In this region there is current flowing with no voltage it is a supercurrent This is the de Josephson effect a resistanceless current that flows through a superconductor Josephson junction A Josephson junction consists of two regions of superconductor that are weakly coupled together The meaning of this statement is that the junction behaves like a superconductor but can only carry a small amount of resistanceless current before it becomes resistive Any supercon
176. ways replace both batteries at the same time STAR Cryoelectronics LLC 47 Mr SQUID User s Guide V I curve has slight hysteresis 1 Check that x and y axis inputs on scope are dc coupled 2 If scope has adjustable filters increase the bandwidth 3 Decrease amplitude of the Mr SQUID box V I curve is linear 1 Check continuity and connection of both x and y cables 2 If slope of V I curve is less than 1 Q see Sec 6 3 on flux trapping and Sec 6 5 on rf interference 3 If slope of the V I curve is less than 1 Q try rotating and moving the dewar 4 If slope of V I curve is greater than about 1 Q and less than about 400 Q check liquid nitrogen level 6 2 Problems in V Mode Assuming Everything Works in V I Mode Output signal is Horizontal line 1 Check scale settings on scope or x y recorder 2 Check that y axis input on scope is ac coupled dc coupled and offset if using an x y recorder or if the ac roll on on your scope is at a high frequency 3 Check for magnetized shield see Sec 6 4 4 Check for rf interference 5 OK Call STAR Cryoelectronics STAR Cryoelectronics LLC 48 Mr SQUID User s Guide V curve has slight hysteresis 1 Check that x axis input on scope is dc coupled 2 If scope has adjustable filters increase the bandwidth 3 Decrease amplitude of the Mr SQUID box 6 3 Magnetic Flux Trapping in SQUIDs By far the most
177. wound so as to be sensitive not to the magnetic field itself but to the gradient of the field in a chosen direction or to a higher derivative of the field In these cases the flux transformer is referred to as a gradiometer Since the gradient of the magnetic field falls off more rapidly with distance from the magnetic source than the field itself a gradiometer tends to reject magnetic interference from distant sources while remaining sensitive to closer objects Again a gradiometer is basically sensitive to changes in the field gradient rather than its absolute value and the technique of controlled resetting can be applied to give a large dynamic range The coils in Mr SQUID are not made of superconducting material so that one cannot couple a superconducting flux transformer to it This limitation comes from economics and simplicity of operation for the Mr SQUID product As a result external static flux cannot be coupled directly to Mr SQUID though an external pickup loop Magnetic Signal Levels 10 4 lt Earth s magnetic field 10 5 10 6 lt Traffic appliances etc 1077 107 8 ag Power transmission lines at 10 m v z z 10 R 49 10 lt Human heart signals Limit of non SQUID ee ee ee ee P technology 107 lt Optic nerve signals 1 Hz bandwidth 107 12 ep Muscle impulses spontaneous brain activity 10718 ag Evoked brain signals 107 14 lt Niobium SQUID limits 10715 Figure 5 10 Magnetic fiel
178. x axis Try turning up the function generator frequency This usually means you would be properly locked except you are clocked too slowly for the flux 5 Even in this day of instant on solid state circuits some components do need time to thermally stabilize STAR Cryoelectronics LLC 106 Mr SQUID User s Guide locked loop to catch up with the swept magnetic field Try turning up the function generator frequency used to provide the TTL clock input to the counters Typically 10 kHz is reasonable for the 8 bit version and 200 kHz is reasonable for the 12 bit version TP3 shows multiple straight line traces similar to Figure 7 15 TP3 or Figure 7 18 TP3 except the traces on the scope display jump the above scope photo is a multiple exposure so it shows several sweeps of the x axis This usually means you would be properly locked except you are exceeding the dynamic range of your flux locked loop This is flux jumping due to outside noise or the AMPLITUDE on the Mr SQUID box is too large Try turning down the AMPLITUDE knob on the Mr SQUID unit It that does not work try moving your Mr SQUID to a different location in the room or building STAR Cryoelectronics LLC 107 Mr SQUID User s Guide 8 ABOUT STAR CRYOELECTRONICS STAR Cryoelectronics is engaged in the business of producing and marketing advanced sensors based on superconductors and related sensor control electronics Application areas for STAR produc

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