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Instrumentation Project Final Report

1. y 8 101E 05x 1 504E 03 MagField gauss R 9 969E 01 y 8 555E 05x 1 276E 03 0 908 R 9 986E 01 0 007 0 006 3 0 005 Up S 0 004 a Dona Linear Up 2 0 003 Linear Down 0 002 0 001 0 0 10 20 30 40 50 60 70 Mag Field gauss Figure 16 50707 Temp 150C Temp Up Cell 120A y 3 114E 05x 3 290E 04 Rotation Vs Mag Field a a R 9 991E 01 y 2 753E 05x 5 477E 04 bng R 9 941E 01 0 0025 G 0 002 x Up P Down 0 0015 E Linear Up 2 0 001 Linear Down 0 0005 0 Figure 17 50707 Temp 160C Temp Up Cell 120A 18 y 1 879E 04x 1 414 E 03 Rotation Vs Mag Field R 9 963E 01 y 1 621E 04x 2 959E 03 TUE 9 912E 01 0 014 0 012 8 0 01 Up 5 0 008 BAN o Linear Up 2 0 006 Linear Down 0 004 0 002 0 70 Mag Field gauss Figure 18 50707 Temp 170C Temp Up Cell 120A y 2 557E 04x 1 464E 03 R ion Vs Mag Field etalon ve mag R 9 944E 01 y 2 531E 04x 1 736E 03 0 02 9 981E 01 0 018 0 016 s 0 014 0 012 Up 5 001 Down 5 a B Linear Up 2 Linear Down 0 006 0 004 0 002 0 0 10 20 30 40 50 60 70 Mag Field gauss Figure 19 50707 Temp 180C Temp Up Cell 120A 19 y 3 876E 04x 1 140E 03 Rotation Vs Mag Field R 9 992E 01 0 03 y 3 785E 04x 1 699E 03 9 99
2. 27 578 587 1926 8 B Chann E Babcock L W Anderson T G Walker Measurements of He spin exchange rates Physical Review A 66 032703 2002 41
3. Down 0 006 0 004 0 002 Mag Field gauss Figure 29 51107 Temp 180C Temp Down Cell 120B 24 Rotation Vs Mag Field du debe E R 9 993E 01 y 1 868E 04x 3 213E 03 mia R 9 980E 01 0 016 0 014 r1 0 012 Up T 0 01 Down g 0 008 Linear Up 2 0 006 Linear Down 0 004 0 002 0 0 10 20 30 40 50 60 70 Mag Field gauss Figure 30 51107 Temp 170C Temp Down Cell 120B Rotation Vs Mag Field dabo aug PLE R 9 995E 01 y 1 078E 04x 3 947E 03 0 012 R 9 995E 01 0 01 H 0 008 sp 5 0 006 DON Linear Up o M H 0 004 Linear Down 0 002 0 0 10 20 30 40 50 60 70 Mag Field gauss Figure 31 51107 Temp 160C Temp Down Cell 120B 25 Rotation rad 0 009 0 008 0 007 0 006 0 005 0 004 0 003 0 002 0 001 y 7 067E 05x 3 643E 03 R 9 977E 01 y 7 025E 05x 3 640E 03 R 9 993E 01 Rotation Vs Mag Field Up Down Linear Up Linear Down Mag Field gauss Figure 32 51107 Temp 150C Temp Down Cell 120B Rotation rad 0 005 0 0045 0 004 0 0035 0 003 0 0025 0 002 0 0015 0 001 0 0005 y 6 869E 05x 3 613E 06 R 9 904E 01 y 6 838E 05x 2 136E 05 R 9 997E 01 Rotation Vs Mag Field Up Down Linear Up Linear Down Mag Field gauss Figure 33 51407 Temp 150C Temp Up Cell 120C 26 y
4. all the laser light was vertically polarized After the series of measurements was taken for this report the polarizer was removed Taking additional measurements showed that the error introduced by not having the polarizer in the setup was small compared to the error from the laser detuning In fact most of the error comes from laser instability Laser instability is particularly noticeable when making the summed photo detector measurement The voltage would change by about 1096 very erratically This can be fixed by ensuring the photo detectors are properly aligned by adjusting the current on the laser power supply and by adjusting the top knob on the ECDL shown in figure 3 To keep from damaging the polarizer used in the set up a relatively modest laser current of about 38 7 mA was used It might be advantageous to increase the laser power especially in the case of cell 120B where so much of the light was absorbed IV CONCLUSION Rubidium vapor density measurements were successfully made using the photoelastic modulator and lock in amplifier The strong linearity of rotation as a function of magnetic field especially for cell 120C indicate that the employment of the PEM and lock in amplifier have significantly increased the sensitivity and reduced the error when compared to the previous setup When compared to the Killian curve the measured Rb vapor densities tend to follow the general form of the curve with increasing deviation for hig
5. elliptically polarized with the semimajor axis oscillating sinusoidally between 45 If the oven and cell were removed from the system then the light would propagate without being rotated through the half waveplate and into the polarizing beam splitting cube p b c The p b c then separates the vertical and horizontal polarization components sending them into photodetector B PDB and photodetector A PDA respectively In the case where there is no rotation e g the oven and cell are not present and the half waveplate is properly oriented the difference of PDA and PDB is egual to zero This can be seen by inspection in Figure 14 that when a 45 and 0 0 then there are equal E field components in the X and Y directions However with the magnetic field turned on and the Rb cell and oven in place the Rb vapor causes the polarization of the light to rotate according to eguation 3 It is important to note that this rotation does not change the angle 0 rather the whole reference frame is rotated by 0 This is shown in Figure 14 14 ADS KY Figure 14 Ellipse rotation diagram illustrating the effect of rotation When 0 0 there are equal components of the E field in the X and Y directions However when 0 0 then the E field seen in the X and Y directions oscillates at the PEM frequency The PEM causes the polarization to morph from an ellipse with some maximum eccentricity with the major axis at 45 into a circle and
6. fast or slow axis that is perpendicular to the post to be lengthened while not affecting the other axis that is inline with the post If the fluctuations only get worse try rotating the quarter waveplate by 90 so the fast and slow axis have swapped positions and repeat the above procedure 8 Continue to make slight adjustments to the rotation of the quarter waveplate about the laser beam and about the mounting post until the fluctuations of the signals as a function of half waveplate being rotated have been minimized The system is now adjusted to produce the best circular polarized light Most of the remaining signal fluctuation is due to error in the half waveplate 2 Using the PEM Introduce the PEM into the system immediately after the quarter waveplate The PEM causes the laser beam to be shifted vertically by about I cm Therefore readjustment of the downstream optics is necessary 2HINDS may 632 8 mn Fa RTD 8 25 a c al Hode Salact User Presets Sys Confis TLLLLLLLL ILLI L vocal Control Mode Hz i WB ssl Figure 47 The PEM driver electrical head and the optical head Operation of the PEM 1 Warning do not turn on the PEM unless the optical head and the electrical head are connect with the interconnect cable Serious damage may result 2 Turn the power on with the power button located on the front bottom left corner of the PEM controller EN The wavelength adjustment WAV is automatically
7. line to vary slightly The laser was believed to be more stable while measuring cell 120C which showed no sign of hysteresis It has been determined through error analysis that for most of the measurements in this report the error is dominated by frequency shifting and not slope variations However the contributions to error from the frequency detuning and the slope variations are both included in the error bars on the final Rb plots Further tests are required to verify that there indeed was no hysteresis in cells 120A and 120B A comparison of the measured Rb vapor density and the Killian curve was made for each of the cells These are shown in the following three figures Each temperature has four data points The four data points correspond to ramping the magnetic field up ramping the magnetic field down ramping the temperature up and ramping the temperature down Rb Vapor Density Vs Temperature Cell 120A 1 2E 15 1E 15 Killian Curve 8E 14 e Temp Up Mag Field Up E 6E 14 m Temp Up Mag Field Down 4 gt Temp Down Mag Field Up K 4E 14 Temp Down Mag Field Down 2E 14 0 T T T 130 150 170 190 210 Temp C Figure 42 50707 Rb Vapor Density Cell 120A 31 Rb Vapor Density Vs Temperature Cell 120B 1 2E 15 4 1E415 Killian Curve 5 8E 14
8. shown in Figure 1 Probe Beam Optics Magnetic Coil and Detection Optics Oven Assembly Figure 1 Setup of the entire instrument A Probe Beam Optics The probe beam optics consists of a temperature controlled extended cavity diode laser ECDL glass plate Ocean Optics spectrometer quarter waveplate and a photoelastic modulator as shown in Figure 2 Ocean Optics Quarter Spectrometer Waveplate Detector Photoelastic Modulator PEM Laser og i Glass Pickoff ff Plate i Na NG Figure 2 Optical components on the probe beam optics table The ECDL and the temperature controller was built by Ryan May The front and top views of the laser are shown in Figures 3 and 4 post adapter mirror mount front plate modified grating mount attachment Screws mirror mount front plate mounting plate diffraction grating Sp acers A d d e d post adapter modified base block mirror mount for fixed direction PZT stack optional output beam optional mirror mount body Figure 3 Front View ECDL modified from 2 Figure 4 Top View ECDL 2 The extended cavity is composed of a diffraction grating and a mirror The details of the grating eguation and how the ECDL works is covered in Ryans report and will not be covered here However it is important to note that the ECDL accomplishes two things first it narrows the line width to about 0 1nm and second it provides a mechanism to adjust
9. the dynamic polarization state of the light as it enters the magnetic coil and oven assembly a 5 oy a an P y a i a Mu X Kat 2E E cos E an Eq 5 1 a 2 2 E B E Figure 8 Orientation of semimajor axis Refer to Equation 5 5 B Magnetic Coil and Oven Assembly The coil assembly consists of three sets of coils the main field coils and a horizontal and vertical set of shim coils as shown in Figure 9 Vertical Shim Coils Horizontal Shim Coils 3 Main Field Coils Selector Switch Figure 9 The 3D magnetic field coil assembly gives precision control over the field conditions inside the oven 10 The main coils are rigidly supported by brackets as shown in Figure 9 The shim coils are nested inside of each other while maintaining the Helmholtz coil configuration Each smaller set of coils is rigidly fastened to the directly bigger set of coils using interconnecting brackets Therefore in this configuration all three sets of coils are all fastened together into one integral unit The shim coils are used to shim out the Earth s magnetic field They are positioned vertically and horizontally to compensate for both the vertical and horizontal components of the Earth s field The instrument is set up with the main field oriented in an east west direction There is essentially no component of the Earth s field in this direction Therefore in theory zero magnetic field is
10. then back into an ellipse with the major axis at 45 This is still the case after the polarization has been rotated except that now the major axis is rotated at 45 relative to the X axis This results in a oscillating signal seen by the two photo detectors that are still in the initial X Y reference plane The oscillating signal from PDA and PDB is sent to the lock in amplifier The lock in takes the difference of the two signals and multiplies it with the reference signal from the PEM driver This results in a DC signal with an extremely high signal to noise ratio that corresponds to the polarization rotation induced by the cell It can be shown that the relation between the output of the lock in and 0 is given by equation 6 6 Vfr VV uc Ji 2 RENI sin eq 6 15 Where Vfr is the output from the lock in amplifier p is the depth of retardation in radians and Vpc is the summed output from the two photo detectors The validity of equation 6 was verified by changing p which resulted in no change in 0 Because the Bessel function is nonlinear this is fairly conclusive evidence that this is an accurate relationship between 0 and Vfr After solving equation 3 for Rb it takes the form shown in equation 7 with the ratio of rotation versus magnetic field This ratio was obtained by measuring the slope of the line from a plot of 0 versus B k oA 180 mh ng gb m 445 4 x ET A dC IV DATA AND RESULTS
11. 1 070E 04x 4 286E 05 Rotation Vs Mag Field R 9 998E 01 y 1 068E 04x 5 316E 05 bag R 9 997E 01 0 007 0 006 3 0 005 Up E aia Down Linear Up 2 0 003 Linear Down 0 002 0 001 0 0 10 20 30 40 50 60 70 Mag Field gauss Figure 34 51407 Temp 160C Temp Up Cell 120C y 1 609E 04x 9 284E 05 Rotation Vs Mag Field g R 9 999E 01 y 1 607E 04x 1 342E 04 0 012 2 9 999E 01 0 01 3 0 008 Up 5 0 006 Dom 5 Linear Up e 0 004 Linear Down 0 002 0 Mag Field gauss Figure 35 51407 Temp 170C Temp Up Cell 120C 27 y 2425E 04x 2 160E 04 Rotation Vs Mag Field o R 9 998E 01 y 2423E 04x 1 959E 04 0 018 2 9 999E 01 0 016 0 014 E 0 012 lt Up 3 0 01 u Dowh 3 0 008 Linear Up Z 0 006 Linear Down 0 004 0 002 0 0 10 20 30 40 50 60 70 Mag Field gauss Figure 36 51407 Temp 180C Temp Up Cell 120C p y 3 547E 04x 5 002E 04 Rotation Vs Mag Field g R 9 999E 01 TT y 3 541E 04x 5 642E 04 R 9 993E 01 0 02 Ss S 0015 Up 5 Down G Linear Up 2 i Linear Down 0 005 0 Mag Field gauss Figure 37 51407 Temp 190C Temp Up Cell 120C 28 o Rotation Vs Mag Field Wr SUR R 9 998E 01 y 2 391E 04x 3 385E 04 0 018 R 9 999E 01 0 016 0 014 0 012 3 e U
12. 2E 01 0 025 E 0 02 Up 5 0015 p Linear Up 2 0 01 Linear Down 0 005 0 70 Mag Field gauss Figure 20 50707 Temp 190C Temp Up Cell 120A Rotation Vs Mag Field YF sede R 9 992E 01 y 2 590E 04x 2 069E 03 pis R 9 996E 01 0 018 0 016 _ 0014 8 0012 Up 5 001 TU Linear Up 2 0 008 Linear Down 0 006 0 004 0 002 Mag Field gauss Figure 21 50707 Temp 180C Temp Down Cell 120A 20 Rotation Vs Mag Field qeu ee R 9 991E 01 y 1 732E 04x 2 027E 03 bana R 9 991E 01 0 012 _ 001 E Up 0 008 Down o a ows Linear Up 2 Linear Down 0 004 0 002 0 0 10 20 30 40 50 60 70 Mag Field gauss Figure 22 50707 Temp 170C Temp Down Cell 120A Rotation Vs Mag Field a a ana R 9 979E 01 y 1 171E 04x 1 753E 03 0 01 R 9 993E 01 0 009 0 008 _ 0 007 S 0 006 Up 5 0005 pagi G Linear Up 2 0 004 Linear Down 0 003 0 002 0 001 0 0 10 20 30 40 50 60 70 Mag Field gauss Figure 23 50707 Temp 160C Temp Down Cell 120A 21 0 10 20 30 40 50 60 70 Rotation Vs Mag Field PDE dE UM R 9 893E 01 y 7 868E 05x 4 427E 03 R 9 935E 01 0 009 0 008 _ 0 007 S 0 006 Up D 5 0 005 ai o Linear Up 2 0 004 Linear Down 0 003 0 002 0 001 0 0 10 20 30 40 50 60 70 Mag Field gauss Figure 24 51107 Temp 150C Tem
13. As mentioned previously the goals of this project were to measure the Rb vapor density compare cell to cell variations compare the Rb vapor densities against the Killian curve and to check for long term changes These measurements were made on the same three cells used by Ryan These cells are listed in table 2 The lengths of the cells used in these measurements were slightly different than those used by Ryan The overall lengths of the cells were measured with a digital caliper The length of the inside of each cell was then estimated by subtracting off 1 8 for the thickness of each end cap Cell Name Gas Pressure mbar Length cm 120A He No Rb 120B He N Rb 1200 PXeFN Rb Table 2 Rb cells Used for Making Measurements The measurements were made by entering both the voltage across the main field resistor and the voltage from the lock in amplifier into an excel spreadsheet Excel calculated the magnetic field strength by plugging this voltage into the main field slope equation in Figure 10 Excel then calculated the rotation by plugging the lock in voltage 16 into equation 6 Rotation was plotted against magnetic field and the slope was plugged into equation 7 resulting in a rubidium vapor density for a given temperature To check for hysteresis due to both B field and temperature fluctuations the field was ramped up and down at each temperature and the temperature was ramped up and down for each cell T
14. Instrumentation Project Final Report Curtiss Melder University of Utah Dated May 11 2007 I INTRODUCTION The instrument built for this project is used to measure rubidium vapor density in glass cells The research group run by Brian Saam is actively researching the properties of hyperpolarized noble gasses The process used by the group to produce the hyperpolarized gas is known as spin exchange optical pumping SEOP Rb vapor is part of the SEOP process and knowing the correct Rb vapor density is a crucial component in producing high percentages of hyperpolarized noble gasses This project is a continuation of a project started by Ryan May while working for Brian Saam in 2006 The fundamental principle upon which Rb vapor density is measured is Faraday rotation The amount of rotation of the polarized light is a function of the rubidium vapor density Therefore the vapor density can be measured by measuring the polarization rotation angle induced by the rubidium cell For magnetic fields ranging from 10 60 gauss typical rotation angles are 6 14 mrad The previous instrument relied on a rotation stage with resolution of 0 6 mrad to make these measurements As Ryan demonstrated this method works however it also attests to the skill involved in making the difficult measurement Killian empirically determined a formula that describes the saturated vapor pressure of Rb as a function of temperature 7 However many groups have measured th
15. and two photodiode detectors The half waveplate is used to rotate the polarization of the laser beam This can be used to zero the system before taking a measurement The polarizing beam splitting cube pbc reflects the vertical polarization and transmits the horizontal polarization The photodiode detectors can then be used to individually analyze the vertical and horizontal polarization states Previously there was a lens positioned before the half waveplate that was used to focus the beam onto the photodiode detectors However it was discovered that because of inhomogeneities in the photodiode a broader beam gives a better response than a pinpoint beam D Theory of Operation This portion of the report will discuss in detail the polarization state of the light as it propagates through the system and it will look at how the signal is interpreted and processed Refer to the block diagram in Figure 13 13 U Photodetector B Ocean Optics Spectrometer Computer R ll M4 i _ Plate Photodetector A rem j em Ls Glass Plate T M2 plate P B C PA e ET b ET Oscilli Ref Signal scope P Driver ectrical head Optical Head Figure 13 Block Diagram of Instrument top view As previously discussed the initial polarization of the laser beam is linear and oriented vertically The guarter waveplate is oriented such that it converts the linear polarized light into circular polarized light After exiting the PEM the light is
16. attainable in the center of the oven Each set of coils has its own power supply The shim coils are wired in series and the main field coils are wired in parallel The only reason the main fields are wired in parallel is because that is the only configuration our power supplies could accommodate The main field coils required two power supplies They are connected together in a master slave configuration Therefore to make current adjustments it is necessary to turn only one knob on the master power supply The current for each set of coils runs through a power resistor located near the selector switch shown in Figure 9 Because the voltage across the resistor is proportional to the current running through it and because the current running through the coil is directly proportional to the magnetic field produced by the coil the voltage across the resistor is also proportional to the magnetic field The relationship of magnetic field and voltage across the resistor is shown for each of the coils in Figure 10 The field of each coil was measured in the center of the oven where the Rb cell sits using a F W Bell model 5070 Gauss Teslameter Hall effect probe The voltage across each power resistor was measured using a digital multimeter Each coil can be selected individually using the selector switch shown in Figure 9 Using the plots in Figure 10 the shim coils were adjusted to compensate for the Earth s magnetic field 11 Magnetic Fie
17. e Temp Up Mag Field Up a o 6E 14 ms Temp Up Mag Field Down a Temp Down Mag Field Up X 4E 14 x Temp Down Mag Field Down 2E 14 O T T T 130 150 170 190 210 Temp C Figure 43 51107 Rb Vapor Density Cell 120B Rb Vapor Density Vs Temperature Cell 120C 1 2E 15 4 1E 15 Killian Curve 5 8E114 e Temp Up Mag Field Up a he a 6E 14 m Temp Up Mag Field Down S ms Temp Down Mag Field Up x 4E 14 Temp Down Mag Field Down 2E 14 0 T T T 130 150 170 190 210 Temp C Figure 44 51407 Rb Vapor Density Cell 120C All three cells showed the same trend of starting at the Killian curve for lower temperatures and then deviating from the curve for higher temperatures All three cells also deviated to the lower side of the Killian curve with cell 120B deviating the most at 32 190 C Cell 120B was also the cell that absorbed the most light therefore the increased deviation from the Killian curve may have been partially caused by low laser power A plot from Ryan s report is included in Figure 45 to show the improvement the PEM made for measuring the slope of rotation versus magnetic field e Faraday Rotation mrad 0727 120B 150C Faraday direct mrad Faraday Rotation Mag Field G FIG 17 Cell 120B 150 C 47 4 mA laser current A 779 46 nm Figure 45 Plot from old instrument illustrating variance in the slope The plot shows much more deviation in t
18. e Rb vapor density in cells and have found the Rb density to vary from cell to cell They have also noted that in some cases the Rb vapor density has varied from the Killian curve by as much as a factor of 2 The goals of this project were to make a reliable instrument for measuring Rb vapor density check for cell to cell variation compare the cells to the Killian curve check for hysteresis caused by either magnetic field fluctuations or by temperature fluctuations and to observe cell variations over long periods of time To accomplish these goals this project has some additions to the one completed by Ryan These additions include A photoelastic modulator PEM Additional optics used with the PEM Lock in amplifier A summing Circuit A power supply for the photodiode detectors Additional shim coils for 3 axis Instrument rigidification Section II of this report will cover Faraday rotation and how it is related to the Rb vapor density Section III will give a detailed description of the instrument It will also discuss the polarization states of the light and how the PEM significantly increases the signal to noise ratio of the system Section IV will show data and results and compare them to the expected values from the Killian vapor density curve Section V is the conclusion II FARADAY ROTATION AND Rb VAPOR DENSITY A Faraday Rotation Faraday rotation was first observed by Michael Faraday in 1845 What he obs
19. en the amount of rotation and the Rb vapor density is described by equation 3 and table 1 is a listing of the constants and units used in equation 3 8 leu B 4 7 2 P eun Ter DO Ka ege VA hb AA Parameter Constant Value Units 0 Measured Radians Solved for em Measured C 4 802e 0 est Bohr magneton 4 p 9 274e 21 erg gauss magnetic field B Measured 84U35 electron mass 9 1095e 28 8 6 62620 27 erg sec speed of light c 2 998e10 cm s A Measured Hz A Detuning from DI resonance Measured Hz Detuning from D2 resonance A Y Table1 Table of values used to solve the rubidium vapor density The DI resonance corresponds to electrons transitioning from the 5P gt 55 state The D2 resonance corresponds to electrons transitioning from the 5P gt 55 state The D1 and D2 resonance lines for Rb occur at 795 nm and 780 nm respectively Equation 3 shows that at D1 and D2 the rotation goes to infinity and that far away from either of the two resonance lines results in very little rotation The laser for this instrument was tuned to 779 5 nm or in other words y 2 47el1Hz After measuring 0 1 B A Ng and 4 y the only unknown is the rubidium vapor density Rb which is solved for HI INSTRUMENT DESCRIPTION The instrument can be divided into three main parts the probe beam optics the magnetic coil and oven assembly and the detection optics as
20. erations of additions made to the instrument that Ryan May already made For operations regarding the ECDL and the temperature controller for the ECDL refer to Ryan May s project report 1 Using the Quarter Waveplate With only the components shown in Figure 46 confirmation of best circular polarized light can be obtained by following the procedures listed below PDB Glass Pickoff Plate Half Wave PDA T Quarter Wave PBC Plate Figure 46 Setup used for producing best circular polarized light 1 Rotate the quarter waveplate so both the fast and slow axis are oriented 45 with respect to the laser beam polarization Either the fast or slow axis on the quarter waveplate corresponds very closely to zero degrees on the rotation stage 2 The quarter waveplate should be mounted on a post that is inline with either the fast or slow axis 3 Plug the outputs of PDA and PDB into an oscilloscope Make sure both channels are on the same scale 4 With the laser on adjust the position of the photodiode detectors PDA and PDB so their signal is maximized 5 Rotate the half waveplate and observe the fluctuations in the two signals on the scope 6 Adjust the quarter waveplate to minimize these fluctuations as the half waveplate is rotated 36 7 Now minimize fluctuations more by making slight rotations of the quarter waveplate about the post that it is mounted on This causes the optical path length of either the
21. erved was that as light propagated in a dielectric material collinear to a magnetic field the plane of vibration of the electric field rotated 1 The rotation is described by equation 1 0 VBI eq 1 where 0 is the rotation angle of the E field B is the magnetic field strength is the length traversed by the light and V is the Verdet constant The Verdet constant is particular to the material the light is propagating through The following description uses classical mechanics to describe the cause of Faraday rotation As the oscillating E field of linear polarized light propagates through a medium it causes the electrons to oscillate in the same plane as the E field When this is done in the presence of a magnetic field that is collinear with the light the electrons vibrate in a direction perpendicular to the B field Because the electrons are vibrating in a direction perpendicular to the magnetic field they experience a force known as the Lorentz force This force is described by equation 2 3 F qE qvx B eq 2 The cross product term of the Lorentz force is felt by the electron in a direction perpendicular to both the propagation of light and the direction of vibration The result is the polarization angle of the light is rotated as it passes through a medium collinear with a magnetic field B Rb Vapor Density As discussed earlier Rb vapor can be used as a medium for inducing Faraday rotation The relationship betwe
22. he data points than those taken using the PEM It is important to note that there are three points of introduction of error into the final Rb equation the slope the length of the cell and the detuning In this study the length of the cell was not found to contribute a significant portion of the error and was not included in the analysis Ryan reported a final error of 10 However he also used a detuning variance of 0 01nm which results in 4 error This indicates from equation 9 that 9 of his error came from the slope Where the S term is the percent of slope error and the q term is the percent of detuning error 2 2 N 7 S q eq 9 N S q Being that the cursor resolution on the spectrometer is 0 04 nm it is in my opinion that 0 01 nm is not a sufficient detuning variance Therefore 0 02 nm or 890 error was chosen for the detuning variance for this error analysis In this report typical total errors for the 33 rubidium vapor density were 8 to 9 This is not much better than 10 however very little portion of the total error came from the slope measurements Most of the total error comes from detuning which is estimated to be higher in this report than in Ryan s This shows that the error coming from the slope has been significantly reduced by adding a PEM and lock in amplifier to the instrument For all the measurements made in this report a polarizer was placed directly after the laser This was to ensure that
23. he empirical formula developed by Killian for measuring the Rb vapor density is shown as equation 8 2 4132 log N 26 41 E log T eq 8 Where N is the Rb vapor density per cm and T is the absolute temperature The measured vapor densities of cells 120A 120B and 120C were compared to the Killian curve produced by equation 8 At low fields below approximately 10 gauss the slope of rotation versus B field is much steeper than that measured between 10 and 60 gauss It is not clear what causes this dual slope behavior However because the slope obtained between 10 and 60 gauss was the one needed to make the calculation all the data reported here was taken from that range One other peculiarity was that the different cells absorbed different amounts of light The same laser power was used on all the cells however the summed photo detector voltages were different for all the cells This is shown in Figure 15 Vdc Vs Temperature o 9 25 ge e Cell 120A Vdc 0 95 15 Cell 120B Vdc a gt _ Cell 120C Vdc 5 9 os 0 S S 140 150 160 170 180 190 200 Temperature degrees C Figure 15 Shows the relationship between the total summed signal from the two photo detectors and temperature The plot indicates that different cells absorb different amounts of light and that they all absorb more light with increased temperature 17 Rotation Vs Mag Field
24. he oven to the desired temperature and let it stabilize Once it is stable it should fluctuate by only 0 3 C 2 Turn on the shim coils and verify with the DVM that they are adjusted to result in zero field in the oven space Turn the laser on 4 Use the Ocean Optics spectrometer to measure the real time lasing wavelength Adjust the ECDL if necessary 5 Plug the output from photodetectors into the oscilloscope UI 10 11 12 13 14 15 16 17 18 19 20 21 22 40 After all the optical elements are in place including the oven and cell adjust the photodetector positions to produce a maximum signal Turn on the PEM Plug the output from the photodetectors into the lock in amplifier Switch between 0 and 909 and adjust the phase knob so one of the positions either 0 or 909 gives zero signal This means that the entire signal is on the other position or channel Go to the channel with the entire signal With the main field power supplies turned off rotate the half waveplate until the signal on the lock in amplifier reads zero Open up the Excel file labeled RbDensityTemplate3 xls and select the tab that corresponds to the correct temperature All the columns with bold inputs require user input all the other columns are either constants or outputs and do not need to be changed Plug the output from the photodiode detectors into the summer and plug the output from the summer into the oscilloscope E
25. her temperatures Unfortunately because of time constraints long term measurements were not feasible for this study Comparing the cells against each other indicate some variation from each other Cell 120C deviated from the curve faster than the other two Cell 120C also absorbed the least amount of light which may be correlated to the increased deviation The variation in 34 cells indicates the necessity to be able to character each cell individually instead of relying on the Killian formula There was some slight hysteresis observed for cells 120A and 120B for variations in the magnetic field Because cells 120A and 120B were the first to be measured it is not clear if some of the apparent hysteresis was due more to inexperience in running the instrument or was characteristic of the actual cells themselves Further testing is recommended to verify this Except in the most extreme cases the error in the slope is dominated by detuning error Therefore hysteresis due to changing magnetic fields have negligible impact on the final Rb vapor density measurement Hysteresis due to varying the temperature also appears to be negligible Except for some outliers the cause of which is believed not to be hysteresis all the points for a given temperature agree with each other within experimental error 35 APPENDIX A OPERATIONS MANUAL This operations manual does not cover the operations of the entire instrument Rather it only covers the op
26. highlighted To highlight the depth of retardation adjustment RTD simply push the blue down button located on the right front face of the PEM controller 4 With WAV highlighted the wavelength can be adjusted by pressing enter 37 5 Now that the number is highlighted Simply enter in the desired wavelength using the numbered keys followed by enter 6 To adjust the depth of retardation follow the same procedure 3 Using the Lock in Amplifier The lock in amplifier used was a Princeton Applied Research model 186A Synchro Het lock in amplifier With the input A B option selected the lock in amplifier takes the difference of the two input signals and then multiplies that signal with the reference signal The output is a DC signal that corresponds to the amplitude of the difference of the two input signals Figure 48 Lock in amplifier used on this instrument Because the input signal is oscillating at 50 kHz the input lowpass filter is set to max which is 100 kHz Because the reference signal out of the PEM is 1f the 1f reference signal mode is selected on the lock in amplifier The correct sensitivity was chosen by choosing one that used the biggest portion of the scale without pegging the needle for a Faraday rotation measurement There are three scales the needle can be read from depending on the sensitivity setting used A typical sensitivity setting used was 20 mV For this setting the scale that goes up to 2 was used The
27. ic field output voltage to the DVM located on the instrument cart as shown in Figure 50 Switch the selector switch to the correct coil and adjust the current on the correct power supply until a voltage output is displayed that corresponds to zero field for that coil Do this for each of the shim coils 39 Magnetic Field Output Voltage C m Figure 50 DVM and coil selector switch used to measure the magnetic field contribution for each of the three coils Adjusting the main field coils is the same as adjusting the shim coils except that there are two power supplies involved The two power supplies are connected in a master slave configuration with the master on top To adjust the main field turn both power supplies on All the knobs on the slave power supply should be turned completely clockwise so both the voltage and current settings are maximum The voltage knobs on the master power supply should also be set to their maximum position The current control knob on the master power supply is then used to adjust the current output of both power supplies When zero magnetic field is required it is necessary to completely turn off both of the power supplies used for the main field coils When the power supply is left on with the current turned all the way down there is still a small current that results in Faraday rotation 5 Making Measurements Measurements can be made by following the list of instructions below l Set t
28. inear polarized light emitted from the laser into circular polarized light To accomplish this the fast and slow axes of the quarter waveplate are oriented at 45 for one axis and 45 for the other axis relative to the vertical polarized laser light Using the setup below in Figure 6 the circular polarized light was analyzed to determine how circular it was l Calcite Calcite Quarter Polarizer Polarizer Waveplate P2 P1 y 4 Photodiode Detector Figure 6 Analyzer setup used to ensure good circular polarization after the quarter waveplate The best results gave 20 25 variation in intensity as the calcite polarizer was rotated A significant portion of this variation was caused by the error inherent in the 780 nm multiorder quarter waveplate To compensate for this error the quarter waveplate was mounted on a post at a 45 angle as shown in Figure 5 Next the waveplate was rotated about the mounting post This effectively lengthens the optical path length of the axis that is positioned perpendicular to the axis of rotation This slight rotation can be seen in Figure 2 With P1 the variations were reduced to 1 796 and without P1 the variations were reduced to 14 The last component on the probe beam optics table is the photoelastic modulator PEM This PEM is a series I FS50 and was purchased from Hinds Instruments It has a nominal operating freguency of 50 kHz and a useful aperture of 16 mm This PEM head has the noninterfe
29. ld gauss Main Field B Vs Voltage y 34 814x 0 0809 R 1 0 5 1 15 Volts Magnetic Field gauss Vertical Shim Coil B Vs Voltage y 7 4 0329x 0 1847 R 0 9995 volts Magnetic Field gauss Horizontal Shim Coil B Vs Voltage y 23 2487x 0 3775 R 0 9993 volts Figure 10 Relationship of magnetic field and voltage across a power resistor for each set of magnetic field coils The equation for the main field line was use in calculating the magnetic field strength during the Rb vapor density measurements The oven assembly is essentially the same as what Ryan previously used with a few modifications The air inlet was modified to fit this particular coil arrangement Two vent holes were added to the top and an extra window was added for the option of using a transverse probe beam for polarimetry experiments The Rb cell sits in the oven as shown in Figure 11 Figure 11 Rb cell shown sitting in the oven without the oven cover 12 C Detection Optics The detection optics consists of a 780 nm multiorder half waveplate a polarizing beam splitting cube and two photodiode detectors as indicated in Figure 12 Photodiode Detectors m F SP 780 nm Half Pe Waveplate s Polarizing Beam Splitting Cube Figure 12 Detection optics consist of a half waveplate a polarizing beam splitting cube
30. nter the summed voltage into the Vdc column overwriting the existing data Plug the photodetector outputs back into the lock in amplifier Set the magnetic field selector switch to observe the main field Turn the main field power supplies on and adjust the current so the DVM reads 400 mV Input the exact voltage into the VB column Read off the voltage on the lock in amplifier and input this value into the column labeled Vfr Repeat steps 17 and 18 incrementing the magnetic field voltage by 200 mV each time until a maximum of 1 800 V is reached When finished Excel will output a Rb vapor density point Columns B and V are uncertainties or variance in the signal from the lock in amplifier and the Ocean Optics spectrometer respectively They are used in the error calculations Repeat steps 1 21 for each temperature REFERENCES 1 E Hecht Optics 4 ed Addison Wesley Reading MA 2002 2 R May Instrumentation Project Final Report University of Utah Utah 2006 3 R A Serway J W Jewett Physics for Scientists and Engineers 6 ed Thomson Brooks Cole 2004 4 PEM100 User s Manual Hinds Instruments 2006 5 K C Hewitt Department of Physics and Atmospheric Science Phys3540 Lecture Dalhousie University Halifax Nova Scotia 2002 6 I A Nelson Thesis University of Wisconsin Madison 2001 7 T J Killian Thermionic phenomena caused by vapors of rubidium and potassium Physical Review
31. output time constant determines how much the needle fluctuates Lower time constants allow the needle to fluctuate more rapidly Typical time constants used were 0 3 and 1 second time constants The phase adjusts the phase between the input and reference signals It can be adjusted by 90 increments using the buttons or continuously by turning the 38 phase knob The output offset can be useful if you wish to adjust the starting point for the output needle Be aware that the phase can only be checked with the output offset turned off The dynamic reserve used was always 3k 4 Magnetic Coils The magnetic coils were each individually calibrated by measuring the magnetic field with a Hall effect probe and comparing that to a voltage measured across a power resistor through which all of the coil current ran Attached to the front of the cart where all the power supplies are located are three equations that relate magnetic field to the voltage measured across a power resistor for each set of coils The shim coils use a dual power supply indicated in Figure 49 Three equations relating field and voltage Dual power supply used by shim coils Main field power supplies Figure 49 Power supplies used by magnetic field coils Also shown is the laser temperature controller To properly adjust the shim coils for zero field simply solve the appropriate equation for V 0 Then connect the magnet
32. p E 0 01 8 Down o G 0 009 Linear Up L 0 006 Linear Down 0 004 0 002 0 0 10 20 30 40 50 60 70 Mag Field gauss Figure 38 51407 Temp 180C Temp Down Cell 120C Rotation Vs Mag Field a SAM R 9 998E 01 y 1 782E 04x 1 518E 04 0 014 R 9 997E 01 0 012 _ 0 01 E Up 0 008 Down o x G dos Linear Up e Linear Down 0 004 0 002 10 20 30 40 50 60 70 Mag Field gauss Figure 39 51407 Temp 170C Temp Down Cell 120C 29 y 1 041E 04x 6 479E 05 Rotation Vs Mag Field R 9 996E 01 y 1 024E 04x 1 530E 04 ee R 9 997E 01 0 007 0 006 amp 0 005 Up t D 5 0 004 Down x Linear Up 2 0 003 Linear Down 0 002 0 001 0 0 10 20 30 40 50 60 70 Mag Field gauss Figure 40 51407 Temp 160C Temp Down Cell 120C x y 6 548E 05x 8 825E 05 Rotation Vs Mag Field a pin Drap y 6 450E 05x 3 642E 05 R 9 995E 01 0 004 0 0035 S 0 003 KU t 0 0025 x Down G 0 002 Linear Up 2 0 0015 Linear Down 0 001 0 0005 Mag Field gauss Figure 41 51407 Temp 150C Temp Down Cell 120C 30 Cells 120A and 120B show some signs of hysteresis do to changes in magnetic field These cells were the first to be measured and the frailties of the system were not completely understood at this point It is believed that this apparent hysteresis may have been a result of laser power fluctuations causing the lasing
33. p Up Cell 120B Rotation Vs Mag Field UE DENM R 9 821E 01 y 1 148E 04x 3 959E 03 0 014 R 9 929E 01 0 012 0 01 E Up 0 008 Down 9 5 0 006 Linear Up 2 Linear Down 0 004 0 002 Mag Field gauss Figure 25 51107 Temp 160C Temp Up Cell 120B 22 Rotation Vs Mag Field y 1 644E 04x 3 452bE 03 o Mag Field gauss R 9 974E 01 y 1 621E 04x 3 349E 03 oe 9 939E 01 0 014 0 012 8 0 01 Up 5 0 008 A 2 Linear Up 2 0 006 Linear Down 0 004 0 002 0 70 Mag Field gauss Figure 26 51107 Temp 170C Temp Up Cell 120B y 2 487E 04x 2 329E 03 Rotation Vs Mag Field oration Ve mag R 9 984E 01 y 2 575E 04x 2 393E 03 0 02 2 9 948E 01 0 018 0 016 gt 0 014 0 012 Up 5 0 01 TUN Bo Linear Up S8 2 0 008 Linear Down 0 006 0 004 0 002 0 Figure 27 51107 Temp 180C Temp Up Cell 120B 23 y 3 205E 04x 9 394E 04 Rotation Vs Mag Field R 9 954E 01 y 3 056E 04x 4 469E 04 0 025 2 9 968E 01 0 02 c 0 015 Up 5 Down Linear U S 001 PESE L Linear Down 0 005 0 70 Mag Field gauss Figure 28 51107 Temp 190C Temp Up Cell 120B Rotation Vs Mag Field y I U R 9 945E 01 ed y 2 607E 04x 1 592E 03 R 9 998E 01 0 018 0 016 _ 0 014 8 0012 Up 5 001 BN z Linear Up 2 0 098 Linear
34. rence option NIO as well as the magnetic field compatibility option MFC The optical head is a resonant device composed of two components the optical element and the transducer as shown in Figure 7 Optical Element Junction Transducer AN 4 Figure 7 Optical Head For PEM 4 The optical element is composed of birefrigent fused silica The amount of birefringence or in other words the amount of retardation between the slow and fast axes is a function strain either in compression or tension The transducer produces this strain in the fused silica sinusoidally on resonance at 50 kHz The result is a retardation that can be described by equation 4 where p is the depth of retardation p sinor eq 4 The PEM is set up on this instrument with the fast or slow axes oriented either vertically or horizontally For circular polarized light incident on the PEM the resulting transmitted light is elliptically polarized with the semimajor axis oscillating between 45 Equation 5 shows that a always equals 45 regardless of the retardation as long as E E where and E are the amplitudes of the electric field in their respective directions Also in the special case where E the angle a changes instantaneously from positive to negative as the polarization passes through circular Changing the retardation only affects the eccentricity of the ellipse with the two extreme cases being a circle ora line This is
35. the lasing freguency The ECDL can do this because the grating can be rotated independent of the laser about two axes It can be rotated about a vertical axis and about a horizontal axis that is perpendicular to the laser beam Rotation about the horizontal axis allows for proper alignment of the reflected 1 order beam back into the laser This adjustment is made by adjusting the top knob shown in Figure 3 If the laser is unstable this knob may need slight adjustment Adjustment of the knob on the lower end of the L in figure 3 causes the diffraction grating to rotate about a vertical axis This adjustment causes the lasing line to shift thus enabling the laser to be tuned to 779 5 nm One of the goals of the project was to rigidify the setup With that in mind there were some additions or modifications made to the laser assembly As shown in Figure 3 spacers that fit around the attachment screws and between the mounting plate and base block were added Without these spacers it was impossible to securely fasten the laser to the base block without causing the mounting plate to bow over the TEC If the mounting plate were allowed to bow over the TEC then it would not maintain good thermal contact and temperature control of the laser would be compromised Also an additional screw was added to the bracket holding the output mirror of the ECDL Using two screws ensured that the bracket could not wobble or pivot Another modification was made
36. to the base block Previously the shear size and mass of the base block was used to keep it in one place It sat flat on the optic table without being fastened down in anyway In the current setup it was necessary to raise the level of the laser Brackets were designed to raise the level of the laser to rigidly hold the laser block and to provide for adjustment both vertically and horizontally side to side This assembly is shown in Figure 5 Figure 5 Laser mount and bracket assembly ensure rigid structure for improved laser stability while maintaining adjustability One more change to the laser assembly was the addition of a cover shown in Figure 2 Without the cover small air currents in the room or even standing near the laser caused the temperature to fluctuate 40 06 C These small fluctuations caused the output power of the laser to fluctuate as well With the cover the laser temperature fluctuates a maximum of 0 01 C which is also the maximum temperature resolution of the controller The glass plate is used to pick off a small portion of the beam and reflect it back into the Ocean Optics spectrometer The Ocean Optics spectrometer provides real time information about the emitted wavelength of laser light This is useful both for adjusting the extended cavity and while making measurements to ensure the laser line is where it is expected to be The 780 nm multiorder quarter waveplate shown in Figure 5 converts the vertical l

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