Entanglement and Bell`s Inequalities
Contents
1. B of a polarizer B QUESTION 4 2 What are the conditions for maximum and minimum coincidence count rates for setup with two polarizers in front of each APD 5 EXPERIMENT 1 ALIGNMENT PROCEDURE FOR PREPARING AN ENTANGLED STATE Caution never switch the APD or EM CCD camera on in room light ALL YOUR EXPERIMENTS SHOULD BE CARRIED OUT IN ABSOLUTE DARKNESS As it was described in Section 4 in this lab you will produce the quantum entangled state H H VV by adjusting both the quartz plate and the BBO crystal set Your first actions will be as follows e Because the laser has a vertical polarization you need to rotate the optical axes of a BBO crystal set which direction for one of the crystal is marked on the crystal mount Rotation angle around a horizontal axis perpendicular to the mount surface 15 should be near 45 from the vertical incident laser polarization direction e By rotating the BBO crystals around two other axes and using an EM CCD camera you should maximize the brightness of the image of the cone of the downconverted photons e You need to maximize singles counts of APD detectors A and B as well as the coincidence count APD detectors in the two arms are kept at an angle of several degrees where maximum counts are observed see photo of the old setup shown in Figure 9 Figure 9 Photograph of the old setup of entanglement lab 5 1 Observing the down converted light cone by an EM C2. Knowing this we can measure the signal polarization and infer with certainty the idler polarization 1 V Y eni gt ai S 12 From Figure 7 you can see that a horizontal photon travels a larger distance inside the BBO crystals than a vertical photon before getting down converted This difference in distances traveled introduces a phase difference between the two polarization states resulting in a quantum state P V V e H H 4 If the incident pump laser beam has a polarization angle 9 from the vertical see Figure 8 in which the crystal optical axis is parallel to the vertical direction in general case the downconverted photons emerge in the state Vnc cosO H H expliglisin V V 5 i H polarized cone BBO crystals Figure 8 Geometry of a downconversion process By placing polarizers rotated to angles a and in the signal and idler paths respectively we measure the polarization of the downconverted photons For a pair produced in the downconverted state y the probability of coincidence detection is Py a P V Val Yoy 6 The vv subscripts on P indicate the measurements outcome V V both photons vertical in the bases of their respective polarizers More 13 generally for any pair of polarizer angles and there are four possible outcomes V V H H H V and H H Using the basis of Eq 2 we find after some trivial cal
3. 5 seconds a polarization angle of Polarizer A B polarization angle of Polarizer B Net count Actual count background count Background Coincidence Count B deg Coincidence Count B deg Coincidence Count Polarizer A Ald Net Polarizer A hast cs removed removed 0 170 10 180 20 190 30 200 40 210 50 220 60 230 70 240 80 250 90 260 100 270 110 280 120 290 130 300 140 310 150 320 160 330 170 340 180 350 20 The plots for the singles counts are not exactly flat as you should have predicted The plots seem to have some sinusoidal characteristic We define a quantity called Visibility V to check the flatness of a curve Ve Max Min x 100 Max Min Here Max and Min are the maximum and minimum counts Find the Max and Min of your data and calculate the visibility Max _ Min Visibility QUESTION 5 1 You know that you have the quantum state Y H H V V How do you expect Count B to change as you rotate Polarizer B from 0 to 360 but Polarizer A is set for a fixed angle a QUESTION 5 2 If Polarizer A was removed how would you expect the coincidence count to change as you rotate Polarizer B form 0 to 360 QUESTION 5 3 What would you expect the visibility to be for a perfectly flat curve QUESTION 5 4 What does it mean to have a 100 visibility 21 6
4. Cartoon of A K Jha and L Elgin illustrating entanglement Entanglement between particles is always through some physical property For example the quantum mechanical state describing particles momentum spin or polarization may be entangled You can read about entanglement in the books 1 3 for advanced undergraduate and graduate students In this laboratory two different photons whose polarization states are entangled will be investigated These entangled photons are produced in a BBO crystal 4 through a process called Spontaneous Parametric Down Conversion 5 This lab experiment was reported in 1999 as a research paper in Ref 6 and developped for the students lab by the authors of Refs 7 and 8 Ref 7 contains also some useful historical background Bell s Inequality 9 11 is a mathematical equation Inequalities of the Bell type by themselves have nothing to do with quantum theory Contexts as different as downhill skiers and laundered socks have been used by Meystre and Bell to demonstrate this Although Bell inequalities are almost tautological expressions they have attracted much attention because they allow one to see the experimental consequences of alternative views of physical reality which are conveniently labeled classical and quantum mechanics 10 In this lab you will calculate Bell s Inequality predicting the maximum value of a sum of probabilities The probabilities involved assume a classical corre
5. EXPERIMENT 2 LOOKING AT THE ENTANGLEMENT In this activity we will see how photons in two arms are entangled and how this entanglement affects the properties of one photon when a measurement is performed on the other photon QUESTION BEFORE STARTING What would you expect for the Coincidence Count if you put Polarizer A at a 0 45 90 135 and in each case rotate Polarizer B from B 0 to 360 Show the mathematical basis for your prediction Hint fixing a at some angle is like making a measurement in that basis Next steps to check your suggestions 1 Set the Labview program for a measurement time of 5 seconds or 5000 ms 2 Fix a 0 and put B 0 Switch the lights off Make sure that the door is locked Make sure that the laser is off 3 Ask the TA to switch on the APD 4 Record the coincidence count by clicking START in the Labview program Note the results in Table 3 Column Il 5 Next put the Polarizer B at B 10 20 360 Record the coincidence count and note the results in Table 3 Column Il 6 Repeat steps 5 and 6 for a 45 90 135 and note down the counts in Table 3 Column Ill Column IV and Column V respectively 7 Plot Coincidence Counts for the different a values versus the angle of polarization B There should be four plots one for each value of a Table 3 Time window 5 seconds a polarization angle of Polarizer A B polarization angle of Polarizer B
6. e Avoid blocking the output beam or its reflection with any part of your body e Try to maintain a high ambient light level in the laser operation area This keeps the eye s pupil constricted thus reducing the possibility of eye damage e Laser safety issue arises also from the high voltage applied to the tube with the argon B EQUIPMENT SAFETY For the safety of the equipment e NEVER TURN ON THE ROOM LIGHTS WHILE THE APDs AND EM CCD CAMERA ARE ON e 1 After turning off the power switch always unplug the APD s before turning on the lights for the long period of time 2 Also make sure your Lab View program is turned off before turning on the lights e If APD count rate will exceed 200 000 counts sec reduce laser power or put the screen in front of APD DON T SWITCH OFF APD UNDER A HIGH COUNT RATE e Don t turn on the BeamLok 2060 argon ion laser without water cooling see instructions in Appendix of this Manual e Keep water running during 15 min after the laser turning off PREPARATORY QUESTIONS You should answer two sets of questions 1 before your first laboratory session and 2 after each section of this Manual All questions have a blue color font Answer these questions before your first laboratory session 1 What is entanglement How will you create polarization entangled photons in this experiment 2 How will you prove in your experiment that you have entangled photons 3 What i
7. 2 Switch the lights off Make sure that the door is locked Make sure that the laser is off 3 Switch the APDs on in the presence of TA 4 Hit START in the labview program That is the background count Note background for singles in Table 1 and that for coincidence in Table 2 5 Switch the laser on While Polarizers A and B are at 0 record the singles count by clicking START in the labview program and note it in Table 1 column II and III 6 Next put the polarizers at 10 20 360 and each time record Count A and Count B and note them in Table 1 7 Remove the Polarizer A and put Polarizer B at 0 and hit the START button and note down the coincidence count in Table 2 8 Next put the Polarizer B at 10 20 360 and each time record the coincidence count and note it down in Table 2 9 Plot Count A Count B and Coincidence count versus the polarization angle of Detector B Table 1 Time window 5 seconds a polarization angle of Polarizer A 6 polarization angle of Polarizer B Net count Actual count background count Background Count A Background Count B Count A Count B a B deg Actual Net Actual Net 220 230 240 250 260 270 280 290 300 310 320 330 340 350 Table 2 Time window
8. Net count Actual count background count 22 Background Coincidence Count Coincidence Count B deg a 0 Coincidence Count a 90 Coincidence Count a 45 Coincidence Count a 135 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 This dependence you observed is actually the evidence of quantum entanglement You should have seen that the maximum coincidence count occur at the angle where a has been fixed For a 0 you get the maximum of coincidence at B 0 For a 90 you get the maximum of coincidence at B 90 23 Question 6 1 What equation of the section 4 matches the experimental results proving the entanglement Question 6 2 Compare the coincidence plot with Polarizer A removed to the plots at different values of a What is the difference between coincidence plot with no polarizer and coincidence plot with the polarizer at a 0 Question 6 3 How does choosing different values of a change the coincidence plots than 8 is fixed 7 EXPERI MENT 3 TESTING QUANTUM THEORY BY BELL S INEQUALITY VIOLATION In this activity we will mathematically check if quantum theory i
9. angles you used in this activity is 2 82 Discuss why you did not get this value of S i e what are the sources of experimental errors 26 APPENDIX 1 Beam Lok Laser Operation je a Startup Procedure 13 14 The output beam of this laser is a safety and fire hazard Avoid directly viewing the beam and its reflection or blocking it with clothing or parts of the body 1 Place a beam block or power meter in the beam path clear the beam path of reflective objects and open the shutter Turn on the cooling water supply The FLOW indicator should turn off within a few seconds Water flow rate should be 3 0 gal min 11 3 I min water pressure should be 25 psig 172 kPa water temperature should be 10 35 C 50 95 F Turn on the main power The P S STATUS indicator on the power supply should turn on Input power should be 3 phase with ground input voltage should be 208 Vas 10 5 maximum current is 60 A per phase at 208 V power consumption is 21 kW Turn on the key switch and wait for 5 10 min Using the left knob on a power supply control box increase the current but don t exceed 50 A To control the power press the right black button into the power mode depending on a switching order the value of current power or voltage will appear on a display The emission indicator turns on and after a 15 second delay the plasma discharge starts and the laser beam emerges if curren
10. are single photon detectors that give rise to an electronic signal TTL pulse when a photon is incident on them 3 Polarizer B Polarizer A BBO Crystals gt Mirror Quartz Blue Plate Filter Figure 2 Schematics of experimental setup The APDs are kept at the same height as that of the BBO crystals The APDs positions are equidistant from the center of the crystal This enables these two APDs to be on two diametrically opposite points of the downconverted cone Data from the APDs are collected using a Lab View interface on a computer with a counter timer board inside The interference filters with 10 nm bandwidth should be placed in front of each APD so that only light near 730 nm i e the down converted photons will reach the detectors Additionally polarizers are located in front of each APD so that the polarization state of photons reaching the detectors can be selected 3 BBO CRYSTALS AND PARAMETRIC DOWN CONVERSION Beta Barium Borate BBO is a negative uniaxial nonlinear crystal with some very interesting and useful properties 12 Crystals can be cut for the different types of nonlinear interactions For a type crystal cut when a horizontally vertically polarized photon of wavelength is incident on the crystal two photons of wavelength 24 emerge from the crystal with vertical horizontal polarization Figure 3 This process is called spontaneous parametric down conversion and is a standar
11. program by hitting Right click on START Go to mechanical action Select switch when pressed Hit the run CON OO 9 button and then START Make sure that it is running continuously Switch the lights off Make sure that the door is locked Make sure that the laser is off Switch on the APDs in a presence of TA Record the counts when the laser is off and APDs are covered by the dark tissue These are dark counts Record the counts when the laser is on but the output from the BBO crystals is blocked by the screen These are background counts Background Count A Background Count B Background Coincidence Count Background counts should not be more than 500 Switch the laser off Remove Polarizers A and B Switch the laser on Work at the laser output power 10 30 mW The counts should now have increased Maximize the counts by adjusting the X Y translator and after that the angle of the APD s direction to the BBO crystals Once you have maximized the counts you should have at least a couple of hundred coincidences Switch the laser off 10 Switch the APDs off 11 Stop the Labview program by hitting Right click on the 12 START button Go to mechanical action and select latch when pressed Put Polarizers A and B at 0 Next step 1 Set the time window to be 5 seconds or 5000 ms Hit the run button and then START
12. water 4 If the unit is not to be used for some time turn off the main power at the circuit breaker 28
13. CD camera Using the imaging lens and two or three interference filters with 10 nm transmission bandwidth at 730 nm in front of the EM CCD camera obtain the images of the cones of downconverted photons Select an optimum cone angle for your setup by rotating a BBO crystal One of the interference filters should be placed at the camera entrance see Figure 10 You will observe a light cone similar to the image in Figure 10 right but with more smeared edges because of much smaller thickness of the crystals in a current lab experiment 100 um Figure 10 Left setup for the observation of a cone of downconverted light Right image of a downconverted light cone for a 2mm thick type I single BBO crystal 5 2 Adjusting APDs for maximum counts If APD count rate will exceed 200 000 counts sec reduce the laser power or put the screen in front of the APDs DON T SWITCH OFF APD UNDER A HIGH COUNT RATE Recall that Count A and Count B in the Labview program refer to the counts in APD A and APD B respectively Coincidence Count measures the number of photon pairs simultaneously reaching the two detectors The term singles count refers to either Count A or Count B 1 Make the time window in a LabView program to be 0 5 seconds or 500 ms Hit the run gt button and then START Check that you have 0 counts when APDs are off If the program is running continuously leave it Jike that Otherwise stop the LabView
14. The Institute of 0m gt OPTICS SS S UNIVERSITY OF ROCHESTER THE INSTITUTE OF OPTICS OPT 453 OPT 253 PHY 434 Lab 1 Entanglement and Bell s Inequalities Instructor Dr Svetlana G Lukishova sluk lle rochester edu Fall 2008 I cannot seriously believe in quantum theory because it cannot be reconciled with the idea that physics should represent a reality in time and space free from spooky actions at a distance Albert Einstein Summary of this Lab e Entanglement is the most exciting and mysterious property of some quantum mechanical systems when property of one particle depends on the property of the other It does not matter how far apart such entangled particles are located Among the best known applications of entanglement are quantum communication and quantum state teleportation e Bell s inequality is a classical relation For entangled particles it is violated e In this lab you will obtain an entangled state of two photons and will calculate Bell s inequality using measurements of the coincidence counts between two single photon detectors You will work on modern cutting edge photon counting instrumentation widely used in quantum information science and engineering The table below shows its other applications Photon counting applications bioluminescence detector primary quantum calibration radiometric standards scales single molecule detection medical ima
15. ally polarized photons Figure 5 Signal V gt H H gt Idler Figure 5 Production of two horizontally polarized photons from one vertically polarized photon Mathematically it can be represented as IV gt 4 4 Here v and H represent a horizontally or a vertically polarized photon For historic reasons photons of a down converted pair are called signal and idler photons denoted by subscripts s and i respectively 10 On the other hand a horizontally polarized photon going through these crystals would get down converted in the second crystal producing two vertical photons Figure 6 Signal IV Vi gt IH gt Idler Figure 6 Production of two vertically polarized photons from one horizontally polarized photon Mathematically it can be represented as H gt VV Now what happens if photons with 45 polarization are incident on a pair of BBO crystals as shown in Figure 7 below H polarized cone pee IH gt IV gt IV Vi gt lH Hi gt 12 ao V polarized cone Figure 7 Production of polarization entangled photon pairs A stream of 45 polarized photons can be considered as a beam with half vertically and half horizontally polarized photons So half of the time these photons would get down converted in the first crystal producing pairs of photons with horizontal polarization and half of the 11 time they would pass through the first crystal and would get dow
16. culations P a B sin sin Bcos 0 cos acos p sin 0 7 sin 2a sin 2p sin 26 cos A special case occurs when y 0 In this case Wean that is when 6 11 4 and l 2 Plt gt C08 B a 8 In this lab you will obtain a relation 8 in your experiment selecting 1 an optimal angle of crystal rotation relative to the incident laser polarization which is fixed and 2 an optimal angle of rotation of a quartz plate to compensate phase In the experiment you will measure a coincidence count rate N a 2 choosing a fixed interval of data acquisition 0 5 20 s Assuming a constanf flux of photon pairs the number of N a 8 will be N a B A sin a sin B cos 6 cos cos B sin 0 9 sin 2a sin 22 sin 20 cos C where A is the total number of entangled pairs produced and C is an offset to account for imperfections in the polarizers and alignment of the crystals This offset is necessary to account for the fact that some coincidences are observed even when the polarizers are set to a 0 B 90 In an ideal case C 0 if is fixed as 45 and is determined to be minimized by rotating the quartz plate 14 N a B A lsin asin B cos cos 8 2sin cosa sin B cos p A x 2 o aco ena 10 Z cos a p QUESTI ON 4 1 How will a count rate of APD detector A singles count rate depend on the angle a of a polarizer A and on the angle
17. d method used to produce polarization entangled photons 4 6 The down converted photons are emitted in a cone from the crystal The efficiency of this down conversion process is only 10 out of 10 incident photons only one photon would get down converted For details in noncolinear phase matching conditions in parametric down conversion Figs 3 4 see paper 12 Figure 3 Down conversion of photon with a horizontal polarization For this orientation of the crystal photons with a vertical polarization pass straight through Figure 4 Down conversion of photon with a vertical polarization For this orientation of the crystal photons with a horizontal polarization pass straight through Since the majority of the laser light simply passes straight through the BBO crystals the intensity of the down converted photons is very low you will not be able to see a down converted light with naked eye We will use single photon counting avalanche photodiodes APDs sensitive to observe the down converted photons 4 PRODUCTION OF POLARI ZATION ENTANGLED PHOTONS THEORY The production of a polarization entangled quantum state using type BBO crystals with a 45 incident polarization is explained below The first crystal s optic axis and the pump beam define the vertical plane Due to Type phase matching a vertically polarized photon going through these crystals would get down converted in first crystal producing two horizont
18. ers but due to the poor quality of the polarizers used this is not the case By subtracting this count from your readings you are correcting for the poor quality of polarizers N 8 is the count after subtracting 0 90 J For a 45 a y a 45 a 90 b 22 5 b 22 5 b 67 5 b 112 5 calculate S in Equation 8 and note it down Table 4 Time window 20 seconds a polarization angle of Polarizer A B polarization angle of Polarizer B Net count Actual count 0 90 25 N 0 90 ei deg B deg e ae 45 22 5 45 22 5 45 67 5 45 112 5 0 22 5 0 22 9 0 67 5 0 112 5 45 22 5 45 22 3 45 67 5 45 112 5 90 22 5 90 22 5 90 67 5 90 112 5 S Violation of Bell s Inequality can be seen at any angle The maximum is observed at the angles chosen above You should observe that there are accidental coincidences or random coincidences in the system These random coincidences result from the probability that the two uncorrelated photons from two different down conversion events will arrive within the coincidence interval This background is small and acts to decrease S A finding S gt 2 thus cannot be a result of the random accidental coincidences Question 7 1 What is the value of experimental error in your measurements of S Question 7 2 The predicted value of S from quantum theory at the
19. ging Biotechnology Information are l Processing hyper spectral imaging Metrology Quantum entertainment Lee neutrino Space Military cherenkow dark Applications Meteorology matter detection IR detectors displays Electronics photon Medical count Physics quantum imaging quantum cryptography quantum computing single photon sources oo medical non interactive imaging radioactivity nuclear devices i remote sensing security robust imaging environmental monitoring chemical bio agent detection Areas of applications of photon counting instrumentation prepared by organizers of second international workshop Single Photon Sources Detectors Applications and Measurements Methods Teddington UK 24 26 October 2005 IMPORTANT SAFETY TIPS A LASER SAFETY The argon ion laser BeamLok 2060 emits laser radiation that can permanently damage eyes and skin To minimize the risk of injury or expensive repairs carefully follow these instructions PRECAUTIONS FOR THE SAFE OPERATION OF CLASS IV HIGH POWER LASERS e Wear protective eyewear at all times selection depends on the wavelength and intensity of the radiation the conditions of use and the visual function required During the alignment of your setup you can reduce the power of the laser e Avoid looking at the output beam even diffuse reflections are hazardous
20. lation between two particles whose polarization states are measured Violating this inequality means that these particles do in fact have a quantum relationship that cannot be explained by classical mechanics 2 EXPERI MENTAL SET UP As shown in the schematic diagram in Figure 2 light from a 100 mW pump argon ion laser with a wavelength A 363 8 nm and a vertical polarization passes through a blue filter and then a quartz plate The blue filter removes parasite fluorescence from an argon plasma tube that may be present in the laser beam Quartz is a birefringent material When light passes through the quartz plate a phase difference is introduced between two polarization components This phase difference can be adjusted by rotating the quartz plate A mirror re directs the beam through a pair of BBO crystals that are mounted back to back at 90 with respect to each other The majority of the laser light passes through the BBO crystals and is collected at the beam stop or rejected by the interference filters The down converted photons from the BBO crystals are emitted in cones a horizontal and a vertical polarization cone for a beam with 45 incident polarization relative to the BBO optical axis Down converted photons from the BBO crystals with wavelength 2A 727 6 nm are detected by a pair of single photon counting avalanche photodiodes APDs modules The x y position of the APDs can be adjusted using the x y translator APDs
21. n converted in the second crystal producing pairs of photons with vertical polarization Hence for an incident beam of 45 polarized photons the same number of photon pairs having vertical and horizontal polarizations will be emitted from the two BBO crystals Mathematically this can be represented as V VV HH 1 gt t 2 J2 en Here ea represents a 45 polarized photon Notice that the state cannot be factored into states purely dependent on the signal and idler photons i e Y 1 2 for any choice of 1 and 2 This means that the state of one particle cannot be specified without making reference to the other particle Particles related thusly are called entangled and Yen is called an entangled quantum state If we measure the polarizations of signal and idler photons in the H V basis there are two possible outcomes both vertical and both horizontal Each occurs half of the time We could instead measure the polarizations with polarizers rotated by an angle a We use the rotated polarization basis V cosa V sina H 2 H sina V cosa H Here v describes a state with polarization rotated by a from the vertical while H describes a state with polarization rotated by a from the horizontal In this basis the entangled state is V HH He 3 Clearly if we measure in this rotated basis we obtain the same results half of the time both are v and half of the time both are H
22. s correct by calculating Bell s Inequality in a form of Clauser Horne Shimony and Holt 4 7 In the previous activity we saw evidence of entanglement In this activity we will try to perform a mathematical check by violating Bell s Inequality Look at the Refs 7 9 11 for an explanation of Bell s inequality The maximum possible value of S in Bell s Inequality is always less than 2 for any classical correlation Getting a value greater than 2 for S would 24 confirm the violation of this inequality S is defined as follows 4 7 S E a b E a b E a b E a b 7 We will calculate the value of S for rape ENE 8 N a B N B N B N Q f N a B is the coincidence count when Polarizer A is at a and Polarizer B is at B 1 2 OAU Set the Labview program for a measurement time of 20 seconds or 20000 ms Switch the lights off Make sure that the door is locked Make sure that the laser is off Ask the TA to switch on the APDs Put Polarizer A at a 45 and Polarizer B at B 22 5 Record the coincidence count by hitting START in the Labview program and note it down in Table 4 Repeat this until you have collected data for all of the Table 4 Finally Put a 0 R 90 and note down the coincidence count Subtract this count from each coincidence reading of Table 4 Ideally you should get 0 counts for this setting of polariz
23. s spontaneous parametric down conversion 4 Make a sketch of your experimental setup and describe its main components 5 For what purpose do you need a quartz plate 6 What are single photon counting avalanche photodiode modules How to work with them without damaging these detectors 7 What are Bell s inequalities Can you calculate them for some classical objects References and recommended literature 1 2 3 10 4 12 13 14 M Fox Quantum Optics An Introduction Oxford University Press 2006 A M Rae Quantum Mechanics loP Publ 2002 G Greenstein and A G Zajonc The Quantum Challenge Jones and Bartlett Publ Boston 2006 P G Kwiat K Mattle H Weinfurter A Zeilinger New high intensity source of polarization entangled photon pairs Phys Rev Lett 75 4337 1995 D N Klyshko Photons and Nonlinear Optics New York Gordon and Breach 1988 P G Kwiat E Waks A G White I Appelbaum P H Eberhand Ultrabright source of polarization entangled photons Phys Rev A 60 R773 1999 D Dehlinger and M W Mitchell Entangled photons nonlocality and Bell inequalities in the undergraduate laboratory Am J Phys 70 903 2002 D Dehlinger and M W Mitchell Entangled photon apparatus for the undergraduate laboratory Am J Phys 70 898 2002 J S Bell Soeakable and Unspeakable in Quantum Mechanics Cambridge Univer
24. sity Press 2004 J Eberly Bell inequalities and quantum mechanics Amer J Phys 70 3 286 March 2002 M A Nielsen I L Chuang Quantum Computation and Quantum Information Cambridge University Press 2000 pp 111 117 N Boeuf D Branning Chaperot E Dauler S Gu rin G Jaeger A Muller A Migdall Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals Opt Eng 39 4 1016 1024 April 2000 http physics nist gov Divisions Div844 facilities cprad index html contents BeamLok 2060 and 2080 Ion Lasers User s Manual Spectra Physics Model 587 Z Lok Etalon and Model 5870 Controller Users Manual Spectra Physics 1 INTRODUCTION The purpose of this laboratory work is to introduce students to entanglement one of the key concepts of quantum mechanics While the concept of entanglement defies the classical intuition in this lab you will gain a better understanding of entangled particles and experimentally verify the predictions of quantum theory If two particles A and B are entangled their wave functions cannot be separated The particles cannot be represented or talked about individually Any measurement performed on A would change the state of B and vice versa no matter how far apart A and B may be The idea is illustrated in the cartoon below There is no classical explanation for this phenomenon Entangled Entangled pA A B A B Figure 1
25. t will exceed 40A During routine start up start the system with BeamLok enabled with the laser output aperture in open position This keeps the output beam aligned while the laser is warming up 2 b BeamLok system 13 14 The BeamLok system provides an automatic means of holding the output beam on a fixed reference point The system consists of an actuator beam position detector and a remote control module When BeamLok is on the beam position detector senses any change in beam position and adjusts the output coupler to compensate When the laser is in power mode BeamLok actively controls both output power and beam position BeamLok will disengage when there is insufficient laser output power to drive it Simply increase output power to relock it onto the beam Beam Lok is controlled through the Model 2474 remote control module The remote controle module has a push button and an indicator a low signal indicator and a x y display The push button in the lower left corner of the remote module has been included for future system enhancements It is not functional at this time c Shutdown procedure 13 14 1 Turn off the key switch 2 Remove the key Do not leave the laser accessible to people who are untrained in laser safety or operation If you leave the main power on the laser will return to the operating condition it was in before shutdown 3 After allowing the unit to cool down for 15 minutes turn off the
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