Quantum Interference & Entanglement
From Physics 111-Lab Wiki
Quantum Interference & Entanglement Description (QIE)
- Pre-requisites: Physics 137A
- Days Alloted for the Experiment: 5
- Sign-up for consecutive days preferential, maximally one break is allowed after day 2 or 3.
Attention: There is NO eating or drinking in the 111-Lab anywhere, except in rooms 282 & 286 LeConte on the bench with the BLUE stripe around it. Thank You, the Staff.
This lab will be graded 30% on theory, 40% on technique, and 30% on analysis. For more information, see the Advanced Lab Syllabus.
Comments: E-mail Don Orlando
Quantum Interference & Entanglement Pictures
Quantum Interference & Entanglement Experiment Click for larger picture
Before the Lab
Complete the following before your experiment's scheduled start date:
- There is no video as of yet for this experiment. Read the references    below.
- Read the Optics Tutorial, in particular the pdf files from CVI Melles Griot. The sections that are especially relevant to this experiment are Polarization and Waveplates (near the end of Fundamental Optics), Optical Coatings (all of our waveplates have antireflection coatings), and Intro to Laser Technology.
- Complete the training for the safe use of lasers detailed on the Laser Safety Training page. This includes readings, watching a video, taking a quiz, and filling out a form.
- Print and fill out the Pre-Lab, Mid-Lab and QIE Evaluation QIE Pre Lab and Evaluation. The pre-lab must be printed separately. Discuss the experiment and pre-lab questions with any faculty member or GSI and get it signed off by that faculty member or GSI. Turn in the signed Pre-lab, Mid-Lab, and QIE Evaluation sheet with your lab report.
You should keep a laboratory notebook. The notebook should contain a detailed record of everything that was done and how/why it was done, as well as all of the data and analysis, also with plenty of how/why entries. This will aid you when you write your report.
Other References [Physics 111 Library Site]
This experiment tests the validity of quantum mechanics against local hidden variable theories in describing entanglement phenomena. It takes the form of a quantum optics experiment using polarization-entangled photon pairs.
Bell's Theorem and the CHSH Inequality
John Bell showed that any theory in which properties are local and are well-defined prior to measurement must obey certain limitations. Interestingly, quantum mechanics exceeds those limits set by these so-called Bell-inqualities. Therefore, observing that nature does exceed these limits makes a good case for quantum mechanics and proves that there exists no local realistic theory that can describe nature accurately. One particular version of the Bell's theorem is the so-called CHSH inequality (named after Clauser, Horne, Shimony, and Holt). To make the discussion more concrete, we will assume a photon source that sends two photons to each of two distant locations. The degree-of-freedom we will study is the polarization of these photons. We will be interested only in events where the polarization of both photons has been detected successfully. First let us define the parity of the polarization correlations:
where Nvv is the number (or rate) of coincidences where both photons are vertically polarized, etc. E can range from -1, meaning that all photon coincidences have opposite polarizations, to 1, meaning they all have the same polarization. Let us then define the quantity, S, which is function of four distinct E measurements.
where α and β are the angles in which we are going to analyse the polarization of each photon. The interest of defining the quantity S is that local realistic theories are always bound to yield |S| ≤ 2, while quantum mechanics allows values of up to 2√2 ≈ 2.8.
At first glance, it would seem that S could range from –4 to 4. However, a careful inspection of the physics reveals that no two pairs of angles (α,α') and (β,β') give a value this large. If the system obeys a local hidden variable theory, then S is restricted by the CHSH inequality: |S| ≤ 2. However, quantum mechanics predicts that |S| can be as high as 2√2 for particular quantum states of the two photons and as well as carefully choosen angles. (For a full derivation, see CHSH's paper.) The goal of this experiment is to violate the CHSH inequality, thereby rejecting local hidden variable theories and affirming the validity of quantum mechanics.
The heart of the experiment is the generation of a particular entangled quantum state of the polarization of two individual photons, a Bell state. In the simplest case, this is a superposition state of both photons beeing either horizontally or vertically polarized. In the experiment, we achieve this by sending photons near 405 nm from a diode laser to a pair of non-linear crystals made of beta barium borate (BBO chrystal). Within the non-linear crystals the violet photon can decay into a pair of red photons with their polarization being determined by the optical axes of the non-linear crystals. The photon pair emitted under a small angle is then detected after passing through polarization optics with an avalanche photodiode. Finding two detectors firing within a short time interval indicates that these events were indeed caused by a photon pair and not stray light.
When you enter the room, you'll notice there are two boxes on the table. These each house different elements of the experiment. The one closer to do the door(Box 1) holds the laser and optical elements for creating a Bell State. The one closest to the computer (Box 2) holds the detection setup. When aligning the laser it is best to take the top off both boxes and use the protective orange glasses when the laser is on. When taking data, you will want easy access to the half wave plates in the detector setup, so you can leave the top off of box 2. Ambient light will flood the detectors, so you will want the lights off in the room (computer light is ok). There is an LED lamp (can you think why we use blue LEDs? hint: you can look at the APD efficiency versus wavelength in the manual if you are interested.) installed so that you can read the values off of the half wave plates in the detector setup. The on switch for the lamp can be found on the back side of the table on the rack above. While taking data, it is ok to not wear the orange glasses as long as the top to box 1 is in place. Inside Box 1, the laser has a power of around 120 mW. At 405nm, this can seriously damage your eye. However, in box 2 the power is down to about .2 mW, which will not cause serious damage. Of course you should avoid looking directly into the beam. This setup makes collecting data efficient.
The experiment is powered by a 120-mW, 405-nm violet laser diode, the same wavelength used by Blu-ray Disc™ players. This is a Class 3B laser and can cause permanent eye damage if the beam directly enters the eye. DO NOT REMOVE THE 405 BANDSTOP FILTER AT THE END OF DOWNCONVERSION SOURCE (BBO-CHRYSTALS) OR THE ORANGE BEAM ENCLOSURES THAT PREVENT STRAY REFLECTIONS FROM LEAVING THE BEAM PATH. Orange protective goggles are available by the door.
Because this is a laser diode, all the photons in the beam have the same polarization, in this case horizontal. The laser beam incident on the BBOs (i.e., after the intermediate optics) is sometimes referred to as the "pump" beam.
The laser diode is powered by a Thorlabs LDC205C laser diode controller, located on top of the optical bench roof. Turn the controller on with the switch in the lower left corner. We run the laser diode in constant current mode and cathode ground (CG) polarity. You will want to view the laser diode current, ILD. To operate the diode, use the button in the upper right corner to turn it on and turn the knob to control the current. Any time the laser diode is on, the light on the QIE room door will be flashing red. The current limit is set to 100 mA to avoid burning out the diode. If you reach this limit, the controller will beep, the red "LIMIT" LED will turn on, and you will not be able to increase the current further. However, it is okay to run the laser diode at its maximum current.
Right after the laser diode, there is an optical isolator which prevents light reflected further down stream from going back into the diode. Isolators are used to reduce or eliminate the effects of optical feedback: reflections of a laser’s energy back into itself. These effects include noise, amplitude fluctuation, and laser damage. Isolators protect the laser, while maintaining beam alignment and providing maximum forward transmission and reverse isolation. Laser light inters the isolator via the input polarizer and is linearly polarized. This light then enters the rotator, which rotates the plane of polarization +45°. The beam exits through the output polarizer, whose axis is oriented +45°.
The isolator used is supposed to have a transmission efficiency of 84%. It is worth while to check for yourself (using a power meter before and after the isolator) to see if the efficiency is at least close to the expected. If it is not, you may need to realign the polarization optics. It is unlikely you need to do this, but if you do, 1) Loosen the cap screw holding the isolator in the slip ring. (in the side facing away from the laser diode). 2) Rotate the isolator until transmission is maximized. This occurs when the input polarizer is aligned to the laser’s plane of polarization. Lock down the slip ring cap screw.
To monitor the behavior of the laser diode, every student is asked to measure the 405 nm laser light power as a function of the supplied current. Use a power meter (ask the staff if you cannot find it in the room. The meter is shared among many experiments.) Start from 0 mA (or the lowest you can get) and measure the power of 405 nm laser light right after the optical isolator. Make sure the wavelength setting of the power meter is set to 405 nm (why?). Measure up to 100 mA. Include the plot in your lab report.
The beam passes through some optics (two steering mirrors, two wave plates, and an iris—see alignment) before reaching the pair of nonlinear beta barium borate (β-BaB2O4 or just BBO) crystals. When a pump photon of a particular polarization enters such a BBO crystal, it can be converted into two photons each with (about) half the initial energy of the pump photon (and twice the wavelength = 810 nm). These photons exit the crystal symmetrically at a small angle. Often those photons referred to as the "signal" and "idler" photons, but we can just as well call them the A and B photons, referring to the two arms of the detection setup along which they will travel. Most importantly, their polarization is entangled, meaning that the photons are guaranteed to have (in this case) the same polarization.
Note that the two beams of the down-converted photons will not be visible to the naked eye because (1) the wavelength of 810-nm photons are infrared and (2) the beams are extremely low-power as the conversion efficiency of the crystals is quite small. (Think about how much power ~1,000 photons per second correspond to and compare this to the laser diode power rating.)
Each BBO only down-converts photons of a single polarization. BBO-1 (farther from detectors) is fixed such that it down-converts horizontally polarized pump photons into two vertically polarized photons. BBO-2 (closer to detectors) can be rotated: 0° means the down-conversion axes of the two BBOs are parallel and 90° means they are perpendicular. Because the rotation axis of the 2nd BBOs is slightly titled with respect to its plane, check both 90° and 270°. As of Oct 2014 90° seems to work much better.
Because the separation between the BBOs is so small, the down-converted photons from each BBO essentially travel along the same cone to the detectors. This means that the horizontally polarized pairs are indistinguishable from the vertically polarized pairs until we perform a polarization measurement on them. In a quantum mechanical picture, each pair of down-converted photons is in a superposition of vertical and horizontal polarization until a measurement collapses the wavefunction into one state or the other. The evolution of the quantum state of the system from emission to down-conversion is summarized below in bra-ket notation with the assumption that the BBOs are perpendicular. H and V refer to horizontally and vertically polarized states of a pump photon, respectively, and h and v refer to horizontally and vertically polarized states of a down-converted photon. hh and vv are short for the combined state of a pair of down-converted photons, and φ is the polarization angle of the pump beam.
The probability of detecting a given polarization depends on the polarization of the pump laser. You can adjust the polarization of the pump laser by rotating the 405-nm half-wave plate located between the two steering mirrors.
We have installed a 405-nm band-stop filter after the BBOs for laser safety reasons. Although approximately 50 mW of power are incident on the BBOs, the filter attenuates this to less than 1 mW. This power can be viewed safely in order to align the detection components. Therefore you do not need to wear laser safety goggles if this band-stop filter is installed AND no pump light is leaking out of encased area before the band-stop.
The detection setup consists of two identical arms separated by a small angle. The angle can be adjusted to match the trajectory of the down-converted photons and should be centered around the violet laser beam.
Each of our detectors consists of a small fiber coupler (FC) lens, which focuses the light into an optical fiber. The optical fiber runs from the lens to an avalanche photodiode (APD), which converts single photons into sizable (~1 V) electronic pulses. They can detect anywhere from hundreds of photons to tens of millions of photons per second. The APDs are powered by a homemade power supply, located above the APDs on the optical bench roof. The power supply has a master on/off switch and four switches to turn the APDs on and off individually. An alarm within the APD power supply will alert you if you are overloading the APDs. If you ever hear this, immediately turn off the APDs to prevent damage. Ambient light conditions are typically okay as long as you do not remove the long-pass filter on the detectors while the APDs are on. Note, however, that this alarm sounds for several seconds every time the APDs are turned on. This is normal.
To measure the polarization of the photon pairs, each detection arm has a half-wave plate to set the measurement basis and a polarizing beam splitter cube. The beam splitter allows horizontally polarized light to pass and reflects vertically polarized light out at 90°. This setup only allows photons to reach a given detector if they have a certain polarization (or, equivalently, their arrival at a given detector means that their wavefunctions have collapsed into a given polarization state). In other words, the beam splitter makes the horizontally polarized photons distinguishable from the vertically polarized photons. Please note that might be an arbitrary offset between the reading on the mounts for the half-wave plates and the actual direction of the optical axis of the half-wave plate. At the time of writing, the half wave plates for detectors A and B are rotated 90 degrees relative to each other when the half wave plate for A is set to 128 degrees and the half wave plate for B is set to 140 degrees. If you suspect these measurements are wrong, check for yourself using two linearly polarizers, which can be found on the table.
Signals from the APDs are sent to a field-programmable gate array (FPGA) [Altera DE-2] that has been programmed to calculate coincidences. A coincidence is the arrival of two photons at different detectors within a short coincidence window, typically 5 ns for our setup. The FPGA sends photon counts for each detector and coincidence counts for each pair of detectors to LabVIEW, which displays the data on the thermometer-like indicators on the front panel. These data can be used to calculate S.
Proper Start-up Procedure
Due to the idiosyncrasies of our software, it is important to follow these steps in the correct order:
- Turn on the computer and log in.
- Turn on the FPGA.
- Run the LabVIEW program (latest version:
C:\QIE_Counter\QIE Counter.exe, see using LabVIEW).
If you turn the FPGA on before the computer, you may not be able to use the mouse. If you run LabVIEW before turning on the FPGA, you will get an error message.
The APDs can be turned on and off at any time, but you should be aware that turning them on while the lights are on influences your results (check this out). Therefore we encourage you not to turn the APDs on while the lights are turned on. It is usually best practice to turn on the main switch to the APD power supply (on the left) and then turn each APD on individually. This allows you to know which APD is overloaded should the alarm sound continuously. Remember that it is normal for the alarm to sound for a few seconds as each APD is switched on.
Because our detector apertures are only a few mm in diameter, proper alignment is essential to obtaining good data.
Violet Beam Path
Do not for any reason fiddle with the adjustment knobs on the BBO crystals. They should be aligned and when they are misaligned it creates problems that are very difficult to diagnose.
We are using an optical cage system between the laser diode and the BBOs to make alignment of this portion of the beam path fairly simple, as well as to ensure laser safety. The orange material around most of the beam path attenuates the laser power enough to be safely viewed by the naked eye but not so much as to obscure the view of the laser dot from the outside. If this material ever glows enough to add significant noise to your data, block the detectors' view of it with the black shields.
The following alignment procedure is based on height of the paper target behind the detector arms being correct. In theory, this target never needs to be moved or adjusted. However, if you notice that the target height seems drastically different than the height of the violet beam, you will need to adjust the target height to match. Ideally you would want to place the target directly in front of the BBOs and adjust its height until the violet dot hits its center. However, the detector arms will be in the way, making this a very difficult task. Therefore, do not mess with the target height unless absolutely necessary!
We want the beam of the violet laser to go through the center of both of the BBO crystals. To do this we want to define two points that form a line through the center of the BBO crystals. For this portion of the calibration you should be using your protective goggles. First, with the laser on, turn down the power to the violet laser using the knob on the laser diode controller. On the front face of the BBO's (the face closed to the detectors) there is a bandstop filter designed to filter out the violate light. Remove the filter. Do not turn the laser up too high now that the filter is removed as it could damage your vision. Next place one of the circular paper targets where the filter was. The center of the paper target will be one of the points we will be calibrating the first stage of the optics to.
The second point is a small collimator on the other side of the BBO crystals. It's very difficult to see, it is between the BBO crystals and the second mirror, close to the BBO's. There is a small lever to open and close the iris, it is labeled with an arrow pointing the direction to close the iris. For now leave the iris completely open.
Carefully turn up the power on the laser until it is faintly visible (without your glasses) on the paper target attached to the BBO's. If you don't see the dot from the laser at any power setting, the front two mirrors are completely misaligned. At this point it will be much easier to work without your glasses, but make sure the laser power is low enough that you won't damage your eyes and that you avoid looking down the beam path regardless.
Use the two turning mirrors to aim the beam down the center of the optical cage to the paper target behind the detectors. Because the first mirror is farther upstream, it is a finer adjustment to the beam spot's position on the iris. Use the first mirror to guide the beam through the iris, then use the second mirror to center the beam on the target. Repeat the process until you have the beam accurately centered on both the BBOs and the target. Once the laser is aligned, you can open the iris all the way or leave it partially closed as you see fit.
Important: at this point it is also wise to check the tilt of the quarter waveplate between the halfwave plate and the second mirror. Make sure that it is roughly perpendicular to the beam path. Angles greater than 45 degrees will limit your observable coincidence rates severely.
Potentially useful additional alignment details - Check to make sure that the laser spot coming out of the BBOs is a concentrated spot. It should not look like a line. If it does look like a line, you may need to adjust the focus of the laser. Only do this once you have tried realigning the mirrors. Adjust the focus by CAREFULLY removing the protective cover of the laser diode by unscrewing it from the front (it looks like a small black tube protruding from the black box that holds the laser diode). This will expose the lens, which can be focused by turning it. You should change the focus slowly while viewing the laser exiting the BBOs. Focus the laser to a spot as best as possible.
Infrared Beam Path
Align the components on each detector arm independently of the other arm using the following procedure. During this procedure, you will have to remove the optical fibers from the APDs. Make sure the APDs are turned off before you do this. Allowing ambient light to enter the APDs directly will overload them. Be careful not to clamp anything down on top of the optical fibers during alignment. They are fragile and expensive to replace. Along similar lines: don't pull on the jacket (the black cover), instead carefully wiggle on the metal connector itself to remove the fiber from the connection. In addition, make sure that you do not scratch the front facets. The fibers are really fragile and they are also expensive, so simply do not break them!
Goal will be to align the detectors such that they "look" at the BBO's where the entangled photon pairs are created. For this, we will send a test beam in the opposite direction through the fibers and the collimation optics and try to match the path of this test beam and the violet pump beam to each other. Note that the light needs to be focused into the core of a multi-mode fiber whose diameter is on the order of 100 μm. That means that precise alignment is critical.
- First we remove the beam splitter cubes, half-wave plates and both detectors A' and B' from the cage (note: in its current form, we are only using two detectors, so A' and B' should already be removed), leaving only the two detectors A and B. Remove the long-pass filters from the detectors.
- Remove the optical fiber from the APD and connect it to the red fiber testing laser (looks like a laser pointer). Turn on the test laser; the red beam should pass through the pinhole in the center of the screw-on target. The resulting red light cone (should be well collimated) represents all the light that will be collected by the detector in your experiment.
- By making small adjustments using either the screws on the back of the detector or your hand, your goal is to aim the test laser precisely at the center of the BBOs. You should use the irises to your advantage, keeping them open at first and then closing them to ensure a small spot focused directly on the center.
Old alignement procedure may be helpful, although out of date (shown below).
- First we remove the beam splitter cubes, half-wave plates and both detectors A' and B' from the cage (note: in its current form, we are only using two detectors, so A' and B' should already be removed), leaving only the two detectors A and B. Remove the long-pass filters from the detectors.
- Attach the screw on paper target to the detector A/B. Remove the optical fiber from the APD and connect it to the red fiber testing laser (looks like a laser pointer). Turn on the test laser; the red beam should pass through the pinhole in the center of the screw-on target. The resulting red light cone (do not expect it to be well collimated) represents all the light that will be collected by the detector in your experiment.
- Detector A/B Height: Swing the detector arm to the center so that the violet beam is centered horizontally on the target. First move the plate on which the detectors are mounted parallel to the back plate with the thumb screws on the back of the detectors. Later, this will allow you to adjust the angle of the detectors in all directions with the thumb screws. Then adjust the height of the detector so that the violet beam passes through the pinhole, i.e., the red and violet beams coincide. Later on, you might be able compensate for slight vertical misalignment by adjusting the second turning mirror to optimize count rates. However, it may be difficult to optimize this way for both detectors.
- Detector A/B Angle: Adjust the thumb screws on the back of the detector until the red circle is well centered on the BBOs. You can use a piece of white paper to see the beam if it helps. If necessary, you can also adjust the thumb screws on the BBOs so that the back-reflection of the red circle is centered on the detector aperture. These thumb screws move both BBOs together. However, it may be difficult to align this back reflection for both arms.
- Remove the screw-on target from the detector. Replace the long-pass filters on each detector and reconnect the optical fibers to their corresponding APDs. Make sure when reconnecting the fibers that the notch on the connector is lined up correctly. You will not be able to insert the fiber all the way in if it is not aligned, meaning light could possibly leak in and out.
Detection Arm Angle
Using the fact that the laser beam exits the diode polarized within a few degrees of horizontal and that the 405-nm half-wave plate is miscalibrated such that a reading of 40° means that the optical axis is vertical, adjust the half-wave plate so that the BBOs, set at 270°, will down-convert as many photons as possible. We use 270° because this is the setup for the actual experiment. If you have the detector half-wave plates set at the same angle as each other, the optimal angle for the detection arms will be the angle at which AB or A'B' coincidences are maximized. Use the micrometers to vary the angle of each arm until you find a setting that maximizes coincidences. Make a note of the exact readings, although you should not need to move these arms again.
Questions: Under which angle do you expect a maximum of the red-photon counts on single arm? Is there a chance to observe coincidences for any pair of angles?
Having successfully answered the above question you should quickly find substantial coincidence rates above 50 counts/s. Now you may want to try to enhance the coincidence rate by changing the angles of the detectors.
Inserting the polarization analysing elements
The photons will be entangled in the polarization degree-of-freedom. Therefore, will will have to analyze the polarization with a combination of a polarizer (polarizing beam splitter cube) and a half-wave plate. For this you can either use the red alignment laser or swing the arms into the center such that you can use the blue beam as guidance.
- Cube Position: Insert the beam splitter with the front face (marked by a dot on top of the cube) towards the BBOs. (There is only one correct position for the dot.) Adjust its position and height so that the red beam passes roughly through the center of the back face.
- Cube Angle: Adjust the thumb screws on the cube mount so that the red back-reflection hits the center of the screw-on target. You maybe also use a piece of paper with a hole punched through to allow the laser to pass through instead of the screw-on target.
- Half-Wave Plate A/B: Insert the half-wave plate in front of the beam splitter. Adjust the position and angle with respect to the laser beam axis the same way as with the beam splitter.
For most settings of the halfwave plates, you should see already coincidences. However, you might want to reoptimize the angle settings of the detector arms. Why?
Producing a Bell State
A Bell state is a maximally entangled state of two qubits, namely
(Note that we can only produce the ψ states because our BBOs down-convert into pairs with like polarization.) Ideally, we would like each pair of down-converted photons in this experiment to be in a Bell state. However, many factors can contribute to deviations from perfect entanglement:
- pump beam not polarized at 45°
- phase shift due to BBOs
- separation between BBOs
- angle between BBOs
- different down-conversion efficiencies of BBOs
The first point is controlled by the 405-nm half-wave plate. You should have set this to output light polarized at 45° during the alignment procedure. However, now that the detector arms are positioned correctly, you should refine this setting using real-time data. If we assume detection efficiencies are equal between the two detectors, then you should be able to find the correct setting by equalizing coincidence measurements on AB and A'B'. This means you are outputting horizontally and vertically polarized photon pairs in equal numbers. Set both detector half wave plates to be in phase, then you can adjust the 405nm half-wave plate slightly around 45° to equalize the counts in detector A and B as best as possible.
A small phase shift between the horizontally and vertically polarized photon pairs can occur due to dispersion and birefringence in the BBOs. (You can also think of this as adding a slight elliptical polarization to linearly polarized light.) Let's say that instead of producing a perfect Bell state, the BBOs introduce a small relative phase shift δ:
This would decrease the number of coincidences when the detector half-wave plates are both set to 22.5°. To compensate for this, we need to delay one component of the pump beam by δ before it reaches the BBOs. We can do this with a birefringent crystal. We have chosen to use a quarter-wave plate rotated about the vertical (so that it functions as a less-than-quarter-wave plate). The quarter-wave plate is installed on a rotational mount with its optical axis parallel to the vertical. When the rotational mount reads 0°, the laser beam is perpendicular to the face of the wave plate. Rotate this wave plate such that you produce an ideal Bell state with δ = 0. For this you can choose particular settings of the halfwaveplates in the analysing paths or you can record the coincidences for a range of the two analyser half waveplate settings (see midlab question). However, note that the analysing halfwave plates might not be calibrated properly, i.e. a reading of 0 degrees might not correspond to the optical axis of the waveplate to be aligned in the same direction. If you suspect this, calibrate the offset in both waveplates by using a test laser and two orthogonally oriented polarizers.
The separation between the BBOs is small enough to be negligible, and as noted above, the angle between the BBOs is practically eliminated when the BBOs are at 270°. We cannot control the down-conversion efficiencies of the BBOs, but they should be very similar.
Before you go on, test the purity of your Bell state by mapping out the dependence of coincidence rates on the detector half-wave plate settings. To fully explore what's going on, you will need to make several plots. In particular, you should plot the coincidence rates and E as a function of the angle one of the two half-wave plates. To better understand what is going on, rotate the other analysing half-wave plate by a certain angle and repeat the measurement. Make sure you understand what you expect to see for each plot, and ask a GSI if you are unsure. If you find that you do not have a reasonable Bell state, use the plots you created to figure out which parameters need adjustment. Adjust these and retake the data until you create the state you are aiming at. Alignment adjustments can also help improve counts on detectors that seem to be missing photons.
Dehlinger and Mitchell is a good resource for tuning your Bell state. See section VI. Tuning the State.
What can you say from these measurements about the phase δ of the Bell state ? If unsure, use the little program you wrote for the prelab, plot the expected coincidence rate as a function of various angles α and β. Note that it will be absolutely crucial that you understand what is going on at this stage before you proceed.
Calculate the contrast (max(coincidences)-min(coincicdences))/(max(coincidences)-min(coincicdences)). What can you say from this about the purity and/or fidelity of your Bell state?
Note that although it is not strictly necessary to do this experiment in the dark, ambient lighting will only increase detector noise.
Violating Bell's Inequality
The actual data can be taken using either a two-detector or a four-detector setup. In the two-detector setup, the beam splitters are just used as polarizers and there is only one coincidence rate: AB. It is simpler to align, and detector efficiencies do not affect the data. However, because it can only detect one polarization on each arm, you must record data for 16 different settings to calculate S. The four-detector setup would a full polarization analysis of the down-converted photons, which can be helpful in understanding the physics of the detection setup, exploring the dependence of the data on wave plate settings, and troubleshooting the equipment when your results are not as expected. Furthermore, only four settings are necessary to calculate S. However, four different detector efficiencies make analysis a bit more complicated. We suggest that you begin with the two-detector setup. It is easier this way to tune the Bell state and the results will be better (due to the efficiency problem).
In the two-detector setup, four angle pairs are needed for each E measurement. (The E Meter in LabVIEW will be meaningless if four detectors are not used.) You essentially need to adjust the half-wave plates to redirect photons to the A and B detectors that would otherwise have been reflected by the beam splitters. If you need help figuring out which angle pairs to use, see the paper by Dehlinger and Mitchell, which describes this experiment with only two detectors.
At this point it is not recommended to try the four-detector setup.
In the four-detector setup, each angle pair corresponds to one measurement of E. Therefore, only four pairs of angles (two settings for α and two for β) are needed to calculate S. In order to achieve maximal violation of the CHSH inequality, i.e. S ≈ 2.8, you need to choose angles such that |β + α| = 11.25° and |β´ – α´| = 11.25° and (α´ – α) = (β´ – β) = 22.5° (e.g. [α / β]=[11.25/0],[11.25/-22.5],[-11.25/0],[-11.25/-22.5]). Make sure you read the correct angles. You should verify that these are the optimal angles yourself, which can be easily done using only basic quantum mechanics.
Using the LabVIEW Program
The most recent version of the LabVIEW program is
C:QIE_Counter\QIE Counter.exe. Make sure the FPGA is powered on before you run LabVIEW or you will get an error message. Upon running the vi, you should see the front panel below.
Count Rate Indicators
If you have the APDs powered on, the first thing you will notice is the eight large "thermometer" indicators. These display count rates on each of the four detectors (at left) and coincidence rates for each pair of detectors (at right). The count rates are calculated by dividing the raw counts from each of the FPGA registers, shown in a column vector at the bottom of the screen, by the update period, controlled in the General Settings box.
Below the coincidence rates are the accidental rates, calculated using the coincidence resolution controls on the following line. You should have derived the formula for this calculation in the pre-lab. The values in the coincidence resolution array may or may not agree with the actual coincidence window used by the FPGA. This is controlled by a physical switch on the FPGA, but it also tends to drift from its nominal value. Keep in mind that the accidental rates are only as accurate as the coincidence resolutions.
To the left of the coincidence resolutions is the E Meter. E is calculated as described in the introduction. Note that E can only be calculated if all four detectors are being used simultaneously.
To the left of the E Meter are the Raw Counts indicators. You can verify that the count rates are indeed the raw counts divided by the update period.
In the upper left corner, you will see the status indicators. The text box has five possible values:
- LabVIEW is starting up and connecting to the FPGA.
- Reading Counters...
- LabVIEW is waiting for one Update Period to elapse.
- Updated Counts
- LabVIEW has read the FPGA registers and recalculated count rates. The green rectangle flashes once each time this occurs.
- Closing Program...
- You have clicked the Stop Program button.
- Program Terminated.
- The vi is not running.
"Counter Port" should be set to COM1 in order to connect to the FPGA.
"Update Period" controls how long LabVIEW will wait between buffer reads. In other words, it will count photons for this amount of time and then display the resulting count rates.
The "Subtract Accidental Counts?" button toggles whether or not LabVIEW will subtract the values in the "Accidental Rates" array from their respective coincidence rates. Note that there is a lag time of one cycle between when you click this button and when LabVIEW actually starts subtracting.
The "Round Count Rates in Display?" button toggles rounding in the eight thermometer indicators. This can be useful because dividing by the update period often gives fractional count rates. Note that this function also exhibits a lag time of one cycle.
Snapshots allow you to take data points and save them to a file. "Snapshot Duration" is the length of time, in seconds, of the snapshot. You also have the option to enter angles for half-wave plates A and B and a comment, which will be saved with the snapshot. When you click "Take Snapshot" for the first time, a new window will pop up displaying the data you have taken. Each subsequent time you click "Take Snapshot," a row will be added to the new window. When you are done taking snapshots, click "Save Snapshots" in the main window. To clear the pop-up window for a new set of snapshots, click "Clear All."
To avoid any false coincidences we suggest that you turn off the lights and monitor before taking snapshots. If your duration is longer than three seconds, it's easier to use some kind of timer, for instance http://www.timeanddate.com/timer/# .
After the Experiment
Make sure all of the following equipment is powered down at the end of each day:
- laser controller
- APD power supply (turn all five switches off)
- computer, monitor, speakers
- room lights
Double slit quantum eraser
Before conducting the quantum eraser experiment as described by Walborn et al , you should perform a single photon double slit experiment. For this you only need to consider detector A. Please follow the steps to align the beam path.
- Center detector A by turning the micrometer to 0 mm and using the inch micrometer (from now on called inchmeter) and screw-on target. Take notice of the position of the inchmeter.
- Mount an iris onto the black optical board and align it so the violet beams passes the iris when closed.
- Remove the screw-on target and carefully screw the 200 μm slit on top of the 800 nm bandwidth filter. (There is one particular filter which has been set further into the black tube.) Screw the filter with the slit back on detector A as far as possible with the slit being vertically aligned.
- Use the micrometer to find the ideal position of the detector. Take a few measurements (10s each) and then fit a Gaussian.
- Put the micrometer to the position of the calculated peak and adjust the angle until you reach the highest possible count rate. The iris in front of the BBOs should be closed and the one downstream opened.
- Center your detector again (micrometer should read 0 mm) and put the double slit right behind the iris. You should use the 0.100 mm slit width. Make sure the double slit slide is not angled. Take a piece of paper and observe the interference pattern you should be able to see.
- Put the detector arm back into the position for the 810 nm photons. You might need to slightly adjust the position of the double slit with the turning knob. The count rate should exceed 1000 s - 1. Both irises should be closed.
- Open the iris in front of the double slit until it reaches a diameter of about 1.5 mm. You should now detect more than 2000 photons per second.
Now you are able to conduct a double slit experiment and verify the theoretical interference pattern (curve). Use the inchmeter to take measurements at different positions. Think about the number of measurements you should take and about the snapshot duration. (Ten seconds are definitely not enough!)
Ask your GSI if the quarter wave plate for the Quantum Eraser has been cut and is ready to use. If this is the case, try to reproduce the results of the Walborn et al Quantum Eraser experiment.
Insufficient single photon counts in each detector (<10k/s)
- enough blue laser power? You should have at least 35 mW (corresponds to about 50 mW at the laser diode) reasonably well collimated and focused after the BBO's before the band stop. If you decide to measure this power please consult the staff because there are safety concerns.
- Are the detectors properly aligned?
- Are the fibers inserted properly into their connectors? The image from the fiber tester at the BBO should be at most twice as large as the BBOs. If his is not the case most likely you have not inserted the fibers correctly into the detector port. Gently rotate the fiber till the notches on the fiber connector line up with the detector port and the connector slides into the port.
Low or no coincidence counts (<100/s without polarization analysis):
- Is half wave plate between the steering mirrors rotated by a reasonable angle? Angles > 45 degrees can distort the blue beam and thus limit the number of coincidences severely.
Vastly different coincidence counts for VV and HH even though the blue polarization is set properly.
- Are the two BBO's parallel to each other?
Coincidence rates as a function of the angle of the measurement basis make no sense
- are you using halfwave plates for 800 nm or 400 nm to rotate the measurement basis?
- ↑ 1.0 1.1 1.2 D. Dehlinger and M.W. Mitchell, "Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory", Am. J. Phys. 70(9),903-910 (2002).
- ↑ J.S. Bell, "On the Einstein Podolsky Roden paradox".
- ↑ 3.0 3.1 J.F. Clauser, M.A. Horne, A. Shimony and R.A. Holt, "Proposed experiment to test local hidden-variable theories", Phys. Rev. Lett. 23, 880 (1969).
- ↑ S. P. Walborn, M. O. Terra Cunha, S. Pádua and C. H. Monken, "Double-slit quantum eraser", Phys. Rev. A 65, 033818 (2002).