Troubleshooting

Here we describe a few tips for future MXP students who may be conducting Hardy's Test again. This is also where we elaborate on a few of our theories as far as what may have gone wrong in our iteration of the test.

Detector alignment:

We had to replace our BBO multiple times in the last few weeks of the project, and went through several cycles of realigning our detectors. In the end our detector alignment was pretty good, but we did not have the time to risk making large adjustments to our alignment to try to make the alignment closer to perfect. Minor issues in detector alignment could have contributed to our failure to get results, and looking into this further is one of the main things we would have done if we had significantly more time.

The main reason we're mentioning this here is to go over some of the nuance we noticed later on after realigning many times, that may have helped us align a lot more consistently.

This is not a comprehensive overview of the alignment procedure for any of the parts of our project. The main reference for that should be the alignment page.

The BBO crystals produce entangled photons in a cone, with photons on opposite ends of the cone being paired with each other. If a detector is roughly in the correct position, then horizontal adjustment will help the detector be more centered on the cone, and vertical adjustment will move it along the cone and help it correspond to another detector's location better. This is the reason why the alignment procedure emphasizes maximizing coincidence rates instead of raw for detectors B, C, and D. When initially aligning detector A there isn't another detector to match to, so the important thing is to get the detector as close to level with the pump beam as you can, which will make alignment of the other detectors easier. Of note, the collimators have fine adjustment knobs for horizontal and vertical position. If one of the collimators has a broken vertical adjustment knob it should be used for detector A as it is the detector for which it is least important.

Attenuation:

One of the first steps in attempting to acquire a Hardy state is configuring the waveplates in front of the polarizing beam splitters so as to get all horizontally polarized photons to go to detectors A and B and all the vertically polarized photons to go to detectors C and D (or A' and B'), then adjusting the polarization of the pump beam to get a 1:4 ratio of AB (horizontal photon) coincidences to CD (vertical photon) coincidences. If, however, detector D were half as efficient as the other detectors, in that it noticed only half of the photons that hit it, then in setting a 1:4 ratio between AB:CD coincidences you would be setting a 1:8 ratio between actual incoming paired horizontal photons and paired vertical photons. Since the thing that we're trying to calibrate is the configuration of the pump beam, the ratio of horizontal and vertical photons coming out should be significantly more important than the portion of the photons that our detectors detect.

Our working theory on how to remedy this potential problem is to put irises in front of various detectors to attenuate in a way that matches the rate of coincident photons. The important thing here is to make sure that the coincident photons being compared are from the same "group" of coincident photons for all the pairs being examined. One way to accomplish this is to set the detector half-wave plates so that detectors A and B only get horizontal photons note the rate of AB coincidences, then adjust the half-wave plate in the B arm by 45 degrees so that detector C (or B') gets only horizontal photons and then note the rate of AC coincidences. After doing the same thing for BD and CD coincidences, the rates can be compared to make decisions about attenuating detectors to more closely match coincidence rates. Ideally measurements should also be done for vertical photons and decisions should be based off of both. After attenuating, it may be worth checking the coincidence levels again to make sure they've improved. When we did this we found that the horizontal and vertical coincidences bunched slightly differently so we weren't able to level out both at the same time (this may have been due to issues in detector alignment, I am unsure), but we were able to get them pretty close.

As a point, attenuating in front of the detectors will not help make the BBO act as a single photon source like attenuating in the pump beam will. You still want most of your attenuation to be in the pump beam, this procedure is just for correction/calibration.

Bruteforce qwp angle:

In the course of the experiment, one of the aspects we understood least was the selection of the quarter wave plate angle, which is the angle that is set by rotating the face of the waveplate (tilt is what we call the angle from top down).

Near the end, one of the things we attempted was using the 405nm HWP to acquire the correct ratio of horizontal and vertical photons without the quarter wave plate in place, then adding it in and adjusting the angle 180 degrees, stopping every 10 degrees to adjust the tilt to try to minimize AB coincidences in the θ_A2,θ_B2 configuration and record it. A graph of the outcomes of this is below. When using full angles for the 810nm HWPs (see description in next section) we found 2 minima from this, but the other probabilities that were supposed to be low were around 50%. When using half angles the AB coincidence rates were not responsive to tilt, and we weren't able to minimize AB coincidences enough to get usable values.

Figure 1: Graphs of the AB coincidence rates from the QWP angle sweep that was attempted. Note the difference in the scale of the y axis.

The next step in this vein that we would have attempted is setting an angle for the QWP, then setting the 405HWP for the correct ratio, then doing the tilt sweep to look for a minimum. The issue with this is that it would be much more time consuming, as we would have to set the 810nm HWPs twice for every measurement, and getting the right ratio of horizontal and vertical photons is also itself rather time consuming.

Half-angles vs full-angles:

One of the main parts of Hardy's test is measuring for certain angles of polarization at our detectors. To do this, heuristically, one should set the half wave plates to half of the relevant angle so that the correct angle gets mapped down to horizontal and goes through the polarizing beam splitter, but when we started having problems with our results, one of the things we tried was directly putting the relevant angles into the half-wave plates to hedge against the possibility that that is what was meant when the papers covering experiments of this type talked about measurement angles. From this point, almost everything we tried was repeated using full angles. While some of the results were interesting, this modification was largely ineffective, and we do not recommend any future groups attempt this.

We will proceed to go over some reasons why the full angle interpretation is likely incorrect.

• • In appendix A of the paper by Carlson, Olmstead, and Beck upon which this experiment is based [1], the angle θ is referred to as the angle at which a photon is polarized with respect to the horizontal. This is consistent with the angles θ being used to define half angles at which the HWPs should be set.

  • In section 3.1.1 of an undergraduate thesis by Peter Wills [2], Peter charts pairs of angles by their corresponding maximal violation. The chart only plots angles within a 90 degree arc, and if the angles were meant to represent half-wave plate angles, the behavior at 90 degrees would be identical to the behavior at 0 degrees, as rotating a half-wave plate by 90 degrees has no effect on polarization. The behavior at the extreme ends of the chart does not, however, match, and the angles θ are within the regions where H should be positive, while the angles 2θ are not.

References:

[1] J. A. Carlson, M. D. Olmstead, and M. Beck. Quantum mysteries tested: An experiment implementing Hardy’s test of local realism. American Journal of Physics, 74(3):180–186, 2006.

[2] Peter E. Wills. Hardy's test of local realism. Undergraduate thesis, Reed College, 2010.