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Sat Jul 20, 2013, 04:16 PM

Quantum Entanglement, Dark Counts, Coincidence Detection [View all]

A while ago, there was a discussion here during which I made the claim that the Copenhagen Interpretation of quantum mechanics sucks balls. Also as a consequence of that discussion, I started working on an experiment similar to that of Dr. John Cramer of the University of Washington that has the goals of first, demonstrating communication using entanglement, then extending it to demonstrate retrocausal effects.

Recently I e-mailed Cramer to see how his experiment was going, and he said that he was having trouble with the dark counts of his detectors. What this means is that the avalanche photon detectors register a number of false detections of photons, measured in counts per second. This, according to Cramer, was swamping the real detections of photons and burying the signal in noise.

Also, I read a book called Exploring Quantum Physics through Hands-on Projects which gets into entanglement near the back. I e-mail the authors about detection rates and such, and they said that if the optics were aligned just right, I could get around 200 coincidence detections per second. What's happening is that some small number of photons from the pump beam are converted to infrared photons and emitted in a cone of about 5 degrees around the pump. Some percentage of those are entangled pairs, on opposite sides of the cone, and by detecting two photons at the same time - coincidence - one is filtering out just entangled pairs.

What I'm trying to understand is which such a low coincidence count? With Cramer's setup, he should be generating around a million entangled photons per second. The detectors I want to get have a dark count of 250, although there are other versions with 1000, or 2000, and well as lower dark-count detectors. They have about 70% efficiency in detecting photons. According to the book, about 6*10^4 entangled pairs per mW of pump power are created per second. That means that 15 million pairs are created per second.

Photons will be picked off from opposing sides of the cone where the wavelengths of the two photons are equal (810nm with a 405nm pump). Assuming one degree is filtered out on each side, that's 41667 photons per second on each side. Forty friggin' thousand! I would think that the coincidence counts, even given the inefficiencies of the detectors, would be many times the 200 quoted by the authors that I e-mailed. So am I stupid? Is there something major I'm missing here? Hopefully in DU's userbase of 200k, someone will have the answer as to why I'm an idiot.


Now, to describe more about the experiment:

What Cramer is trying to do is kind of an extension of an experiment done by Birgit Dopfer or Austria in 1998. In that, two beams containing entangled photons were generated and one beam was sent through a classic double-slit, and the other beam went to a lens and detector:




The beam going through the double-slit creates an interference pattern on the other side: each photon goes through both slits since they are in a superposition state with respect to their momentum, and the quantum waves from the slits interfere with each other. However, is any measurement is made on which slit a each photon goes through, the interference pattern is destoryed - the superposition state is destroyed. Dopfer made a measurement on the other beam of photons that didn't go through the double slit but were entangled with the photons that did, and this also destroyed the interference pattern. The coincidence detector filters out only entangled pairs of photons, so that unentangled, single photons are not counted.

Instead of using a double slit, which sinply blocks the vast majority of photons, Cramer is using a Mach-Zehnder interferometer and so am I:



What happens here is that a laser beam is fed in at the left and hits a beam splitter. Each photon is BOTH reflected and transmitted (superposition again), hit both of the two mirrors which reflect it to the second beam splitter, or recombiner in this case. From that second beam splitter, the photons recombine with themselves, then go out of one of the two outputs of the beam splitter. Two interference patterns are generated. I've made a couple of these and am currently redesigning the mounts for the optics to make it easier to tune the interferometer to get the path lengths equal and to adjust the beam angles so that I get more or fewer interference fringes.

The outputs directly from the beam splitter look just like laser beams - they're tight, pencil-like threads of light. Only by spreading them out with lenses can I actually see the interference patterns. Without the lenses, the beam widths are like the original laser beam - about 1/8th inch diameter. The detectors have an active area of about 1/5th of a millimeter, so a good amount of light will miss the detector. There should still be a lot more than 200 per second. I plan to use a couple of galvanometers to adjust the beam angle in two dimensions so that I can scan out the interference pattern on the detectors. I have a pair of galvos and will get a couple more pairs. They're really cheap on Ebay and I got some a while ago to do laser animation.

The first beam splitter will be implemented as a mirror that reflects the bottom half of the beam. Since position of a photon within the laser beam (or downconverted, infrared beam) is in a state of superposition, again the photons will both be reflected and transmitted. The other beam with the other entangled photons can also be split this way, and the momentum/position entanglement of the two beams will them be maintained. By making the information as to the momentum of each photon available, even just in principle, the superposition state will be destroyed and thus, the interference patterns from the Mach-Zehnder interferometers will be altered. Only a percentage of photons in each beam are part of the entangled pairs (I think 20%-30%), and the unentangled photons will continue to make interference patterns. However, some parts of those patters should have very few photons hitting them, ideally zero, and when the entangled photons are knocked out of superposition, they won't make nice interference patterns but rather just blobs of light. So it should be possible to detect more photons in the normally dark parts of the patterns. Thus, it should be possible to send information using entanglement.

The really strange and cool part of this whole experiment is that it should be possible to delay the measurement of momentum of the entangled beam - the one not going through the interferometer - simply by moving the beam splitter for it and the detector further away from the BBO crystal that downconverts the pump beam. The decision to focus the two beams from the splitter to the same spot or not, which determines whether photons are allowed to stay in momentum-superposition or not, can be made after detection of the interference pattern. In this way, it should be possible to send information backwards in time slightly. An enhancement would be to split the entangled beam and send both halves into separate fiber optics, then focus the outputs onto a detector or not after the fibers, thus delaying the measurement by a lot more. This should allow for a delay of around 50 microseconds which isn't a lot, but it's enough that digital electronics can do something interesting with the data before using it to determine whether to maintain or destroy the interference pattern, thus sending the data back again 50uS.

Anyway, I'm just about to buy the BBO crystal set and the detectors. I really do want to know if somehow, I'm stupid in my calculations as to how many entangled photons should be detected. Also, I need to get to work on these optics mounts this weekend.

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