Quantum Entanglement, Dark Counts, Coincidence Detection

[caraher]

11. Coincidence count rates from downconversion vary a LOT

I've done experiments where I've had over 100,000 coincidences/second and ones with a few hundred per second. A lot depends on exactly how you get the photons to your detectors, wavelength, pump powers, and exactly what your experiment is.

What detectors are you using? I have some "bare" Perkin-Elmer/Pacer SPCMs and those can a pain to work with because the active area of the detector is a square region about 180 microns on a side. Sounds like the same detectors you're looking at. This means you need to use a short focal length lens and you should have some way of translating either the lens or the detector transverse to the beam. I'd say you'd be very luck to get 200 coincidences per second without lenses in place. Bear in mind that a downconverted beam is not going to look like a collimated laser. The usual BBO crystal pairs companies like Newlight sell give you same-wavelength pairs that come out along a 3 degree cone, and that cone spreads with distance. That can be another big source of variability in detection rates - whether you do anything to collimate that beam. For most simple Bell Inequality test experiments it's not necessary.

Especially if you're a beginner, it's better to pay extra for the fiber-coupled detectors. Also, the usual SPCMs have 70% efficiency at around 700 nm; at 810, you're going to be under 60%, which is still quite good.

Either way, it's very helpful to have a visible alignment laser to set things up. Kiko Galvez has some nice tricks and tips on doing alignment. His lab manual also includes some experiments using the Mach-Zehnder, and I think some tips on aligning it but especially finding the equal-delay position (if you have a grating spectrometer, like Ocean Optics sells, there's a neat trick using white light fringes that gets you close enough).

Back-calculating from your numbers, it sounds like you're planning to use a 250 mW diode laser at (nominally) 405 nm? Don't order your BBO until you have your laser, because anything with that much power is likely not to be single mode and probably doesn't operate at exactly 405. It's better to measure your laser's wavelength (and possibly its bandwidth) so they can cut your crystal at the right angle. It's not a huge problem if your laser is, say, 407 nm instead, because you can just tilt your crystals to achieve phase matching, but it just becomes one more thing to fiddle with, and it's probably more of a hassle if you're using the 2-crystal Type I phase matching scheme because your "tuning" tilt has to happen in the plane of the pump laser (which is typically set 45 degrees from vertical/horizontal).

One thing you haven't touched on much is the bandwidth of the downconverted photons. It's hard to assess guesstimates about how "bright" a downconversion source will be from rules-of-thumb like N pairs per second per mW pump power because how many of those you can "use" depends on the bandwidth of the pump laser, its spatial mode, what degree of entanglement you want (in the 2-crystal scheme, the degree of entanglement depends on how well the cone giving you pairs with one polarization overlaps the cone giving you pairs with the orthogonal polarization; you can make gobs of pairs and have poor entanglement!), and how much bandwidth you want in the downconverted beam. In the experiment I've been doing I have bandpass filters that introduce significant loss even within the band of wavelengths they pass (typically 70-80% transmission for a good filter) with passband widths of 10, 20 and 40 nm. It's pretty close to a factor of 10 loss in coincidence rate going from my 40 nm filter to the 10 nm filter, and some people use filters as tight as 1 nm depending on the experiment.

I'll have to come back to your post later to sift through more of the details. The main thing with count rates is to have some notion of what you really need them to be relative to the experimental noise. The good news is that your dark count rates probably won't cause a problem, because that won't really affect your coincidence rates. The rule of thumb for "random" coincidences is that they occur at a rate equal to the product of your single-detector rates times your coincidence window width. If the latter is 10 ns, that gives a randoms rate of 200 * 200 * 10^-8 = 4 x 10^-4, far less than one count per second. But you can get significant rates of accidental coincidences from detection of stray light, etc.