Our team works with single photon counters all the time. For various reasons involving utility, and cost, we have settled on the semiconductor technology known as the Geiger-mode avalanche photodiode (GM-APD), which converts single photon signals into discrete electronic pulses that are readily digitized. Typically, we use COTS devices that have a thick junction because the figure of merit we are concerned about is the the detection efficiency of the devices. We use GM-APDs in our quantum communication systems (like SPEQS), for testing our photonic circuits and event to build random number generators. For use in SPEQS instruments, we have developed our own technique for operating the GM-APDs. An interesting feature of GM-APDs is that the devices have a finite recovery time after each avalanche that produces the electronic pulse. This leads to a maximum rate of detection for the device. The recovery rates can range from over a microsecond to about 20 ns, depending on the mode of operation. Nevertheless, all devices have a saturation regime where the output of the detector does not scale linearly with input, and can even fall. This is prevalent when the detectors are observing a light source where the inter-arrival time of the photons is governed by Poisson statistics.Fig. 1. An illustration of the interplay between event rate and recovery time. The waiting time distribution for a Poissonian source of rate (lambda) is shown alongside a simple stepwise model for the detection probability, exhibiting a well defined deadtime (0 to B), with unit efficiency elsewhere. It is clear that a portion (A) of the event sequence will be detected, with a rate dependent efficiency, A/(A+B). When using GM-APDs to detect pairs of time-correlated photons, it is important to be able to estimate the rate of false positives known as accidental correlations (or accidental coincidences). When you are far away from the saturation regime, it is a simple linear equation. When you are in the regime, it gets more complicated. It turns out that you may be interested in working in the saturation regime because of reasons outside your control, e.g. stray light getting into the setup, or if you are imaging a scene, a sudden increase in flux could swamp your detector. Fig. 2. The output behavior for a GM-APD given increasing input rate (x-axis) whose inter-arrival time is governed by Poisson statistics. The output is almost linear with input at the start, but the rate of increase slows down until there is a turning point. The effective duty cycle, or the fraction of time when the detector is ready to detect another pulse, falls steadily. This duty cycle is very useful for estimating the rate of false positives in the saturation regime, which begins to occur when the input is about half-million events per second To get a reliable estimate of the false positives, our team has extended the simple linear equation to include the actual detection rates. We then modeled this with light from a Poisson light source and showed that we were able to estimate the rate of false positives throughout the range of detector operation reliably. This result was published in Optics Express. The method is applicable to any combination of detector and light source provided you have a good model of the photon statistics, and the recovery behavior of your detector. We are confident this can help to extend the useful range for GM-APD operation. |

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