# Laser beam photon counting

I'd like to know if devices exist that are able to detect the single photon missing out of a normal laser beam.

I am aware of the fact that single photon counters do exist, but I'd like to ask some expert in optics if they can cope with high intensity laser beams (number of photons $\sim10^{10}$) with single-photon accuracy.

• So in essence you are asking what the highest number of photons is that can be detected with a photon-number-resolving detector? Commented Feb 2, 2015 at 19:22
• Actually I'm asking if there exist detectors able to resolve the single photon in a laser beam (with $\sim 10^{10}$ photons). Commented Feb 2, 2015 at 19:26
• "The" single photon? Or do you want to get a precise counting estimate with 10 digits of precision? Commented Feb 2, 2015 at 19:30
• You should also be aware that laser beams obey Poissonian statistics, which means that their photon-number uncertainty is $\sqrt{n}$ for a state with $n$ photons on average. For that kind of intense beam, you're looking at deviations in the tens of thousands. Commented Feb 2, 2015 at 19:31
• @EmilioPisanty no, Emilio, I think that he wants to know whether there are detectors with such a high efficiency. A detector may also have some cycle, after detecting a photon it has to be made ready to record another one. Commented Feb 2, 2015 at 19:32

No, so far no detector featuring such a tremendous dynamic range of the photon number is known. In the optical regime, state-of-the-art photon number resolving detectors can resolve numbers in the single digit range. (This paper has a slightly different take on the topic). In the microwave regime, numbers in the double digit range, or up to $10\,$dB, may be possible. But a dynamic range of $100\,$dB is just out of the question.

That is about (the limitations of) detectors. Now for light sources, as Emilio has rightly pointed out, typical lasers display Poissonian statistics. If you imagine a pulsed laser and a hypothetical detector that were to count and tell the precise number of photons in each pulse, you would then observe a gaussian distribution centered at some value $\mu >> 1$ and with the same variance; see figure 3a from this reference as an example.

If you want to consider light sources that spew exactly $n$ photons every time, then again you have single digit performance in the optical regime and slightly better numbers in the microwave regime. However, here (as garyp wrote in a comment), one can also generate states that are squeezed in the photon number and the mean value can be fairly high. To compare with the laser output, the statistics here would be sub-Poissonian.

Between the statistical detection limits defined as "quantum efficiency" and the huge dynamic range you're proposing, the answer is very much "no." There are a number of commercial single-photon detectors, all of which come with both their quantum efficiency, or probability of detecting a photon, and their "recovery time," which indicates how long after a photon detection the device needs to wait before it's capable of reporting another detection. In normal use, these two parameters are applied to actual readings to produce an estimate of the actual input photon rate. So far as I recall, the best you can get is a few decades of dynamic sensing range.

It's all statistical :-)

No, nowhere near that. There is no single detector that would really discriminate between 10000000000 and 10000000001 photons reaching the detector.

• Ok I understand, thank you. What is a good estimate of the efficiency percentage in terms of the (nominal) number of beam photons? I.e., for instance, can a device detect variations of order, say, 5% on the number of photons? Commented Feb 4, 2015 at 15:23