# What is meant by shot noise?

Question

In the context of quantum mechanics and more specifically photon counting, what is meant by shot noise?

Here is what I already know. The number of photons hitting a photosensitive screen follows a possion distribution with a signal to noise ratio of $\sqrt{\langle n \rangle}$. But I cannot find any where what is meant by shot noise and how this proves the quantisation of light. Sources would be much appreciated.

• "The number of photons hitting a photosensitive screen follows a possion distribution..." is a perfect description of shot noise. I'm not sure there's much else to say, you answered your own question. – Steve Byrnes Jun 13 '15 at 15:39

It is known that in a statistical experiment such as tossing a fair coin and counting the occurrences of heads and tails, the numbers of heads and tails after a great many throws will differ by only a tiny percentage, while after only a few throws outcomes with a significant excess of heads over tails or vice versa are common; if an experiment with a few throws is repeated over and over, the outcomes will fluctuate a lot. [...] These fluctuations are shot noise.

Here is an example that could help: Imagine to listen to an old clock that ticks every minute, approximately (some times ticks twice in a minute, some times ticks after three). If you listen to it for a long time $T$ (compared to 1 minute,say a year), you will count approximately $\frac{T}{1 min}$ ticks. Now, repeat the experiment for the same (long) time $T$, many times. Write down all those counts, and plot their frequency. You will see that the results are distributed as a gaussian.

Now, if you wouldn't know the mechanism of the clock, and you weren't able to distinguish every single ticks, you'll probably end up thinking that clocks emits continuous sound along time. This is how you perceive light in the everyday life.

Now, what you would expect to see after many experiments but with $T$, let's say, 2 mins? There could be experiments without any counting, experiments with two counting. The outcome of every experiment will fluctuate more, and than the resulting distribution will be affected. The same plot done before would be a poisson distribution, and the obvious explanation will be that ticks are discrete, and the shape of the distribution depends directly upon that.

In the end, if you are really precise with your measure, you would be able to recognize this effect of the discreteness of ticks, for the long time experiments, too. This is what we usually call shot noise.

• So are we basically saying that shot noice is the fluction in teh singal recived in a small, given, interval of time? – Quantum spaghettification Jun 13 '15 at 15:39
• Exactly, but pay attention. Mine was a metaphor. I used time instead of the amount of light, and ticks as a metaphor of the single packet of light, the photon. When you see light your eyes actually sum up all the photons arriving, and send to your brain an average of this amount (that is the intensity). In other words, you always average over the amount of photons arriving, that is why our perception of light is continuous, and not discrete (unlike the clock ticks). – Riccardo Buscicchio Jun 13 '15 at 16:09
• More in general, shot noise is the fluctuation of a signal assumed distributed with a given rate, at timescale (or space, or length, or any other) where that rate is no more a good approximation. – Riccardo Buscicchio Jun 13 '15 at 16:12