Photon antibunching generally refers to a light field with photons more equally spaced than a coherent laser field, a signature being a measured two-time correlation suppressed below that of a coherent laser field. More specifically, it can refer to sub-Poissonian photon statistics, that is a photon number distribution for which the variance is less than the mean. A coherent state, as output by a laser far above threshold, has Poissonian statistics yielding random photon spacing; while a thermal light field has super-Poissonian statistics and yields bunched photon spacing. In the thermal (bunched) case, the number of fluctuations is larger than a coherent state; for an antibunched source they are smaller.

The variance of the photon number distribution is

Using commutation relations, this can be written as

This can be written as

The second-order intensity correlation function (for zero delay time) is defined as

This quantity is basically the probability of detecting two simultaneous photons, normalized by the probability of detecting two photons at once for a random photon source. Here and after we assume stationary counting statistics.

Then we have

Then we see that sub-Poisson photon statistics, one definition of photon antibunching^{[clarification needed]}, is given by ${\displaystyle g^{(2)}(0)<1}$. We can equivalently express antibunching by ${\displaystyle Q<0}$ where the Mandel Q parameter is defined as