Photon antibunching

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.

where the Mandel Q parameter is defined as If the field had a classical stochastic process underlying it, say a positive definite probability distribution for photon number, the variance would have to be greater than or equal to the mean.

Sub-Poissonian fields violate this, and hence are nonclassical in the sense that there can be no underlying positive definite probability distribution for photon number (or intensity).

Photon antibunching by this definition was first proposed by Carmichael and Walls[3] and first observed by Kimble, Mandel, and Dagenais in resonance fluorescence.

An experiment with more precision that did not require subtraction of a background count rate was done for a single atom in an ion trap by Walther et al. A more general definition for photon antibunching concerns the slope of the correlation function away from zero time delay.

It can also be shown by an application of the Cauchy–Schwarz inequality to the time dependent intensity correlation function It can be shown that for a classical positive definite probability distribution to exist (i.e. for the field to be classical)

[4] Hence a rise in the second order intensity correlation function at early times is also nonclassical.

Another way of looking at this time dependent correlation function, inspired by quantum trajectory theory is where with

Spatial antibunching has been observed in photon pairs produced by spontaneous parametric down-conversion.