Photon antibunching - AbsoluteAstronomy.com

Photon antibunching generally refers to a light field with photons more equally spaced than a coherent laser field and a signal at detectors is anticorrelated. More specifically, it can refer to sub-Poisson photon statistics, that is a photon number distribution for which the variance is less than the mean. Nevertheless this kind of statistics was not observed directly with photon number resolving detector. A coherent state, as output by a laser far above threshold has Poissonian

Poisson distribution

In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since...

statistics yielding random photon spacing; while a thermal light field has super-Poisson 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, is given by

. We can equivalently express antibunching by

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. This can be shown by an application of the Cauchy-Schwarz inequality to the definition of

. 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 observed by Kimble

H. Jeff Kimble

H. Jeff Kimble is the William L. Valentine Professor and Professor of Physics at Caltech. His research is in quantum optics and is noted for groundbreaking experiments in physics including one of the first demonstrations of teleportation of a quantum state , quantum logic gate, and the development...

, Mandel

Leonard Mandel

Leonard Mandel was the Lee DuBridge Professor Emeritus of Physics and Optics at the University of Rochester when he died at the age of 73 at his home in Pittsford, New York. He contributed immensely to theoretical and experimental optics...

, and Dagenais in resonance fluorescence

Resonance fluorescence

Resonance fluorescence is fluorescence from an atom or molecule in which the light emitted is at the same frequency as the light absorbed.In resonance fluorescence, a photon is absorbed, causing an electron to jump to a higher level from which, after a delay, it falls back to its original level, ...

. A driven atom cannot emit two photons at once, and so in this case

. 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.

For historical reasons, another definition for photon antibunching is sometimes used. 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)

. Hence a rise in the second order intensity correlation function at early times is also nonclassical. This initial rise is sometimes referred to as photon antibunching.

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

where

with

is the state conditioned on previous detection of a photon at time

Source

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: see Photon Antibunching

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See also