Mandel Q parameter
The Mandel Q parameter measures the departure of the occupation number distribution from Poissonian statistics. It was introduced in quantum optics by L. Mandel. It is a convenient way to characterize non-classical states with negative values indicating a sub-Poissonian statistics, which have no classical analog. It is defined as the normalized variance of the boson distribution:
where is the photon number operator and is the normalized second-order correlation function as defined by Glauber.Non-classical value
Negative values of Q corresponds to state which variance of photon number is less than the mean. In this case, the phase space distribution cannot be interpreted as a classical probability distribution.
The minimal value is obtained for photon number states, which by definition have a well-defined number of photons and for which .Examples
For black-body radiation, the phase-space functional is Gaussian. The resulting occupation distribution of the number state is characterized by a Bose–Einstein statistics for which.
Coherent states have a Poissonian photon-number statistics for which.
