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.[1] 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.[2]

Non-classical value

Negative values of Q corresponds to state which variance of photon number is less than the mean (equivalent to sub-Poissonian statistics). 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 photon 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 .[3]

Coherent states have a Poissonian photon-number statistics for which .

References

  1. Mandel, L., Sub-Poissonian photon statistics in resonance fluorescence, Opt. Lett. 4:205 (1979)
  2. Glauber, R. J., The Quantum Theory of Optical Coherence, Phys. Rev. 130:2529 (1963)
  3. Mandel, L., and Wolf, E., Optical Coherence and Quantum Optics (Cambridge 1995)

Further reading

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