Mandel Q parameter
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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:
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 (Fock states), which by definition have a well-defined number of photons and for which .
Coherent states have a Poissonian photon-number statistics for which .
- Mandel, L. (1979). "Sub-Poissonian photon statistics in resonance fluorescence". Optics Letters. 4 (7): 205–7. doi:10.1364/OL.4.000205. ISSN 0146-9592. PMID 19687850.
- Glauber, Roy J. (1963). "The Quantum Theory of Optical Coherence". Physical Review. 130 (6): 2529–2539. doi:10.1103/PhysRev.130.2529. ISSN 0031-899X.
- Mandel, L., and Wolf, E., Optical Coherence and Quantum Optics (Cambridge 1995)