For two-mode squeezed light with Gaussian density matrix, the photon distribution function is found explicitly and expressed in terms of four-variable (for mixed state) and two-variable (for pure state) Hermite polynomials. Generating functions for the joint photon distribution in both modes and for the photon distribution in one-mode subsystem are obtained.

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arXiv:quant-ph/9612008 · Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Properties of squeezed-state excitations

Vladimir I Man'ko, Alfred Wünsche

Published Jun 1, 1997• 44 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1355-5111/9/3/010

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The review of the following results of the Refs. \cite{Sem} - \cite{Ans} is presented: For mixed state light of

N

-mode electromagnetic field described by Wigner function which has generic Gaussian form the photon distribution function is obtained and expressed expliciltly in terms of Hermite polynomials of

2N

-variables.The momenta of this distribution are calculated and expressed as functions of matrix invariants of the dispersion matrix.The role of new uncertainty relation depending on photon state mixing parameter is elucidated.New sum rules for Hermite polynomials of several variables are found.The photon statistics of polymode even and odd coherent light and squeezed polymode Schrödinger cat light is qiven explicitly.Photon distribution for polymode squeezed number states expressed in terms of multivariable Hermite polynomials is discussed.