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arXiv:hep-th/9311043

Some Rules for Polydimensional Squeezing

Vladimir I. Man’ko

Published Nov 8, 1993• 0 citations

Abstract

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.

DOI: 10.48550/arxiv.hep-th/9311043

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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.

The photon distribution function of an N-mode mixed state of light described by the Wigner function of generic Gaussian form is calculated explicitly in terms of the Hermite polynomials of 2N variables with equal pairs of indices. Simple formulas for the mean values and dispersions of photon numbers are found. The N-mode photon distribution functions for squeezed photon number states and for squeezed coherent states are expressed in terms of the Hermite polynomials of 2N and N variables, respectively.

The multimode even and odd coherent states (multimode Schroedinger cat states) are constructed for polymode parametric oscillators of the electromagnetic field. The evolution of the photon distribution function is evaluated explicitly. The distribution function is expressed in terms of the multivariable Hermite polynomials, its means and dispersions are calculated. The conditions for the existence of squeezing are formulated. The correlations among the different modes of Schroedinger cat states are studied.

The multimode even and odd coherent states (multimode Schroedinger cat states) are constructed for polymode parametric oscillators of the electromagnetic field. The evolution of the photon distribution function is evaluated explicitly. The distribution function is expressed in terms of the multivariable Hermite polynomials, its means and dispersions are calculated. The conditions for the existence of squeezing are formulated. The correlations among the different modes of Schroedinger cat states are studied.

The multimode even and odd coherent states (multimode Schr\"odinger cat states) are constructed for polymode parametric oscillators of the electromagnetic field. The evolution of the photon distribution function is evaluated explicitly. The distribution function is expressed in terms of multivariable Hermite polynomials; the means and dispersions of the function are calculated. The conditions for the existence of squeezing are formulated. The correlations between the different modes of the Schr\"odinger cat states are studied. The transformation of the initial Schr\"odinger cat states under the action of a resonant external force is investigated.