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Physical Review A

Even and odd coherent states for multimode parametric systems

V. V. Dodonov, Vladimir I. Man’ko, Dmitri E. Nikonov

Published Apr 1, 1995• 84 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.51.3328

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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.
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 review of the following results of the Refs. \cite{Sem} - \cite{Ans} is presented: For mixed state light of NNN-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 2N2N2N-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 two-mode even and odd coherent Schrödinger cat states are introduced for the generalized stationary and non-stationary harmonic oscillator. The expected values of positions and momenta and their dispersion matrices are calculated for the Schrödinger cat states. The quadrature squeezing and correlation phenomenon are studied and the Wigner and Husimi functions are constructed explicitly for these states. The photon statistics of the two-mode even and odd coherent states of the generalized oscillator is described in terms of the photon distribution function, which is expressed in terms of Hermite polynomials. The photon number, means and dispersions show oscillations which are characteristics of squeezing and correlation phenomenon.