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arXiv · hep-th/9308033

Multidimensional Hermite polynomials and photon distribution for polymode mixed light

V. V. Dodonov·O. V. Man'ko·V. I. Man'ko
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Abstract

For N-mode light described by the Wigner function of generic Gaussian form the photon distribution function is obtained explicitly and expressed in terms of Hermite polynomial of $2N$ variables with equal pairs of indices.The mean values and dispersions of photon numbers are obtained for this generic mixed state.Generating function for photon distribution is obtained explicitly. The expression for $N$-mode photon distribution function for squeezed photon number states in terms of Hermite polynomials of $2N$ variables and for squeezed coherent states in terms of Hermite polynomials of $N$ variables is discussed.

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V. V. Dodonov, O. V. Man'ko, V. I. Man'ko. 1993-08-24. Multidimensional Hermite polynomials and photon distribution for polymode mixed light. https://doi.org/10.1103/physreva.50.813

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