Abstract
Abstract A single-mode radiation field with Gaussian Wigner functions (Gaussian state field) is studied. The single-mode Gaussian-field generating function for both the density matrix elements and the moments of the creation and annihilation operators is calculated. It is shown that the matrix elements as well as the moments of different orders can be expressed in terms of Hermitian polynomials of two variables. Furthermore, the cumulants of the Gaussian state field are calculated. Finally, we generalize the Gaussian state field and compute the corresponding moments and density matrix elements.
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