DENSITY-MATRIX ELEMENTS AND MOMENTS FOR GENERALIZED GAUSSIAN STATE FIELDS

A single-mode radiation field with Gaussian Wigner functions (Gaussian state field) is studied. The single-mode Gaussian-field generating fu nction for both the density matrix elements and the moments of the cre ation and annihilation operators is calculated. It is shown that the m atrix elements as well as the moments of different orders can be expre ssed 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 mome nts and density matrix elements.