Statistical Properties of the Time Evolution Operator for Two Coupled Oscillators

Abstract

In the present work we study the effects of squeezing on coherent states, number states, and on the thermal field states related to the time evolution operator, which is the result of the Hamiltonian describing the simultaneous non-degenerate parametric amplifier with mixing of two modes a and b via a rotation of their polarization. By using the Glauber second-order correlation function we examined the statistical properties of these various squeezed states. The quasi-probabilities of the W Wigner and Q functions are calculated. The Glauber P representation for the squeezed thermal state explicitly shows the limit of its applicability.