Nonclassicality criteria: Quasiprobability distributions and correlation functions

We use the exact calculation of the quantum mechanical, temporal characteristic function chi(eta) and the degree of second-order coherence g((2))(tau) for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz., a displaced-squeezed thermal state, to study the different criteria for nonclassicality. In particular, we contrast criteria that involve only one-time functions of the dynamical system, for instance, the quasiprobability distribution P(beta) of the Glauber-Sudarshan coherent or P representation of the density of state and the Mandel Q(M) (tau) parameter, versus the criteria associated with the two-time correlation function g((2))(tau).