Gaussian-Wigner distributions and hierarchies of nonclassical states in quantum optics: The single-mode case

A recently introduced hierarchy of states of a single-mode quantized radiation field is examined for the case of centered Gaussian-Wigner distributions. It is found that the onset of squeezing among such states signals the transition to the strongly nonclassical regime. Interesting consequences for the photon-number distribution, and explicit representations for them, are presented. The effects of nonideal detection are also carefully analyzed.