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 quantised radiation field is examined for the case of centered Guassian 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.