Quasiprobabilities Based on Squeezed States
This chapter generalizes quasiprobabilities based on coherent states to ones based on squeezed states. Especially, the representation of an operator as a diagonal mixture of squeezed states defines an analogue of the Glauber-Sudarshan P-function. The new quasiprobabilities can be useful tools in describing processes the intrinsic quantum nature of which forbids the existence of the familiar P-function. The chapter illustrates the concepts for a linearized model of subharmonic generation. It is important to express the coherent-state based Q function in terms of its squeezed-state based generalization. The chapter illustrates the squeezed-state techniques for a simple dynamical model of subharmonic generation. It confines to the subthreshold regime where the oscillation, to be down converted, can be treated parametrically.