Quasiprobabilities based on squeezed states

Alfred Wünsche

Xiang‐Guo Meng, Ji‐Suo Wang, Bao‐Long Liang

Sunil Datta, Richard D’Souza

Fritz Haake, Martin Wilkens

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.

T. Kiesel, W. Vogel, Boris Hage +1 more

Although squeezed states are nonclassical states, so far, their nonclassicality could not be demonstrated by negative quasiprobabilities. In this work we derive pattern functions for the direct experimental determination of so-called nonclassicality quasiprobabilities. The negativities of these quantities turn out to be necessary and sufficient for the nonclassicality of an arbitrary quantum state and are therefore suitable for a direct and general test of nonclassicality. We apply the method to a squeezed vacuum state of light that was generated by parametric down-conversion in a second-order nonlinear crystal.

Skylar Turner, Brian R. La Cour