Nonclassicality criteria: Quasiprobability distributions and correlation functions

TL;DR

This paper compares various nonclassicality criteria for Gaussian states in quantum optics, analyzing their effectiveness using exact calculations of characteristic functions and correlation functions in a parametric amplifier system.

Contribution

It provides a detailed comparison between one-time quasiprobability criteria and two-time correlation function criteria for detecting nonclassicality in Gaussian states.

Findings

Quasiprobability distributions can indicate nonclassicality.

Two-time correlation functions provide complementary nonclassicality insights.

The study clarifies the applicability of different criteria in quantum optical systems.

Abstract

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 $g^{(2)}(\tau)$.