Multitime correlation functions in nonclassical stochastic processes

TL;DR

This paper introduces a method to verify multitime quantum correlations using characteristic functions of the P functional, accounting for time ordering effects, and applies it to an optical parametric process with frequency mismatch.

Contribution

It presents a novel approach for analyzing multitime quantum correlations via the P functional, including the impact of time ordering, with practical application to optical systems.

Findings

The method effectively identifies quantum effects at multiple time points.

Time ordering significantly influences the multitime characteristic function.

Application to optical parametric processes reveals detailed quantum correlation properties.

Abstract

A general method is introduced for verifying multitime quantum correlations through the characteristic function of the time-dependent P functional that generalizes the Glauber-Sudarshan P function. Quantum correlation criteria are derived which identify quantum effects for an arbitrary number of points in time. The Magnus expansion is used to visualize the impact of the required time ordering, which becomes crucial in situations when the interaction problem is explicitly time dependent. We show that the latter affects the multi-time-characteristic function and, therefore, the temporal evolution of the nonclassicality. As an example, we apply our technique to an optical parametric process with a frequency mismatch. The resulting two-time-characteristic function yields full insight into the two-time quantum correlation properties of such a system.