Approaches in evaluating two-time correlation function

TL;DR

This paper presents a method for evaluating two-time correlation functions using coherent-state propagators and Q-functions, simplifying the calculations involved in quantum optical systems.

Contribution

It introduces a procedure that reduces the calculation of two-time correlation functions to simple integrations using coherent-state techniques.

Findings

Two-time correlation functions can be computed via straightforward integrations.

The method simplifies calculations by transferring time dependence to the density operator.

Using c-number equations makes the process more manageable.

Abstract

Derivation of the procedures that can be applied in evaluating two-time correlation function in terms of coherent-state propagator and corresponding Q-function is presented. On the basis that the involved functions are generally exponential in nature, obtaining the two-time second-order correlation function is essentially claimed to be reduced to carrying out relatively simple integrations. Fundamentally, the time dependence of the operators is transferred to the density operator. Moreover, manipulation in reordering the operators is performed by applying the usual trace operation. With all details, it is basically observed that the two-time correlation can be readily determined once the pertinent coherent-state propagator or Q-function is known. Since working with c-number equation is far more handy than the associated operator equation, it is expected that the results derived in this contribution can aid in easing the otherwise involving mathematical rigor.