Non-Markovian two-time correlation functions for optomechanical systems

TL;DR

This paper investigates the two-time correlation functions in cavity optomechanical systems, highlighting differences between Markovian and non-Markovian regimes and demonstrating that time-dependent TTCF provides richer environmental information.

Contribution

It introduces a stochastic Schrödinger equation approach to analyze TTCF in optomechanical systems, emphasizing the importance of non-Markovian effects and time dependence.

Findings

Long-time steady states differ between Markovian and non-Markovian regimes.

Time-dependent TTCF reveals more environmental information than spectral methods.

Numerical simulations support the theoretical distinctions.

Abstract

In this paper, we focus on the two-time correlation function (TTCF) of the cavity optomechanical system, which serves as the most popular tool in precision detection technologies. We utilize the stochastic Schrodinger equation approach to study TTCF for the cavity optomechanical system in the long-time steady state TTCF and time-dependent case. Our numerical simulations support two major conclusions: (1) long-time steady states in Markovian and non-Markovian regimes are different, resulting in the distinct TTCF, and (2) the time-dependent TTCF can reveal more information about the environment, rather than the traditional spectral function method.