A Green's function approach to the linear response of a driven dissipative optomechanical system

TL;DR

This paper develops a Green's function approach to analyze the linear response of driven-dissipative optomechanical systems, clarifying ambiguities in open quantum system response theory and explaining key phenomena like OMIT and sideband amplification.

Contribution

It introduces a generalized linear response theory for open quantum systems using Green's functions, linking quantum Langevin equations to response phenomena in optomechanics.

Findings

Explains anti-resonance, normal mode splitting, and OMIT phenomena.

Clarifies the amplification and attenuation of sidebands in different detuning regimes.

Provides a consistent theoretical framework aligning with Raman scattering insights.

Abstract

In this paper, we first try to shed light on the ambiguities that exist in the literature in the generalization of the standard linear response theory (LRT) which has been basically formulated for closed systems to the theory of open quantum systems in the Heisenberg picture. Then, we investigate the linear response of a driven-dissipative optomechanical system (OMS) to a weak time-dependent perturbation using the so-called generalized LRT. It is shown how the Green's function equations of motion of a standard OMS as an open quantum system can be obtained from the quantum Langevin equations (QLEs) in the Heisenberg picture. The obtained results explain a wealth of phenomena, including the anti-resonance, normal mode splitting and the optomechanically induced transparency (OMIT). Furthermore, the reason why the Stokes or anti-Stokes sidebands are amplified or attenuated in the red or blue detuning regimes is clearly explained which is in exact coincidence, especially in the weak-coupling regime, with the Raman-scattering picture.