Investigation of intrinsic nonlinear effects in driven-dissipative optomechanical systems using the generalized linear response theory

TL;DR

This paper investigates how intrinsic nonlinear interactions affect the linear response of driven-dissipative optomechanical systems, using generalized linear response theory and Green's functions, revealing conditions under which nonlinear effects become significant.

Contribution

It introduces a generalized linear response framework to analyze nonlinear effects in optomechanical systems, deriving equations of motion for Green's functions and identifying resonance conditions for nonlinear manifestations.

Findings

Nonlinear effects are negligible unless the system is at a specific resonance.

The approach confirms the validity of linearization off-resonance.

Resonance occurs when the upper mode frequency is twice the lower mode frequency.

Abstract

In this article, we study the effects of intrinsic nonlinear optomechanical interaction on the linear response of a driven-dissipative optomechanical system to a weak time-dependent perturbation. By calculating the linear response of the cavity optical mode to a weak probe laser in the framework of the generalized linear response theory, it is shown how the Stokes and anti-Stokes sideband amplitudes as well as the power reflection coefficient, and the density of states of the cavity optical mode are expressed in terms of photonic retarded Green's functions. Then, we derive the equations of motion of retarded Green's functions of the system from nonlinear quantum Langevin equations and solve them. It is shown that for a single-photon optomechanical coupling of the order of the cavity linewidth, the nonlinear effect does not manifest itself unless the system satisfies a resonance condition, where the frequency of the upper normal mode of the system is twice that of the lower one. Based on the generality of the present approach which works at all regimes, the validity of linearization approximation is also confirmed at the off-resonance regime.