Enhanced optomechanical nonlinearity through non-Markovian mechanical noise

TL;DR

This paper provides an exact analytical solution for the nonlinear dynamics of cavity optomechanical systems interacting with both Markovian and non-Markovian mechanical baths, revealing how bath structure influences optomechanical nonlinearity.

Contribution

It offers a full quantum treatment of nonlinear optomechanics with non-Markovian noise, extending understanding beyond Markovian approximations and enabling control of nonlinearity via bath engineering.

Findings

Markovian baths generally reduce nonlinearity strength.

Non-Markovian baths can enhance optomechanical nonlinearity.

Exact analytic solutions for full quantum dynamics in nonlinear regime.

Abstract

Cavity optomechanical systems in the quantum regime consist of a cavity mode and mechanical element coupled together through radiation pressure. In the nonlinear optomechanical regime, open-system dynamics is generally challenging to treat analytically, since the noise terms do not commute with the optomechanical interaction term. Specifically, a general treatment of both Markovian and non-Markovian mechanical noise in the nonlinear optomechanical regime is still outstanding. Here we address this question by solving the full dynamics of an optomechanical system in the nonlinear regime where the mechanical element interacts with a bath of harmonic oscillators, representing full quantum Brownian motion. The solutions, which are exact and analytic, allow us to consider the strength of the optomechanical nonlinearity in the presence of both Markovian (Ohmic) and non-Markovian (sub-Ohmic and super-Ohmic) baths. We show that that while the strength of the nonlinearity is generally reduced by a Markovian bath spectrum, it can be enhanced by constructing a bath with a highly non-Markovian structure. The results have potential implications for future optomechanical experiments which seek to achieve a strong optomechanical nonlinearity.