Optomechanical damping basis

TL;DR

This paper provides an exact analytical solution for the eigenvalue problem of the dissipative dynamics in a standard optomechanical system, covering various coupling regimes and environmental conditions.

Contribution

It introduces the optomechanical damping basis by explicitly deriving the eigenvectors and eigenvalues of the Liouville operator for the system.

Findings

Exact eigenvalues and eigenvectors are derived.

Solution applicable to both weak and strong coupling regimes.

Includes effects of separate environments at different temperatures.

Abstract

We present a closed-form analytical solution to the eigenvalue problem of the Liouville operator generating the dissipative dynamics of the standard optomechanical system. The corresponding Lindblad master equation describes the dynamics of a single-mode field inside an optical cavity coupled by radiation pressure to its moving mirror. The optical field and the mirror are in contact with separate environments, which are assumed at zero and finite temperature, respectively. The optomechanical damping basis refers to the exact set of eigenvectors of the generator that, together with the exact eigenvalues, are explicitly derived. Both the weak- and the strong-coupling regime, which includes combined decay mechanisms, are solved in this work.