Master equation approach to optomechanics with arbitrary dielectrics

TL;DR

This paper develops a comprehensive quantum master equation framework for light interacting with arbitrary dielectric objects, accounting for complex scattering and mode interactions, and applies it to analyze cavity cooling beyond common approximations.

Contribution

It introduces a generalized master equation formalism that includes mode interactions and scattering for arbitrary dielectric objects, extending standard approaches.

Findings

Derived a master equation for arbitrary dielectric objects including all scattering processes.

Applied the formalism to cavity cooling of large spheres, surpassing typical approximations.

Provided an expression for steady-state phonon numbers without resolved-sideband or bad-cavity assumptions.

Abstract

We present a master equation describing the interaction of light with dielectric objects of arbitrary sizes and shapes. The quantum motion of the object, the quantum nature of light, as well as scattering processes to all orders in perturbation theory are taken into account. This formalism extends the standard master equation approach to the case where interactions among different modes of the environment are considered. It yields a genuine quantum description, including a renormalization of the couplings and decoherence terms. We apply this approach to analyze cavity cooling of the center-of-mass mode of large spheres. Furthermore, we derive an expression for the steady-state phonon numbers without relying on resolved-sideband or bad-cavity approximations.