Non-Degenerate Multimode Optomechanics

TL;DR

This paper develops a comprehensive theoretical framework for non-degenerate multimode optomechanics, deriving a master equation that accounts for decoherence and back-action, and demonstrating controllable strong interactions between mechanical oscillators.

Contribution

It introduces a unified master equation for weakly coupled optomechanical systems that includes all decoherence effects and applies it to achieve tunable strong interactions.

Findings

Effective interactions can be made arbitrarily strong relative to decoherence.

The master equation is valid for all weak coupling optomechanical systems.

Resonant coupling schemes can be optimized for strong unitary interactions.

Abstract

We theoretically investigate interactions between non-degenerate mechanical oscillators mediated by a time-dependent cavity field. We obtain a reduced master equation valid for all optomechanical systems operating in the weak coupling regime. This master equation includes all forms of decoherence and back-action due to the dissipation of the field mediating the interaction. We apply the master equation to study two resonant coupling schemes within a rotating-wave approximation: the beam splitter Hamiltonian and the two-mode parametric amplifier. In both cases, the effective unitary interaction can be made arbitrarily strong compared to the decoherence due to dissipation of the mediating field by choosing appropriate detunings.