Optically mediated nonlinear quantum optomechanics

TL;DR

This paper theoretically explores how multiple mechanical modes interact with a single optical cavity mode through linear and quadratic couplings, revealing new effective interactions and potential quantum control applications in optomechanics.

Contribution

It introduces a formal analysis of multimode optomechanical interactions with dominant optical dissipation, including effective interactions and potential quantum protocols.

Findings

Effective multimode interactions derived under optical dissipation dominance

Quadratic coupling enables nonlinear optical analogs like second-harmonic generation

Application to Bose-Einstein condensate coupled to a cavity mirror

Abstract

We consider theoretically the optomechanical interaction of several mechanical modes with a single quantized cavity field mode for linear and quadratic coupling. We focus specifically on situations where the optical dissipation is the dominant source of damping, in which case the optical field can be adiabatically eliminated, resulting in effective multimode interactions between the mechanical modes. In the case of linear coupling, the coherent contribution to the interaction can be exploited e.g. in quantum state swapping protocols, while the incoherent part leads to significant modifications of cold damping or amplification from the single-mode situation. Quadratic coupling can result in a wealth of possible effective interactions including the analogs of second-harmonic generation and four-wave mixing in nonlinear optics, with specific forms depending sensitively on the sign of the coupling. The cavity-mediated mechanical interaction of two modes is investigated in two limiting cases, the resolved sideband and the Doppler regime. As an illustrative application of the formal analysis we discuss in some detail a two-mode system where a Bose-Einstein condensate is optomechanically linearly coupled to the moving end mirror of a Fabry-P\'erot cavity.