Cavity quantum optomechanical nonlinearities and position measurement beyond the breakdown of the linearized approximation

TL;DR

This paper develops a nonlinear cavity quantum optomechanical framework to enable position measurements beyond the linear approximation, facilitating advances in quantum metrology and control in experiments entering the nonlinear regime.

Contribution

The paper introduces a comprehensive nonlinear formalism for cavity quantum optomechanics and proposes a method for position measurement beyond the linearized approximation using optical general-dyne detection.

Findings

Framework captures nonlinear radiation-pressure and cavity response effects

Proposes measurement scheme using general-dyne detection for enhanced position info

Enables quantum measurement and control improvements in nonlinear regime

Abstract

Several optomechanics experiments are now entering the highly sought nonlinear regime where optomechanical interactions are large even for low light levels. Within this regime, new quantum phenomena and improved performance may be achieved, however, a corresponding theoretical formalism of cavity quantum optomechanics that captures the nonlinearities of both the radiation-pressure interaction and the cavity response is needed to unlock these capabilities. Here, we develop such a nonlinear cavity quantum optomechanical framework, which we then utilize to propose how position measurement can be performed beyond the breakdown of the linearized approximation. Our proposal utilizes optical general-dyne detection, ranging from single to dual homodyne, to obtain mechanical position information imprinted onto both the optical amplitude and phase quadratures and enables both pulsed and continuous modes of operation. These cavity optomechanical nonlinearities are now being confronted in a growing number of experiments, and our framework will allow a range of advances to be made in e.g. quantum metrology, explorations of the standard quantum limit, and quantum measurement and control.