Back-action evasion and squeezing of a mechanical resonator using a cavity detector

TL;DR

This paper presents a quantum theory for a cavity-based measurement scheme that enables back-action evasion and squeezing of a mechanical resonator, with potential applications in optomechanics and electromechanics.

Contribution

It provides a complete quantum analysis of a two-tone driven cavity scheme for back-action free measurement and squeezing of a mechanical resonator.

Findings

Conditions to surpass quantum noise limit identified

Scheme enables generation of squeezed states of the resonator

Relevance demonstrated for optomechanical and electromechanical systems

Abstract

We study the quantum measurement of a cantilever using a parametrically-coupled electromagnetic cavity which is driven at the two sidebands corresponding to the mechanical motion. This scheme, originally due to Braginsky et al. [V. Braginsky, Y. I. Vorontsov, and K. P. Thorne, Science 209, 547 (1980)], allows a back-action free measurement of one quadrature of the cantilever's motion, and hence the possibility of generating a squeezed state. We present a complete quantum theory of this system, and derive simple conditions on when the quantum limit on the added noise can be surpassed. We also study the conditional dynamics of the measurement, and discuss how such a scheme (when coupled with feedback) can be used to generate and detect squeezed states of the oscillator. Our results are relevant to experiments in optomechanics, and to experiments in quantum electromechanics employing stripline resonators coupled to mechanical resonators.