Position Estimation of a Parametrically Driven Optomechanical System

TL;DR

This paper analyzes the position estimation of a parametrically driven optomechanical system using continuous quantum measurement, deriving formulas for uncertainty reduction and optimal filtering, with insights on the effects of cooling on squeezing.

Contribution

It introduces a stochastic master equation approach to derive formulas for position uncertainty reduction and optimal filtering in a parametrically driven optomechanical system.

Findings

Derived general formulas for quadrature position uncertainty reduction.

Developed an optimal filter for position estimation from measurement records.

Found that resolved-sideband cooling marginally improves squeezing in the back-action regime.

Abstract

We study the position estimation of a mechanical oscillator undergoing both detuned parametric amplification and continuous quantum measurement. This model, which can be utilised to produce squeezed states, is applied to a general optoelectromechanical system. Using a stochastic master equation formalism, we derive general formulae for the reduction in position uncertainty of one quadrature of motion. The filter for extracting the optimal position estimate from the measurement record is derived. We also find that since this scheme does not work far into the back-action dominated regime, implementing resolved-sideband cooling improves the squeezing only marginally.