Estimation of disorders in the rest positions of two membranes in optomechanical systems

TL;DR

This paper applies quantum estimation theory to determine the disorders in the positions of two membranes in optomechanical systems, comparing classical and quantum strategies under various conditions.

Contribution

It introduces a detailed quantum estimation framework for membrane position disorders in optomechanical cavities, analyzing different models and measurement strategies.

Findings

Quantum and classical Fisher information differ significantly across models.

Temperature has minimal impact on estimation accuracy but complicates reaching quantum limits.

Quadrature measurements of the output field are optimal for estimation.

Abstract

The formalism of quantum estimation theory is applied to estimate the disorders in the positions of two membranes positioned in a driven cavity. We consider the coupled-cavities and the transmissive-regime models to obtain effective descriptions of this system for different reflectivity values of the membranes. Our models consist also high temperatures Brownian motions of the membranes, losses of the cavity fields, the input-output formalism and a balanced homodyne photodetection of the cavity output field. In this two-parameter estimation scenario we compare the classical and quantum Fisher information matrices and evaluate the accuracies of the estimations. We show that models prefer very different estimation strategies and the temperature does not have a detrimental effect on the estimation accuracies, but makes more difficult to attain the quantum optimal limit. Our analysis also reveals that best estimation strategies with unit effiecient detectors are measurements of the quadratures of the output field.