Optomechanical parameter estimation

TL;DR

This paper introduces a statistical framework for parameter estimation in noisy optomechanical systems, deriving bounds and comparing algorithms, with practical implications for experiment design and sensing applications.

Contribution

It develops a Cramér-Rao bound for long-time estimation errors and demonstrates the effectiveness of the EM algorithm in approaching this bound in optomechanical systems.

Findings

EM estimator achieves lowest error in force noise power estimation

Cramér-Rao bound provides a fundamental limit for estimation accuracy

Analytic results aid in optomechanical experiment design

Abstract

We propose a statistical framework for the problem of parameter estimation from a noisy optomechanical system. The Cram\'er-Rao lower bound on the estimation errors in the long-time limit is derived and compared with the errors of radiometer and expectation-maximization (EM) algorithms in the estimation of the force noise power. When applied to experimental data, the EM estimator is found to have the lowest error and follow the Cram\'er-Rao bound most closely. Our analytic results are envisioned to be valuable to optomechanical experiment design, while the EM algorithm, with its ability to estimate most of the system parameters, is envisioned to be useful for optomechanical sensing, atomic magnetometry, and fundamental tests of quantum mechanics.