Optimal estimation of the optomechanical coupling strength

TL;DR

This paper uses quantum estimation theory to determine the optomechanical coupling strength, identifying optimal interaction times and analyzing the limits of inference accuracy in quantum systems.

Contribution

It introduces a quantum estimation framework for optomechanical coupling, highlighting optimal measurement strategies and the impact of quantum statistical inference limitations.

Findings

Optimal interaction times are around one mechanical oscillation period.

Quantum statistical inference can be inconclusive, reinforcing prior expectations.

Higher photon and phonon excitations influence estimation accuracy.

Abstract

We apply the formalism of quantum estimation theory to obtain information about the value of the nonlinear optomechanical coupling strength. In particular, we discuss the minimum mean-square error estimator and a quantum Cram\'er--Rao-type inequality for the estimation of the coupling strength. Our estimation strategy reveals some cases where quantum statistical inference is inconclusive and merely result in the reinforcement of prior expectations. We show that these situations also involve the highest expected information losses. We demonstrate that interaction times in the order of one time period of mechanical oscillations are the most suitable for our estimation scenario, and compare situations involving different photon and phonon excitations.