Optimal estimation with quantum optomechanical systems in the nonlinear regime

TL;DR

This paper derives fundamental bounds on measurement precision in nonlinear quantum optomechanical systems, providing a framework for optimizing parameter estimation in complex quantum setups.

Contribution

It introduces a general method to calculate quantum Fisher information for nonlinear optomechanical Hamiltonians, enabling improved parameter estimation strategies.

Findings

Derived a general expression for quantum Fisher information in nonlinear optomechanics.

Applied the method to estimate nonlinear light-matter coupling strength, mechanical displacement, and squeezing.

Demonstrated the approach's effectiveness in resonance-modulated systems.

Abstract

We study the fundamental bounds on precision measurements of parameters contained in a time-dependent nonlinear optomechanical Hamiltonian, which includes the nonlinear light-matter coupling, a mechanical displacement term, and a single-mode mechanical squeezing term. By using a recently developed method to solve the dynamics of this system, we derive a general expression for the quantum Fisher information and demonstrate its applicability through three concrete examples: estimation of the strength of a nonlinear light-matter coupling, the strength of a time-modulated mechanical displacement, and a single-mode mechanical squeezing parameter, all of which are modulated at resonance. Our results can be used to compute the sensitivity of a nonlinear optomechanical system to a number of external and internal effects, such as forces acting on the system or modulations of the light--matter coupling.