Optomechanical systems with linear and quadratic position couplings: Dynamics and optimal estimation

TL;DR

This paper analyzes the dynamics of an optomechanical system with both linear and quadratic position couplings, providing an analytical solution and demonstrating optimal estimation of quadratic coupling strength via homodyne detection.

Contribution

It introduces an analytical solution for a combined linear and quadratic optomechanical Hamiltonian using two-phonon coherent states and applies quantum estimation theory to optimize parameter measurement.

Findings

Quantum Fisher information can be saturated by homodyne detection.

The phase of the local oscillator is crucial for optimal estimation.

Analytical solution enhances understanding of nonlinear optomechanical interactions.

Abstract

We study the dynamics of an optomechanical system consisting of a single-mode optical field coupled to a mechanical oscillator, where the nonlinear interaction includes both linear and quadratic terms in the oscillator's position. We present an analytical solution to this quantum-mechanical Hamiltonian problem by employing the formalism of two-phonon coherent states. Quantum estimation theory is applied to the resulting state of the optical field, with a focus on evaluating the quantum Fisher information with respect to the strength of the quadratic coupling. Our estimation scheme employs balanced homodyne photodetection and demonstrates that the corresponding classical Fisher information can reach the quantum Fisher information limit, with the phase of the local coherent oscillator playing a crucial role.