Optimal estimation of time-dependent gravitational fields with quantum optomechanical systems

TL;DR

This paper investigates the ultimate sensitivity limits of quantum optomechanical systems for detecting time-dependent gravitational fields, proposing methods to enhance measurement precision and exploring applications like gravitational wave detection.

Contribution

It introduces a novel approach to optimize quantum optomechanical sensors for gravitational measurements by using nonlinear dynamics, squeezing, and coupling modulation.

Findings

Sensitivity can be improved with squeezed states and coupling modulation.

Detection of nano-gram oscillating masses is theoretically feasible.

Identifies parameter regimes for gravitational wave detection with quantum sensors.

Abstract

We study the fundamental sensitivity that can be achieved with an ideal optomechanical system in the nonlinear regime for measurements of time-dependent gravitational fields. Using recently developed methods to solve the dynamics of a nonlinear optomechanical system with a time-dependent Hamiltonian, we compute the quantum Fisher information for linear displacements of the mechanical element due to gravity. We demonstrate that the sensitivity can not only be further enhanced by injecting squeezed states of the cavity field, but also by modulating the light--matter coupling of the optomechanical system. We specifically apply our results to the measurement of gravitational fields from small oscillating masses, where we show that, in principle, the gravitational field of an oscillating nano-gram mass can be detected based on experimental parameters that will likely be accessible in the near-term future. Finally, we identify the experimental parameter regime necessary for gravitational wave detection with a quantum optomechanical sensor.