Quantum estimation of rotational speed in optomechanics

Abstract

We study the quantum Fisher information (QFI) of the angular velocity of rotation in an optomechanical system. Based on the Gaussian measurements method, we derive the explicit form of a single-mode Gaussian QFI, which is valid for arbitrary angular velocity of rotation. The information about the angular velocity to be measured is contained in the optical covariance matrix, which can be experimentally determined via homodyne measurement. We find that QFI increases rapidly when driving the system close to the unstable boundary. This result can be attributed to the strong nonlinearity of the system at the unstable boundary. Our results indicate the possibility of using an optomechanical system for high precision detection of the angular velocity of rotation.