Fluctuations of Quantum Radiation Pressure in Dissipative Fluid

TL;DR

This paper investigates the quantum and thermal fluctuations of a mirror's position in a dissipative fluid under laser radiation, with implications for improving gravitational wave detectors.

Contribution

It introduces a generalized Langevin equation approach to analyze quantum and thermal noise effects on a mirror in a fluid, extending understanding of measurement limits.

Findings

Derived the minimum uncertainty in position measurement considering quantum and thermal noises.

Analyzed the large-time velocity fluctuations of the mirror in a dissipative environment.

Applied results to enhance the sensitivity of ground-based gravitational wave detectors.

Abstract

Using the generalized Langevin equations involving the stress tensor approach, we study the dynamics of a perfectly reflecting mirror which is exposed to the electromagnetic radiation pressure by a laser beam in a fluid at finite temperature. Based on the fluctuation-dissipation theorem, the minimum uncertainty of the mirror's position measurement from both quantum and thermal noises effects including the photon counting error in the laser interferometer is obtained in the small time limit as compared with the "standard quantum limit". The result of the large time behavior of fluctuations of the mirror's velocity in a dissipative environment can be applied to the laser interferometer of the ground-based gravitational wave detector.