Displacement power spectrum measurement of a macroscopic optomechanical system at thermal equilibrium

TL;DR

This study measures the displacement power spectrum of a macroscopic optomechanical system at thermal equilibrium, demonstrating consistency with theoretical predictions and minimal external noise influence.

Contribution

It provides experimental validation of thermal equilibrium behavior in a macroscopic optomechanical system using a high finesse optical cavity.

Findings

Measured displacement power spectrum matches thermal equilibrium predictions.

System exhibits stationary and Gaussian behavior above 3 Hz.

External noise sources are below measurement levels.

Abstract

The mirror relative motion of a suspended Fabry-Perot cavity is studied in the frequency range 3-10 Hz. The experimental measurements presented in this paper, have been performed at the Low Frequency Facility, a high finesse optical cavity 1 cm long suspended to a mechanical seismic isolation system identical to that one used in the VIRGO experiment. The measured relative displacement power spectrum is compatible with a system at thermal equilibrium within its environmental. In the frequency region above 3 Hz, where seismic noise contamination is negligible, the measurement distribution is stationary and Gaussian, as expected for a system at thermal equilibrium. Through a simple mechanical model it is shown that: applying the fluctuation dissipation theorem the measured power spectrum is reproduced below 90 Hz and noise induced by external sources are below the measurement.