Determination of the vacuum optomechanical coupling rate using frequency noise calibration

TL;DR

This paper introduces a simple experimental method to accurately determine the vacuum optomechanical coupling rate by applying known frequency modulation and measuring mechanical occupation, verified on micromechanical and nanomechanical systems.

Contribution

The paper presents a straightforward technique to measure the vacuum optomechanical coupling rate using frequency noise calibration, reducing ambiguity in coupling parameter estimation.

Findings

Method successfully applied to a micromechanical mode in a whispering-gallery resonator.

Method verified on a nanomechanical oscillator coupled to a toroidal cavity.

Provides accurate measurement of the vacuum optomechanical coupling rate.

Abstract

The strength of optomechanical interactions in a cavity optomechanical system can be quantified by a vacuum coupling rate $\vcr$ analogous to cavity quantum electrodynamics. This single figure of merit removes the ambiguity in the frequently quoted coupling parameter defining the frequency shift for a given mechanical displacement, and the effective mass of the mechanical mode. Here we demonstrate and verify a straightforward experimental technique to derive the vacuum optomechanical coupling rate. It only requires applying a known frequency modulation of the employed electromagnetic probe field and knowledge of the mechanical oscillator's occupation. The method is experimentally verified for a micromechanical mode in a toroidal whispering-gallery-resonator and a nanomechanical oscillator coupled to a toroidal cavity via its near field.