Thermal noise of whispering gallery resonators

TL;DR

This paper calculates the fundamental thermal noise limits of crystalline CaF2 whispering gallery resonators using the fluctuation-dissipation theorem, revealing a lower bound on frequency stability at cryogenic temperatures.

Contribution

It introduces the analysis of elasto-optic noise in whispering-gallery resonators and quantifies the fundamental noise limits imposed by thermal fluctuations at various temperatures.

Findings

Dimensional fluctuation limits frequency stability to 1E-16 at 5 K.

Elasto-optic noise significantly affects the resonator's frequency stability.

Thermal noise sets a fundamental limit on whispering gallery resonator performance.

Abstract

By direct application of the fluctuation-dissipation theorem, we numerically calculate the fundamental dimensional fluctuations of crystalline CaF2 whispering gallery resonators in the case of structural damping, and the limit that this noise imposes on the frequency stability of such resonators at both room and cryogenic temperatures. We analyze elasto-optic noise - the effect of Brownian dimensional fluctuation on frequency via the strain-dependence of the refractive index - a noise term that has so far not been considered for whispering-gallery resonators. We find that dimensional fluctuation sets a lower limit of 1E-16 to the Allan deviation for a 10-millimeter-radius sphere at 5 K, predominantly via induced fluctuation of the refractive index.