Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization

Abstract

We have stabilized an external cavity diode laser to a whispering gallery mode resonator formed by a protrusion of a single-crystal magnesium fluoride cylinder. The cylinder's compact dimensions ($\ensuremath{\lesssim}1 {\mathrm{cm}}^{3}$) reduce the sensitivity to vibrations and simplify the stabilization of its temperature in a compact setup. In a comparison to an ultrastable laser used for precision metrology we determine a minimum Allan deviation of $20 \mathrm{Hz}$ at an optical wavelength of 972 nm, corresponding to a relative Allan deviation of $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$, at an integration time of $100 \mathrm{ms}$. This level of instability is compatible with the limits imposed by fundamental fluctuations of the material's refractive index at room temperature.