Chasing the thermodynamical noise limit in whispering-gallery-mode resonators for ultrastable laser frequency stabilization

Ultrastable high-spectral-purity lasers have served as the cornerstone behind optical atomic clocks, quantum measurements, precision optical-microwave generation, high resolution optical spectroscopy and sensing. Hertz-level lasers stabilized to high finesse Fabry-P\'erot mirror cavities are typically used for these studies but are large and fragile such that they have remained laboratory instruments. There is a clear demand in rugged miniaturized lasers operating potentially at comparable stabilities to those bulk lasers. Over the past decade, ultrahigh-Q optical whispering-gallery-mode (WGM) resonators have served as a platform for low-noise microlasers but have not yet reached the ultimate stabilities defined by their fundamental noise. Here, we show the noise characteristics of WGM resonators and demonstrate a resonator-stabilized laser at the fundamental limit by compensating the intrinsic thermal expansion of a WGM resonator, allowing a sub-25 Hz linewidth and a 32 Hz Allan deviation on the 191 THz carrier in 100 ms integration. We also reveal the environmental sensitivities of the resonator at the thermodynamical noise limit and long-term frequency drifts governed by random-walk-noise statistics.