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The thermal stability of monolithic optical microresonators is essential formany mesoscopic photonic applications such as ultrastable laser oscillators,photonic microwave clocks, and precision navigation and sensing. Theirfundamental performance is largely bounded by thermal instability. Sensitivethermal monitoring can be achieved by utilizing cross-polarized dual-mode beatfrequency metrology, determined by the polarization-dependentthermorefractivity of a single-crystal microresonator, wherein the heterodyneradio-frequency beat pins down the optical mode volume temperature forprecision stabilization. Here, we investigate the correlation between thedual-mode beat frequency and the resonator temperature with time and theassociated spectral noise of the dual-mode beat frequency in a single-crystalultrahigh-Q MgF2 resonator to illustrate that dual-mode frequency metrology canpotentially be utilized for resonator temperature stabilization reaching thefundamental thermal noise limit in a realistic system. We show a resonatorlong-term temperature stability of 8.53 {\mu}K after stabilization and unveilvarious sources that hinder the stability from reaching sub-{\mu}K in thecurrent system, an important step towards compact precision navigation, sensingand frequency reference architectures.

Probing 10 {\mu}K stability and residual drifts in the cross-polarized dual-mode stabilization of single-crystal ultrahigh-Q optical resonators