Single-crystal sapphire resonator at millikelvin temperatures: Observation of thermal bistability in high-Q factor whispering gallery modes

Resonance modes in single crystal sapphire (alpha-Al(2)O(3)) exhibit extremely high electrical and mechanical Q factors (approximate to 109 at 4 K), which are important characteristics for electromechanical experiments at the quantum limit. We report the cool down of a bulk sapphire sample below superfluid liquid-helium temperature (1.6 K) to as low as 25 mK. The electromagnetic properties were characterized at microwave frequencies, and we report the observation of electromagnetically induced thermal bistability in whispering gallery modes due to the material T(3) dependence on thermal conductivity and the ultralow dielectric loss tangent. We identify "magic temperatures" between 80 and 2100 mK, the lowest ever measured, at which the onset of bistability is suppressed and the frequency-temperature dependence is annulled. These phenomena at low temperatures make sapphire suitable for quantum metrology and ultrastable clock applications, including the possible realization of the quantum-limited sapphire clock.