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Resonance modes in single crystal sapphire ($\alpha$-Al$_2$O$_3$) exhibitextremely high electrical and mechanical Q-factors ($\approx 10^9$ at 4K),which are important characteristics for electromechanical experiments at thequantum limit. We report the first cooldown of a bulk sapphire sample belowsuperfluid liquid helium temperature (1.6K) to as low as 25mK. Theelectromagnetic properties were characterised at microwave frequencies, and wereport the first observation of electromagnetically induced thermal bistabilityin whispering gallery modes due to the material $T^3$ dependence on thermalconductivity and the ultra-low dielectric loss tangent. We identify "magictemperatures" between 80 to 2100 mK, the lowest ever measured, at which theonset of bistability is suppressed and the frequency-temperature dependence isannulled. These phenomena at low temperatures make sapphire suitable forquantum metrology and ultra-stable clock applications, including the possiblerealization of the first quantum limited sapphire clock.

physical review. b, condensed matter and materials physics

Single Crystal Sapphire at milli-Kelvin Temperatures: Observation of  Electromagnetically Induced Thermal Bistability in High Q-factor Whispering  Gallery Modes