The microwave properties of a crystalline sapphire dielectric whisperinggallery mode resonator have been measured at very low excitation strength(E/hf=1) and low temperatures (T = 30 mK). The measurements were sensitiveenough to observe saturation due to a highly detuned electron spin resonance,which limited the loss tangent of the material to about 2e-8 measured at 13.868and 13.259 GHz. Small power dependent frequency shifts were also measured whichcorrespond to an added magnetic susceptibility of order 1e-9. This work showsthat quantum limited microwave resonators with Q-factors > 1e8 are possiblewith the implementation of a sapphire whispering gallery mode system.
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