  The microwave properties of a crystalline sapphire dielectric whispering
gallery mode resonator have been measured at very low excitation strength
(E/hf=1) and low temperatures (T = 30 mK). The measurements were sensitive
enough 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 13.868
and 13.259 GHz. Small power dependent frequency shifts were also measured which
correspond to an added magnetic susceptibility of order 1e-9. This work shows
that quantum limited microwave resonators with Q-factors > 1e8 are possible
with the implementation of a sapphire whispering gallery mode system.
