Measurements of Radiation Pressure Effect in Cryogenic Sapphire Dielectric Resonators

We report observations of the radiation pressure induced expansion of a solid dielectric resonator. This effect causes a fundamental limit to the frequency stability of the resonator. The measurements were made on four high $Q$-factor quasi-TE “whispering gallery” modes from 9.9 to 12.6 GHz in a monocrystalline sapphire resonator at liquid helium temperatures. The fractional frequency shift is $-1.0\mathrm{}\pm 0.1\times {10}^{-12\mathrm{}}$ per μJ of energy stored in the resonator. This result is consistent in sign, magnitude, and linearity with the radiation pressure induced lattice expansion term predicted by Braginsky.