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We report the first observation of low power drive level sensitivity,hyperparametric amplification, and single-mode hyperparametric oscillations ina dielectric rutile whispering-gallery mode resonator at 4.2 K. The lattergives rise to a comb of sidebands at 19.756 GHz. Whereas, most frequency combsin the literature have been observed in optical systems using an ensemble ofequally spaced modes in microresonators or fibers, the present work representsgeneration of a frequency comb using only a single-mode. The experimentalobservations are explained by an additional 1/2 degree-of-freedom originatingfrom an intrinsic material nonlinearity at optical frequencies, which affectsthe microwave properties due to the extremely low loss of rutile. Using a modelbased on lumped circuits, we demonstrate that the resonance between thephotonic and material 1/2 degree-of-freedom, is responsible for thehyperparametric energy transfer in the system.

Hyperparametric effects in a whispering-gallery mode rutile dielectric resonator at liquid helium temperatures