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The confinement of high frequency phonons approaching 1 GHz is demonstratedin phonon-trapping acoustic cavities at cryogenic temperatures using alow-coupled network approach. The frequency range is extended by nearly anorder of magnitude, with excitation at greater than the 200$^{\text{th}}$overtone achieved for the first time. Such high frequency operation revealsRayleigh-type phonon scattering losses due to highly diluted lattice impuritiesand corresponding glass-like behaviour, with a maximum $Q_L\times f$ product of$8.6\times 10^{17}$ at 3.8K and $4\times10^{17}$ at 15mK. This suggests a limiton the $Q\times f$ product due to unavoidable crystal disorder. Operation at 15mK is high enough in frequency that the average phonon occupation number isless than unity, with a loaded quality factor above half a billion. This workrepresents significant progress towards the utilisation of such acousticcavities for hybrid quantum systems.

physical review letters

Observation of Rayleigh phonon scattering through excitation of  extremely high overtones in low-loss cryogenic acoustic cavities for hybrid  quantum systems