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Whispering Gallery (WG) mode resonators have been machined from a boule ofsingle-crystal isotopically pure silicon-28. Before machining, the as-grown rodwas measured in a cavity, with the best Bragg confined modes exhibitingmicrowave $Q$-factors on the order of a million for frequencies between 10 and15 GHz. After machining the rod into smaller cylindrical WG mode resonators,the frequencies of the fundamental mode families were used to determine therelative permittivity of the material to be $11.488\pm0.024$ near 4 K, with theprecision limited only by the dimensional accuracy of the resonator. However,the Q-factors were degraded by the machining to below $4\times10^4$. Ramanspectroscopy was used to optimize post-machining surface treatments to restorehigh $Q$-factors. This is an enabling step for the use of such resonators forhybrid quantum systems and frequency conversion applications, as silicon-28also has very low phonon losses, can host very narrow linewidth spin ensemblesand is a material commonly used in optical applications.

Low temperature properties of whispering gallery modes in isotopically pure silicon 28