Whispering-gallery-(WG) mode resonators are machined from a boule of single-crystal isotopically pure silicon-28. Before machining, the as-grown rod is measured in a cavity, with the best Bragg confined modes exhibiting microwave Q factors on the order of a million for frequencies between 10 and 15 GHz. After machining the rod into smaller cylindrical WG-mode resonators, the frequencies of the fundamental mode families are used to determine the relative permittivity of the material to be 11.488±0.024 near 4 K, with the precision limited only by the dimensional accuracy of the resonator. However, the machining degraded the Q factors to below 4×104. Raman spectroscopy is used to optimize postmachining surface treatments to restore high-Q-factors. This is an enabling step for the use of such resonators for hybrid quantum systems and frequency-conversion applications, as silicon-28 also has very low phonon losses, can host very narrow linewidth spin ensembles, and is a material commonly used in optical applications.
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