Low-Temperature Properties of Whispering-Gallery Modes in Isotopically Pure Silicon-28

Abstract

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 postm..