Normal-mode splitting in coupled high-Q microwave cavities

Three-dimensional radio frequency cavities demonstrate excellent frequency selectivity and, as such, are known for their use in RF filters. These cavities have potential applications in quantum information science, precision displacement metrology, and quantum electrodynamics. Additionally, coupled cavities that form a spectral doublet allow for parametric gain when incorporating mechanical elements. Here, we investigate normal-mode splitting in a pair of quarter-wave stub microwave cavities at room temperature and cryogenic environments in order to identify coupling mechanics for normal and superconducting systems. Superconducting quarter-wave stub cavities with a resonant frequency of 10 GHz are made from reactor-grade niobium and exhibit Q ranging from 10 5 to 10 9. We varied cavity-to-cavity coupling to observe several normal-mode splittings of increasing peak separation until we observed a mode crossing. The minimum observed peak separation was 7 MHz for room temperature tests and 200 kHz for cryogenic tests. We also report on values of an intrinsic quality factor for the tuning cavity as a dielectric rod is translated along its symmetry axis. The realization of coupled superconducting radio frequency (SRF) cavities of this type is a necessary step toward implementation of parametric SRF-mechanical gain.