Electromagnetic Response of Nb Superconducting RF Cavities

Niobium superconducting radio-frequency (SRF) cavities have been improved in terms of the quality factor Q by infusing N into the Nb surface [1]. These high-Q cavities provide a new technology platform for both quantum processors and quantum sensors for dark matter (DM) candidates. The sensitivity to axion DM signals depends on the quality factors of both the emitter and receiver cavity [2]. To understand the fundamental limitations on Q we have developed nonequilibrium theory of superconducting Nb with impurity disorder, including numerical methods to compute the quality factor and frequency shift of N-doped Nb cavities. For strong disorder, h/2π τT_c » 2π, pair breaking limits the Q, but for intermediate disorder, Q has a peak of upper convexity as a function of the quasiparticle-impurity scattering rate, suggesting that with ``impurity engineering'' Q ∼ 10¹² are possible. We present new theoretical results for the effects of inhomogeneous disorder on the transition temperature and frequency shift of SRF cavities. Our results are excellent agreement with experimental results reported in Ref.[3], and provide a new tool for characterization of high-Q SRF cavities.