Floquet theory of periodically-driven superconductors

We use Floquet theory to describe dynamics and losses of superconductors under extremely high fields and frequencies. Periodically-driven superconductors at high fields provides an unexplored theoretical territory relevant in modern applications (lower cryogenic costs for particle accelerators), allowing for experimental validation using Superconducting-Radio-Frequency (SRF) cavities. We use the Floquet formalism to solve the Cooper problem in the limit of strong AC fields (in which linear-response analysis does not apply). We also discuss preliminary results combining BCS and Floquet theories to develop an experimentally-verifiable new approach for periodically-driven superconductors that provides explanation and control of dissipation, with relevance for condensed matter physics and the ‘positive Q slope’ of SRF cavities.