Dynamical phase transitions in periodically driven Bardeen-Cooper-Schrieffer systems

We present a systematic study of the dynamical phase diagram of a periodically driven BCS system as a function of drive strength and frequency. Three different driving mechanisms are considered and compared: oscillating density of states, oscillating pairing interaction, and oscillating external paring field. We identify the locus in parameter space of parametric resonances and four dynamical phases: Rabi-Higgs, gapless, synchronized Higgs, and time-crystal phases. We demonstrate that the main features of the phase diagram are quite robust to different driving protocols and discuss the order of the transitions. By mapping the BCS problem to a collection of nonlinear and interacting classical oscillators, we shed light on the origin of time-crystal phases and parametric resonances appearing for subgap excitations.