Nonlinear dynamics of driven superconductors with dissipation

In the absence of dissipation a periodically driven BCS superconductor can enter a coherent nonlinear regime of collective Rabi oscillations which last for arbitrary long times [Ojeda Collado et al., Phys. Rev. B 98, 214519 (2018)2469-995010.1103/PhysRevB.98.214519]. Here we show that dissipation effects introduce dramatic changes: (i) The collective Rabi mode becomes a transient. (ii) At long times a steady state is reached showing strong nonlinear effects for large enough drive strength. We identify the physical parameters governing the various crossovers and present a detailed computation of time- and angle-resolved photoemission spectroscopy (tr-ARPES) and time-resolved tunneling spectra aiming at detecting the collective Rabi oscillations and the steady-state nonlinearities. We show also that second harmonic generation is allowed for a drive which acts on the BCS coupling constant.