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We investigate the interplay between gap oscillations and damping in thedynamics of superconductors taken out of equilibrium by strong optical pulseswith sub-gap Terahertz frequencies. A semi-phenomenological formalism isdeveloped to include the damping within the electronic subsystem that arisesfrom effects beyond BCS, such as interactions between Bogoliubov quasiparticlesand decay of the Higgs mode. Such processes are conveniently expressed as$T_{1}$ and $T_{2}$ times in the standard pseudospin language forsuperconductors. Comparing with data on NbN that we report here, we argue thatthe superconducting dynamics in the picosecond time scale, after the pump isturned off, is governed by the $T_{2}$ process.

Impact of damping on superconducting gap oscillations induced by intense Terahertz pulses