Impact of damping on superconducting gap dynamics induced by intense terahertz pulses

Recent advances in terahertz pump-probe spectroscopy opened a new route to investigate non-equilibrium superconductivity and gap dynamics. The time-dependent BCS theory predicts 2Δ gap oscillations after an ultrafast non-adiabatic perturbation is turned off, a consequence of the excitation of the Anderson-Higgs mode. Because gap relaxation due to the coupling to the phonons happens usually at longer time scales, the average gap is expected to be constant after the pump is off. This is at odds with recent experiments using intense THz pulses with subgap frequencies in NbN, where the gap is seen to be suppressed already at the tens of ps time scale, after the pump is turned off. We show that this behavior arises from damping within the electronic subsystem due to effects beyond BCS theory, such as interactions between Bogoliubov quasiparticles and decay of the Higgs mode. We develop a semi-phenomenological model where these relaxation processes are conveniently expressed as T₁ and T₂ relaxation times in the pseudospin formalism. We discuss the impact of each relaxation process to the gap dynamics and show the quantitative agreement with the experiments.