Transient excitation of Higgs and high-harmonic generation in superconductors with quench-drive spectroscopy

Time-resolved terahertz spectroscopies are powerful techniques to excite and probe non-equilibrium states of superconductors, directly addressing collective modes. Over the last decade, most of the debate was focused on the contribution of the amplitude collective mode (Higgs) and the quasiparticles to the superconducting response, both having the same excitation energy of twice the superconducting gap. In pump-probe spectroscopies, THz pulses are used to either quench or drive the system, which is subsequently probed by either a THz or optical pulse. In this work, we analyze and discuss a new spectroscopy setup where we both quench and drive the superconductor, changing the time delay between the two pulses, and we calculate the time evolution of the current generated by the superconductor. We calculate the superconducting response in Fourier space with respect to both the real time and the quench-drive delay time. In particular, we notice the presence of a transient modulation of higher harmonics, induced by a difference-frequency generation (DFG) process of the quench pulse, which excites the quasiparticles and the Higgs mode at the same time.