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. In pump-probe spectroscopies, THz pulses are used to quench a system, which is subsequently probed by either a THz or optical pulse. In contrast, third harmonic generation experiments employ a single multicycle driving pulse and measure the induced third harmonic. In this work, we analyze a new spectroscopy setup where both, a quench and a drive, are applied and 2D spectra as a function of time and quench-drive-delay are recorded. We calculate the time evolution of the nonlinear current generated in the superconductor within a Anderson-pseudospin framework and analyze all experimental signatures in 2D Fourier space using a quasi-equilibrium approach. We analyze the superconducting response in Fourier space with respect to both the frequencies corresponding to the real time and the quench-drive delay time. In particular, we show the presence of a transient modulation of higher harmonics, induced by a wave mixing process of the drive with the quench pulse, which excites the quasiparticles and the Higgs mode at the same time.