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Time-resolved terahertz spectroscopies are powerful techniques to excite andprobe non-equilibrium states of superconductors, directly addressing collectivemodes. 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 pulseand measure the induced third harmonic. In this work, we analyze a newspectroscopy setup where both, a quench and a drive, are applied and 2D spectraas a function of time and quench-drive-delay are recorded. We calculate thetime evolution of the nonlinear current generated in the superconductor withina Anderson-pseudospin framework and analyze all experimental signatures in 2DFourier space using a quasi-equilibrium approach. We analyze thesuperconducting response in Fourier space with respect to both the frequenciescorresponding to the real time and the quench-drive delay time. In particular,we show the presence of a transient modulation of higher harmonics, induced bya wave mixing process of the drive with the quench pulse, which excites thequasiparticles and the Higgs mode at the same time.

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