Tracing the dynamics of superconducting order via transient terahertz third harmonic generation

Ultrafast optical control of quantum systems is an emerging field of physics. In particular, the possibility of light-driven superconductivity has attracted much of attention. To identify non-equilibrium superconductivity, it is necessary to measure fingerprints of superconductivity on ultrafast timescales. Recently non-linear THz third harmonic generation (THG) was shown to directly probe the collective degrees of freedoms of the superconducting condensate, including the Higgs mode. Here we extend this idea to light-driven non-equilibrium states in superconducting La2-xSrxCuO4 establishing an optical pump-THz-THG drive protocol to access the transient superconducting (SC) order-parameter quench and recovering on few-picosecond timescales. We show in particular the ability of two-dimensional (2D) TH spectroscopy to disentangle the effects of optically-excited quasiparticles from the pure order-parameter dynamics, that are unavoidably mixed in the pump-driven linear THz response. Benchmarking the gap dynamics to existing experiments shows the ability of driven THG spectroscopy to overcome these limitations in ordinary pump-probe protocols.