Multidimensional nonlinear THz spectroscopies in superconductors

This thesis presents an in-depth analysis of the nonlinear optical response in super- conductors exposed to intense THz pulses, using a quasi-equilibrium approach rooted in many-body perturbation theory. By establishing connections between nonlinear response functions and experimentally measurable quantities, we investigate how superconducting systems respond to single-pulse and two-pulse (multidimensional) protocols. Special focus is given to understanding how diverse light-matter coupling mechanisms and electronic excitations shape the observable outcomes across different experimental setups. We examine, for instance, the role of phase fluctuations in single-layer and bilayer cuprates, which show marked differences in third harmonic generation (THG) along the CuO2 stacking direction due to the combined action of their momentum dispersion and light polarization. Our work then moves to two- dimensional (2D) THz spectroscopy, which offers unique capabilities to distinguish various nonlinear pathways in quantum materials. We begin with a simplified semi- conductor model where we can explicitly compute different light-matter interaction processes and analyze two applications in superconducting systems, applying insights from the THG analysis. We then examine 2D THz spectroscopy of cuprates, where internal screening effects present challenges in disentangling distinct contributions, and subsequently turn to NbN thin films. In the latter case, we demonstrate how specific nonlinear pathways can be uniquely sensitive to amplitude fluctuations, revealing a fresh perspective on the analysis of superconducting dynamics.