Thesis title: Nonlinear optical response in interacting electron systems
This Thesis work provides a detailed analysis of the nonlinear optical response in different classes of materials where electronic interactions play a central role, ranging from wide-band insulators, to metallic and superconducting compounds. Focusing on recent spectroscopic techniques taking advantage of intense low-frequency (THz) light pulses, such as third-harmonic generation or time-resolved pump-probe measurements, we present a general theoretical framework able to reproduce some of the most striking experimental features. As an example, we provide a comprehensive description for the light-induced coherent generation of different Raman-active modes, such as optical phonons in insulating and metallic systems or electronic collective fluctuations in conventional and unconventional superconductors, and for the THz Kerr effect affecting the nearly instantaneous response in pump-probe experiments. The whole derivation mainly focuses on non-linear optical effects but still relies on a quasi-equilibrium approach, similar to the one used to describe conventional spectroscopic techniques in the weak-field limit, like (spontaneous) Raman scattering. With this respect, we show that time-resolved and Raman experiments provide similar information when high-frequency (eV) light pulses are applied, while THz-driven excitations are in principle subjected to different selection rules, as explicitly demonstrated by the case of disordered superconductors.