Non-equilibrium response of quantum materials to resonant low-energy electronic photo-excitations

The properties of quantum materials are determined by the delicate balance among many interacting degrees of freedom. The existence of several competing orders makes these systems highly susceptible to even small perturbations that can induce giant responses and eventually change the macroscopic state of the material. The microscopic understanding of the intricate interplay between electrons, ions and spins is thus the key to attain new material functionalities. Pump-probe optical experiments are a powerful tool to study the non-equilibrium states of quantum materials, offering unique insight into the sub-picosecond dynamics of the energy redistribution among the coupled modes. The aim of the first part of this thesis is to implement a three-pulse experiment in which, by combining a visible pump, a mid-infrared push and a supercontinuum probe, the high- and low-energy degrees of freedom are simultaneously excited in the material and its transient optical response is probed over a broad energy range. The large frequency-tunability of the sources allows to selectively target specific excitations in matter and to dynamically study their coupling. The high versatility of this setup makes it ideally suited to study a wide range of different materials. We will discuss the application to a cuprate superconductor, in which pulses with photon energy either above or below the superconducting d-wave gap are found to photo-excite an anisotropic quasiparticle distribution. We will then investigate the role of dd orbital excitations in determining the magnetic properties of TiOCl, a one-dimensional spin-Peierls compound at low temperatures. Finally, we will study the optical response of bulk black phosphorus, a layered van der Waals material in which the photo-excitation by suitable sub-gap pulses is found to possibly trigger a non-adiabatic modification of the screening environment. In the second part of the thesis, we develop a covariance-based technique to study time-resolved electronic Raman scattering in cuprates. By probing the system with randomized pulses and implementing a single-shot frequency-resolved acquisition, we are able to unveil the spectral correlations imprinted in the pulses by the inelastic scattering from the pump-induced Cooper pair breaking. The momentum selectivity peculiar to Raman scattering, in combination with the sub-picosecond temporal resolution of the technique, allows to measure the correlation dynamics projected onto different regions of the Brillouin zone, thus enabling the isolation of the nodal and antinodal contributions. The observation of gap-size correlations in the pseudogap phase hints at the presence of a local pairing that survives even when the superconducting state is macroscopically melted.