The microscopic coupling between atomic lattice vibrations (phonons) and charge carriers are at the origin of a plethora of condensed matter physics phenomena, such as superconductivity and charge density waves. These phonon-carrier interactions are also essential for explaining electrical and thermal transport, as well as energy conversion processes in materials for photovoltaics or future quantum technologies. Given their central role in nearly all condensed matter phenomena, gaining access to these microscopic interactions is essential. In this talk I will show how femtosecond electron diffraction yields unique insights into electron-phonon and phonon-phonon interactions, in systems such as two-dimensional materials, lead-halide perovskites and molecular crystals.

Recent years have seen the advent of prototypical quantum simulators: synthetic quantum systems which can be used to investigate quantum many-body physics in controlled conditions. Their tremendous potential is however constrained by our capability to accurately control them and to understand their intrinsically non-equilibrium behaviour, which poses formidable challenges. I will present ideas we are pursuing in this area. I will start by discussing an efficient approach to use state-of-the art simulators to realize interacting topological systems, whose excitations behave like exotic quantum particles (known as anyons). I will then discuss how low-energy states of such systems can be prepared and stabilized with the help of controlled dissipative effects. Finally, I will propose a novel non-equilibrium phenomenon, where temporal modulations of an anyon system lead to the emergence of more complex anyon classes, of interest for topological quantum computing.