Laboratoire de Physique Théorique
Toulouse - UMR 5152

I will discuss how the non-equilibrium electronic structure of pump-probe experiments can be viewed in terms of Floquet theory. The periodic nature of an optical excitation allows to decompose the solutions of the time-dependent Schrödinger equation in terms of quasi-static dressed states of electron-photon quasiparticles. Using results from time-dependent density functional theory, I will show how the spectrum of these quasiparticles determines the spectral function in pump-probe photo-emission spectroscopy. The non-equilibrium Floquet electronic structure can have different topological properties leading to the concept of Floquet engineering of materials properties. While for optical pumping the time-periodicity of the system is delivered by an external perturbation, the Floquet concept can be equally applied to internal modes of a solid, such as phonons, leading to electron-phonon dressed states, that are characterised by the inherent electron-phonon coupling of the material. I will finally briefly describe how the Floquet concept leads to a general first principles numerical approach to treat electron-boson coupling solids.