A theory for pump-probe core XPS and XAS experiments in electron-phonon coupled materials

The advent of high power, ultrafast x-ray sources from x-ray free electron laser (XFEL) facilities is enabling cutting edge experiments to explore previously unseen features of complex correlated material systems. Pump-probe experiments, where an incident laser pump pulse electronically excites a sample of interest and a subsequent probe pulse provides a ''snapshot'' which can be observed, are a central tool used to understand correlated materials. Interest in non-equilibrium experiments on correlated materials arises from the desire to uncouple correlated degrees of freedom giving rise to atypical equilibrium behaviors, as well as to explore ''hidden phases''- stable or metastable phases such as charge density waves and possibly superconductivity--which are not present in the equilibrium phase diagram. We seek to understand how a simple model of electrons coupled to a static (zero frequency) phonon (static Holstein model) in a charge density wave (CDW) state interacts with a core-level hole state, such as would be created by an x-ray photoemission (XPS) or x-ray absorption (XAS) experiment, both in and out of equilibrium. This simple microscopic model, which has fully quantum mechanical electrons and semi-classical phonons could indicate features of XPS or XAS experiments which arise from core-level coupling to the electron-phonon subsystem in charge-density wave materials when driven out of equilibrium.