Theory of time-resolved non-resonant x-ray scattering for imaging ultrafast coherent electron motion

Future ultrafast x-ray light sources might image ultrafast coherent electron motion in real-space and in real-time. For a rigorous understanding of such an imaging experiment, we extend the theory of non-resonant x-ray scattering to the time-domain. The role of energy resolution of the scattering detector is investigated in detail. We show that time-resolved non-resonant x-ray scattering with no energy resolution offers an opportunity to study time-dependent electronic correlations in non- equilibrium quantum systems. Furthermore, our theory presents a unified description of ultrafast x-ray scattering from electronic wave packets and the dynamical imaging of ultrafast dynamics using inelastic x-ray scattering by Abbamonte and co-workers. We examine closely the relation of the scattering signal and the linear density response of electronic wave packets. Finally, we demonstrate that time-resolved x-ray scattering from a crystal consisting of identical electronic wave packets recovers the instantaneous electron density.