Imaging instantaneous electron flow with ultrafast resonant x-ray scattering

We propose a way to image dynamical properties of nonstationary electron systems using ultrafast resonant x-ray scattering. Employing a rigorous theoretical analysis within the framework of quantum electrodynamics, we demonstrate that a single scattering pattern from a nonstationary electron system encodes the instantaneous interatomic electron current in addition to the structural information usually obtained by resonant x-ray scattering from stationary systems. Thus, inelastic contributions that are indistinguishable from elastic processes induced by a broadband probe pulse, instead of being a concern, serve as an advantage for time-resolved resonant x-ray scattering. Thereby, we propose an approach combining elastic and inelastic resonant x-ray scattering for imaging dynamics of nonstationary electron systems in both real space and real time. In order to illustrate its power, we show how it can be applied to image the electron-hole current in an ionized diatomic molecule.