Quantum model simulations of attosecond electron diffraction

Ultrafast diffraction with free attosecond electron pulses promises insight into the four-dimensional motion of charge density in atoms, molecules and condensed matter. Here we consider the quantum dynamics of the electron-electron scattering process on an attosecond time scale. By numerically solving the time-dependent two-electron Schrodinger equation, we investigate the interaction of an incoming keV-range electron wavepacket by the bound electron of an aligned H (2) (+) molecule, using a one-dimensional model. Our findings reveal the ratio of elastic to inelastic contributions, the role of exchange interaction, and the influence of the molecular electron density to diffraction. Momentum transfer during the scattering process, from the incoming to the bound electron mediated by the nuclei, leaves the bound electron in a state of coherent oscillation with attosecond recurrences. Entanglement causes related state-selective oscillations in the phase shift of the scattered electron. Two scenarios of distinguishable and indistinguishable free and bound electrons yield equivalent results, irrespective of the electronic spins. This suggests to employ the scenario of distinguishable electrons, which is computationally less demanding. Our findings support the possibility of using electron diffraction for imaging the motion of charge density, but also suggest the application of free electron pulses for inducing attosecond dynamics.