  Scattering of a tightly focused electron beam by an atom forms one of the
bases of modern electron microscopy. A fundamental symmetry breaking occurs
when the target atom is displaced from the beam center. This displacement
results in an asymmetry in the angular distribution of the scattered electrons.
Here we propose a concept to control the sign and magnitude of the asymmetry by
shaping the incident high-energy electron wave packet in momentum space on the
atto- to picosecond time scale. The shaping controls the ultrafast real-space
dynamics of the wave packet, shifting the balance between two competing
contributions of the impact-parameter-dependent quantum interference and the
momentum distribution of the wave packet on the target. We find a strong
sensitivity of the scattering on the wave packet properties, an effect that
opens promising new avenues for ultrafast electron microscopy.
