On the physics of ultrashort single-electron pulses for time-resolved microscopy and diffraction

Abstract

Pump–probe electron diffraction and ultrafast microscopy, based on laser excitation and probing with electrons, can provide a four-dimensional visualization of atomic motion in space and time. Electron pulses consisting of only single electrons have recently been used in order to avoid the deterioration of temporal resolution by Coulomb forces. Here it is discussed how one can define the pulse duration, the beam size and divergence, the transverse and longitudinal coherences, the energy spread and temporal dispersion, and the relation between bandwidth and shortest possible pulse duration, for single electrons and in practical context. Relations are provided on how to estimate these parameters from measurable quantities in a single-electron diffraction or microscopy experiment.