Time-resolved Electron Momentum Spectroscopy with Ultrashort Electron Pulses: Confined Probing and Effects of Vacuum Dispersion

TL;DR

This paper investigates how ultrashort electron pulses in electron momentum spectroscopy (EMS) can capture attosecond electron dynamics, emphasizing the effects of finite wave packet size and vacuum dispersion on measurement accuracy.

Contribution

It introduces a spatial filtering approach in wave packet scattering analysis and demonstrates how vacuum dispersion influences the interpretation of EMS results.

Findings

Target momentum distribution is probed in a finite spatial region.

Spatially shifting the target affects the measured scattering probability.

Vacuum dispersion causes spatial broadening of the electron wave packet.

Abstract

Previous theoretical studies have shown that attosecond electron dynamics can, in principle, be captured in electron momentum spectroscopy (EMS) using ultrashort electron pulses. By including further analytical considerations on the scattering probability, we here study the effect of the finite transversal extend of the projectile electron wave packet. We find that in wave packet scattering, the target momentum distribution is probed solely in a finite spatial region. This is evident from a spatially filtering Gabor transform appearing in the scattering probability, replacing the full momentum wave function appearing in the conventional plane wave treatment. In addition, by spatially shifting the target with regard to the wave packet focus, we illustrate the influence of vacuum dispersion, i.e., the spatial broadening of the wave packet as it propagates. Our findings are significant for the possibility to correctly interpret future attosecond-EMS results and the considered effects reflect fundamental aspects of wave packet scattering. The EMS setup may, therefore, constitute a useful framework for understanding scattering with finite wave packets.