Role of electron-electron interference in ultrafast time-resolved imaging of electronic wavepackets

TL;DR

This paper analyzes how electron-electron interference affects ultrafast x-ray scattering imaging of electronic wavepackets, highlighting differences between semiclassical and quantum-electrodynamical theories in interpreting scattering signals.

Contribution

It provides a detailed comparison of semiclassical and QED theories on electron-electron interference effects in time-resolved x-ray scattering of many-electron systems.

Findings

QED predicts non-vanishing time-dependent interference effects.

Semiclassical theory shows interference vanishing over time.

Differences depend on detector energy resolution and pulse duration.

Abstract

Ultrafast time-resolved x-ray scattering is an emerging approach to image the dynamical evolution of the electronic charge distribution during complex chemical and biological processes in real-space and real-time. Recently, the differences between semiclassical and quantum-electrodynamical (QED) theory of light-matter interaction for scattering of ultrashort x-ray pulses from the electronic wavepacket were formally demonstrated and visually illustrated by scattering patterns calculated for an electronic wavepacket in atomic hydrogen [Proc. Natl. Acad. Sci. U.S.A., {\bf 109}, 11636 (2012)]. In this work, we present a detailed analysis of time-resolved x-ray scattering from a sample containing a mixture of non-stationary and stationary electrons within both the theories. In a many-electron system, the role of scattering interference between a non-stationary and several stationary electrons to the total scattering signal is investigated. In general, QED and semiclassical theory provide different results for the contribution from the scattering interference, which depends on the energy resolution of the detector and the x-ray pulse duration. The present findings are demonstrated by means of a numerical example of x-ray TRI for an electronic wavepacket in helium. It is shown that the time-dependent scattering interference vanishes within semiclassical theory and the corresponding patterns are dominated by the scattering contribution from the time-independent interference, whereas the time-dependent scattering interference contribution does not vanish in the QED theory and the patterns are dominated by the scattering contribution from the non-stationary electron scattering.