Time-resolved ultrafast x-ray scattering from an incoherent electronic mixture

TL;DR

This paper develops a quantum electrodynamical theory for time-resolved ultrafast x-ray scattering from incoherent electronic mixtures, clarifying how signals encode electronic and vibrational dynamics in different systems.

Contribution

It provides a rigorous theoretical framework for understanding x-ray scattering signals from incoherent electronic states, highlighting conditions for heterodyning and interference effects.

Findings

Total scattering signal is an incoherent sum for gas-phase molecules.

Heterodyning is not possible in incoherent electronic mixtures of gas-phase molecules.

Interference effects can be observed in crystalline solids with electronic excitation.

Abstract

Time-resolved ultrafast x-ray scattering from photo-excited matter is an emerging method to image ultrafast dynamics in matter with atomic-scale spatial and temporal resolutions. For a correct and rigorous understanding of current and upcoming imaging experiments, we present the theory of time-resolved x-ray scattering from an incoherent electronic mixture using quantum electrodynamical theory of light-matter interaction. We show that the total scattering signal is an incoherent sum of the individual scattering signals arising from different electronic states and therefore heterodyning of the individual signals is not possible for an ensemble of gas-phase photo-excited molecules. We scrutinize the information encoded in the total signal for the experimentally important situation when pulse duration and coherence time of the x-ray pulse are short in comparison to the timescale of the vibrational motion and long in comparison to the timescale of the electronic motion, respectively. Finally, we show that in the case of an electronically excited crystal the total scattering signal imprints the interference of the individual scattering amplitudes associated with different electronic states and heterodyning is possible.