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

Abstract

Time-resolved ultrafast x-ray scattering from photoexcited 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 photoexcited 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 time scale of the vibrational motion and long in comparison to the time scale 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.

Electronic Coherence in Ultrafast X-Ray Scattering from Molecular Wave Packets

“…The opportunity for x-ray scattering experiments that exploit the short duration and coherence of XFEL pulses to reach beyond structural dynamics [17][18][19][20] is explored in this Letter. Via accurate simulations of scattering from a molecular wave packet, we identify three distinct contributions to the total scattering signal: elastic, inelastic, and coherent mixed.…”

“…The strongest contribution comes from terms with f ¼ i or f ¼ j, where one of the matrix elements is elastic and, thus, large. These interferences, mediated by the inelastic scattering matrix elements, are intramolecular in a noncrystalline sample [18][19][20]46]. We explore the behavior implied by Eq.…”

Simulation of ultrafast excited-state dynamics and elastic x-ray scattering by quantum wavepacket dynamics

“…Theoretical frameworks for the simulation of TR X-ray scattering of molecules 19,20 are under continuous development; most recent contributions were achieved by Kirrander et al [21][22][23] Their ab initio method is based on the evaluation of matrix elements of the scattering operator, utilizing high-level multiconfigurational electronic wave functions and nuclear wavepackets (WPs) obtained from quantum dynamics (QD) simulations. Their approach did not only yield high-accuracy results, but also accessed the inelastic and coherent mixed components 20,[24][25][26] of the scattering signal, in addition to elastic X-ray scattering. However, due to its high computational cost, the method has been applied so far to very small molecules (H 2 and CO 2 ).…”

Theory of ultrafast x-ray scattering by molecules in the gas phase

“…28 It is worth mentioning that the coherent mixed component is caused by intramolecular interference of scattering amplitudes from different electronic states coherently occupied by the molecular wave packet, and should not be confused with the heterodyne interferences that were rejected in a recent debate. 37,[43][44][45] Those erroneous heterodyne terms were ascribed to interference between different elastic scattering amplitudes or atomic form factors in an incoherent superposition of states. The coherent mixed component discussed herein always involves at least one electronically inelastic scattering amplitude and can only be detected if the molecule displays some degree of electronic coherence.…”

“…Despite the advances made, it is clear that aspects of the theory of time-resolved x-ray scattering remain opaque, as exemplified by a recent debate regarding heterodyne interferences in the scattering signal of photoexcited molecules in the gas phase. 37,[42][43][44][45] It is therefore necessary that the theory is discussed in greater detail and that the nature of the different contributions to the scattering signal are illustrated by simulations. With this in mind, we elaborate the theoretical framework for ultrafast scattering from molecules that was partially applied in our previous work 28 , in particular with respect to different detection window limits and total scattering.…”