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

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 [G. Dixit, O. Vendrell, and R. Santra, Proc. Natl. Acad. Sci. U.S.A. 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 time-resolved imaging 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 do not vanish in the QED theory and the patterns are dominated by the scattering contribution from the non-stationary electron scattering.

Contribution of Coulomb explosion to form factors and mosaicity spread in single particle X-ray scattering

“…In the present work, we describe the X-ray laser-matter interaction in a quantum-mechanical ab initio approach, the size of the system under study has been limited to the small water cluster (H 2 O) 8 . Due to the dipole approximation and the description of atomic core electrons employing pseudopotentials, in the current implementation the OCTOPUS program package cannot take hard X-ray energies of the external laser pulse into account.…”

“…Thus, in principle all 64 valence electrons of the octamer water cluster treated in this work can be excited in the simulation the time step of which is chosen to be 0.1 attoseconds. With respect to the size of the cluster, the description is kept well within the dipole 8 with symmetrically independent atom groups colored separately. The arrow indicates the axis of the C 4 rotation, which followed by a reflection with respect to the horizontal plane is the generator of the S 4 symmetry group of the cluster.…”

“…The simulations of the (H 2 O) 8 water cluster in its electronic ground state start with the initial guess for the geometry optimization obtained from the Cambridge Cluster Database. 21 …”

“…Thus, the octamer (H 2 O) 8 water cluster with S 4 symmetry was chosen as a test system (see Fig. 1) in our calculations, 3 being small enough to keep the computational costs of TDDFT reasonable, yet allowing for the inclusion of volume effects, e.g.…”

Imaging instantaneous electron flow with ultrafast resonant x-ray scattering

“…[21,22]. This is particularly relevant for the measurement of valence electron dynamics in heavy elements, where the vast majority of electrons are stationary, since nonresonant x-ray scattering probes simultaneously electrons involved in the dynamics and electrons that are essentially stationary [23]. In resonant scattering, one can selectively enhance the scattering contribution from those * daria.gorelova@desy.de † robin.santra@cfel.de (quasi)particles that are actually moving.…”