Quantum model simulations of attosecond electron diffraction

Abstract

Ultrafast diffraction with free attosecond electron pulses promises insight into the four-dimensional motion of charge density in atoms, molecules and condensed matter. Here we consider the quantum dynamics of the electron-electron scattering process on an attosecond time scale. By numerically solving the time-dependent two-electron Schrödinger equation, we investigate the interaction of an incoming keV-range electron wavepacket by the bound electron of an aligned H + 2 molecule, using a one-dimensional model. Our findings reveal the ratio of elastic to inelastic contributions, the role of exchange interaction, and the influence of the molecular electron density to diffraction. Momentum transfer during the scattering process, from the incoming to the bound electron mediated by the nuclei, leaves the bound electron in a state of coherent oscillation with attosecond recurrences. Entanglement causes related state-selective oscillations in the phase shift of the scattered electron. Two scenarios of distinguishable and indistinguishable free and bound electrons yield equivalent results, irrespective of the electronic spins. This suggests to employ the scenario of distinguishable electrons, which is computationally less demanding. Our findings support the possibility of using electron diffraction for imaging the motion of charge density, but also suggest the application of free electron pulses for inducing attosecond dynamics. ultrafast electron diffraction, scattering theory, attosecond dynamics, entanglement, coherence

Single-electron pulses for ultrafast diffraction

“…Ultrafast diffraction is an interference process, and electrons are scattered individually from the sample's atoms as quantum wave packets (17,18). On the detector, each electron interferes with itself and generates an event with highest probability at the positions of diffraction features and unlikely in-between.…”

“…The interplay of laser parameters and surface morphology defines the initial phase space of photoemission. Second, the provided data and relations shall be useful for energy-filtered diffraction and microscopy (43,44), femtosecond needle sources (45,46), propagation of elliptical packets (47), and for electron pulse compression with time-dependent fields (2,14,15,17). The outlined measurement approach is a practical way to investigate and optimize the energetic, temporal, and spatial characteristics of femtosecond electron packets for these and other applications.…”

“…Recently reported studies include such of reaction pathways during phase transformations (2), chemical reactions (3), laser ablation (4), molecular alignment (5), changes at interfaces (6), heating and melting processes (7)(8)(9), cantilever motion (10), or evanescent fields around nanostructures (11), among many others (12). Possibilities to access the attosecond regime of charge density motion are also discussed (13), taking into account the generation of pulses (14)(15)(16) and the quantum dynamics of the scattering process (17).…”

Detecting Electron Motion in Atoms and Molecules

“…Only one of these studies [22] showed how to produce the coherent states and, by using a one-dimensional (1D) approximation, how nuclear motion affects the results: The electronic superposition state coherence survived even for times comparable to the beat period. Very recently, ultrashort electron pulse diffraction from the H þ 2 molecule has been investigated by using a 1D approximation [23]. Inelastic and exchange processes were found to play minor roles.…”

“…The elastic scattering amplitude and the elastic DSCS for this superposition state of T þ 2 can be obtained in the Born approximation by using procedures similar to those used for the H atom. In particular, inelastic processes and exchange effects are neglected [19,23]. Since the temporal scales of nuclear rotation and separation for the heavy tritium nuclei are much larger than the temporal width of the electron pulse, treating the nuclear separation as stationary should be a good approximation.…”