Attosecond Charge Migration in Molecules Imaged by Combined X-ray and Electron Diffraction

Abstract

We show how ultrafast gas-phase X-ray and electron diffraction signals can be combined to generate real-space movies of charge migration dynamics in molecules. Charge migration denotes short time electronic charge redistribution upon photoexcitation of molecules where the nuclei are frozen. In this regime, we identify a mixed electronic–nuclear interference term that can be cleanly singled out. Using the ground-state nuclear structure as a reference, the phase information in this signal allows its inversion to real space and the capture of electronic charge density movies on the attosecond time scale.

Novel Ultrafast Molecular Imaging Based on the Combination of X-ray and Electron Diffraction

“…Heterodyne-detected X-ray diffraction could achieve this in molecules, , but its experimental realization is more complex. Below we discuss a novel technique for the real-space imaging of attosecond electron dynamics in isolated molecules based on combining ultrafast homodyne-detected X-ray and electron diffraction signals . This is achieved by isolating the mixed contribution, S̃ hom mixed ( q , t ), in eq .…”

“…We assume a window function much broader than the relevant electronic transition energies of the system so that W 0 (Δω) is independent of the molecular response. 9,12,13 We note that homodyne signals constitute coherent spontaneous emission whereas heterodyne signals are generated by stimulated emission. 14 The homodyne-detected diffraction signal in eq 2 thus measures the modulus square of an amplitude, so that it is not sensitive to the phase of the probe pulse.…”

“…Below we discuss a novel technique for the real-space imaging of attosecond electron dynamics in isolated molecules based on combining ultrafast homodyne-detected X-ray and electron diffraction signals. 9 This is achieved by isolating the mixed contribution, S ̃hom mixed (q, t), in eq 6. By subtracting the ultrafast homodyne-detected X-ray (eq 4) and electron diffraction (eq 6) signals with careful normalization, one obtains S hom diff (q, t) as…”

“…The time-resolved single-molecule (gas-phase) homodyne diffraction signal is given by , S hom false( boldq , T false) ∝ W 0 false( normalΔ ω false) ∫ d t false| boldA normalX ( t − T ) false| 2 S̃ hom false( boldq , t false) where A X ( t – T ) is the X-ray/electron probe pulse vector potential at delay time T from the pump pulse, q is the scattering momentum transfer, W 0 (Δω) is a window function for a frequency detection widow Δω, and S̃ hom ( q , t ) is the time-dependent molecular response in homodyne diffraction. We assume a window function much broader than the relevant electronic transition energies of the system so that W 0 (Δω) is independent of the molecular response. ,, …”

“…In this theoretical article, we show how ultrafast X-ray diffraction (XRD) and ultrafast electron diffraction (UED) signals may be combined to reveal novel information unavailable through either of them alone. We consider two types of combined X-ray and electron diffraction signals: (1) By subtracting homodyne-detected ultrafast X-ray and electron diffraction, a mixed electronic–nuclear interference in electron diffraction can be isolated for the direct imaging of attosecond electron dynamics in real space (Figure top). (2) By subtracting heterodyne-detected ultrafast X-ray and electron diffraction, the purely nuclear charge density can be singled out, allowing the direct imaging of nuclear wavepacket dynamics (Figure , bottom).…”