Toward Real-Space Imaging of Electronic Motions with Attosecond X-Ray Scattering

Ultrafast X-ray scattering has emerged as a groundbreaking technique for directly imaging the evolution of molecular structures, providing insights into complex processes such as conformational changes, and bond breakage at atomic-scale spatial and temporal resolutions. Ultrafast scattering experiments have thus far utilized pulses from X-ray free-electron lasers to probe atomic motion on the scale of tens of femtoseconds. Extending this approach into the attosecond time domain would enable imaging of coherent dynamics of electronic densities and currents.

However, this regime introduces complexity in experimental setup and analysis, necessitating a different set of tools than those traditionally employed. This is due to the nature of scattering information, which encompasses both elastic and inelastic scattering and their cross-terms, rendering the simple Fourier relationship between the intensity detected and the charge density invalid.

Here, we outline a methodology for utilizing attosecond hard X-ray scattering to recover electronic charge densities and currents in real space and time from an experimental perspective. We delve into several critical aspects necessary to accomplish a "movie" of electronic motion. These aspects include the application of pump-probe phase tagging through single-shot characterization of attosecond hard X-ray pulses, strategies for controlling the detection bandwidth to highlight scattering from specific electronic states, and methods for distinguishing between densities and currents by leveraging the anisotropy and symmetry properties inherent to the attosecond scattering process. Additionally, we describe an inversion technique required to achieve sub-angstrom resolution in the reconstruction process. Together, these steps facilitate capturing a comprehensive view of electronic coherent motions within molecules, marking a significant advancement in the field of imaging.