Ultrafast Imaging and the "Phase Problem" for Inelastic X-Ray Scattering

TL;DR

This paper introduces a novel causality-based method for directly imaging ultrafast electron dynamics in condensed matter using inelastic x-ray scattering, achieving attosecond temporal and sub-angstrom spatial resolution.

Contribution

It presents a new inverse scattering approach that reconstructs charge propagators without Fourier transforms, enabling ultrafast imaging of electron density dynamics.

Findings

Achieves ~1 attosecond temporal resolution

Provides < 1 Å spatial resolution

Applicable to x-ray, electron, and neutron scattering

Abstract

We describe a new method for imaging ultrafast dynamics in condensed matter using inelastic x-ray scattering (IXS). We use the concepts of causality and irreversibility to construct a general solution to the inverse scattering problem (or "phase problem") for inelastic x-ray scattering, which enables direct imaging of dynamics of the electron density with resolutions of ~1 attosecond (10-18 sec) in time and < 1 A in space. This method is not a Fourier transform of IXS data, but a means to impose causality on the data and reconstruct the charge propagator. The method can also be applied to inelastic electron or neutron scattering. We give a general outline of phenomena that can and cannot be studied with this technique, and provide an outlook for the future.