Ultrafast coherent excitation control and nanometer-scale imaging: a conceptual design integrating FEL interference modulation with electron probing

Abstract

This work proposes a system integration framework and conceptual design that synergizes Free-Electron Laser (FEL)-induced transient gratings with ultrafast electron beam probing to explore non-equilibrium dynamics. Leveraging the extreme ultraviolet (EUV) wavelength, high coherence, and element-selective resonant FEL excitation combined with broadband electron imaging of post-excitation dynamics of the Shenzhen Superconducting Soft X-ray Free-Electron Laser (S³FEL), we present an instrument coupling scheme governed by an adaptive grating phase-matching law to establish coherent transient gratings (\({\Lambda}_{\text{T}\text{G}}\approx 14-49 \text{n}\text{m}\)). This setup is designed to access high-momentum (\(q\)) excitations that are kinematically inaccessible to conventional optical techniques, offering a prospective platform for exploring collective electronic orders—such as polarons and photo-ionized Charge Density Waves (CDWs)—at the nanometer scale. By targeting nanoscale spatial regimes (\(\approx 20 nm\)), the scheme provides a promising framework for potential future studies on the transition from classical diffusion to phase-coherent transport and element-resolved proximal spin exchange. To detect these transient states under realistic constraints, the platform integrates a THz-driven compact electron gun operating consistently at a 1.5 keV baseline. Utilizing particle tracking and electron-optics simulations, we model the far-field non-coherent deflection mapping and real-space intensity modulation of a compressed 49 fs electron probe across a 10 \(\upmu \text{m}\) field of view, successfully resolving the spatiotemporal mismatch and coherence budget limitations. These comprehensive simulations validate the technical feasibility of the proposed cooperative instrumentation path, providing a self-consistent theoretical foundation for future experimental realization dedicated to mapping many-body interactions across mesoscopic scales.