Ultrafast Stern-Gerlach and Anomalous Bragg Diffraction Regimes of Low-energy Free Electron Interaction with Light

Recent advances in photon-induced near-field electron microscopy (PINEM) have significantly impacted allied disciplines such as laser-driven accelerators and free electron radiations, collectively fostering the emergence of free-electron quantum optics (FEQO). A central objective of FEQO is to achieve coherent optical control of free electrons, analogous to light manipulation of atoms in atom optics. Motivated by this analogy, we propose an ultrafast Stern-Gerlach (USG) regime for low-energy quantum electron wavepacket (QEW), which crucially incorporates the effects of second-order dispersion inherent to slow electrons. We demonstrate that the USG diffraction induces spectral splitting and shifting of the QEW via a longitudinal electric field gradient, with the two dominant truncated sidebands forming a pseudospin degree of freedom for an effective "two-level" electron. Furthermore, by examining the wave-particle duality of the QEW during light interaction, we identify a dispersion-induced anomalous Bragg diffraction regime. This regime exhibits a distinct spectral pattern, differentiating it from these reported PINEM (Raman-Nath), dielectric laser accelerators (DLA), anomalous PINEM, and Bragg diffraction regimes. Our study provides a comprehensive classification for light-induced diffraction regimes for both swift and slow electrons. These findings underscore the pivotal role of slow-electron dispersion and duality nature in free-electron optics, offering promising avenues for electron wavefunction quantum engineering ultrafast interferometers.