Light-induced Pairing Instability of Ultrafast Electron Beams with Space Charge Interactions

Ultrafast electron beams are essential for many applications, yet space-charge interactions in high-intensity beams lead to energy dissipation, coherence loss, and pulse broadening. Existing techniques mitigate these effects by using low-flux beams, preserving beam coherence into the quantum regime. Here, we propose a novel approach by treating the electrons as a strongly correlated Fermi gas rather than merely as an ensemble of charged point-like particles. We introduce a photon-induced pairing mechanism that generates a net attractive force between two electrons, thereby forming "flying bound states" analogous to Cooper pairs of conduction electrons in superconductors. Employing the setting of photon-induced near-field electron microscopy (PINEM), we demonstrate that the effective interaction via single-photon exchange among PINEM electrons can suppress the inherent repulsive Coulomb interaction, enabling a pairing instability mediated by structured electromagnetic fields at near-resonant velocity matching regimes. Finally, we analyze the dynamics of the free-electron pairs in a bunched beam, underscoring the potential to facilitate a phase-coherent condensate of electrons, which can further enhance beam coherence and multi-particle correlation for high-intensity electrons.