Quantum Interaction Between Free Electrons and Light Involving First-order and Second-order Process

Abstract: Photon-induced Near-field Electron Microscopy (PINEM) effect has revealed the quantum interaction between free electrons and optical near filed, which demonstrated plenty of novel phenomena of manipulating free electron wave packet and detecting/shaping quantum photonic states. However, free electrons generally only absorb/emit one photon at a time, while the physical mechanism and phenomena of free electron-two-photon interaction have not been studied yet. Moreover, the relationship between PINEM and Kapitza-Dirac (KD) effect and nonlinear Compton scattering is still unclear. Here we develop the full quantum theory of electron-photon interaction considering the two-photon process. It is revealed that the emission/absorption of two photons by electrons can be greatly enhanced by manipulating the electric field component of optical near field, and the quantum interference between single-photon and two-photon processes can occur in some circumstances, which affects the photon number state, electron energy states and electron-photon entanglement. Meanwhile, it is found that the KD effect (elastic electron-photon scattering) and nonlinear Compton scattering (inelastic electron-photon scattering) are also a kind of two-photon process and the distribution of electrons can be deduced analytically based on the full quantum theory. Our work uncovers the possible abundant phenomena when free electron interacting with two photons, paves the way for more in-depth studies of nonlinear processes in electron-photon quantum interactions in the future.