Low-energy Free-electron Rabi oscillation and its applications

We propose free-electron Rabi oscillation by creating an isolated two-level system in a synthetic energy space induced by laser. The {\pi}/2-pulse and {\pi}-pulse in synthetic Rabi dynamics can function as 'beam splitters' and 'mirrors' for free-electron interferometry, allowing us to detect local electromagnetic fields and plasmonic excitations. When the coupling field is quantized, we can observe quantum and vacuum Rabi oscillations of the two-level electron, which can be used to investigate the quantum statistics of optical excitations and electron-photon entanglement. Recent advances in laser control of electron microscopes and spectroscopes makes the experimental detection of synthetic Rabi oscillations possible. However, observing the quantum Rabi oscillation of electrons remains challenging. Our work has the potential to advance various fundamentals and applications of resonant light-matter interactions between low-energy electrons and quatum light.