Phonon-assisted free-electron recoil control and mechanical sensing

Abstract

Mechanical vibrations are fundamental to a wide range of physical phenomena and technologies, yet their ability to actively shape free-electron dynamics remains largely unexplored. Here we theoretically show how an optomechanical membrane provides a phonon-assisted optical interface for controlling free-electron recoil and sensing localized forces. Transverse membrane motion scatters cavity light into high-momentum evanescent sidebands that enable phase-matched interaction with electrons traveling in vacuum. Beyond supplying momentum for phase matching, the vibration amplitude controls the electron-light interaction strength and redistributes electron populations among recoil orders. External forces that perturb the vibration are thereby encoded in the electron recoil spectrum. Under the modeled conditions, electron readout of localized stochastic forces can yield a higher signal-to-noise ratio than a Gaussian optical homodyne benchmark at equal detected probe rates. These results provide a theoretical basis for mechanically reconfigurable free-electron optics and mode-selective mechanical sensing.