Electron matter waves coherently diffract when passing through a periodic structure of light formed by two interfering light waves. In this so-called Kapitza-Dirac effect, the electron momentum changes due to absorption and emission of photons via stimulated Compton scattering. Until now, the effect has only been observed with low energy electrons due to the small momentum of a visible photon compared to the momentum of high energy electron leading to diffraction angles of ${10}^{-4}\mathrm{rad}$ or smaller. We report on the observation of the Kapitza-Dirac effect in a scanning electron microscope using high energy (20 and 30 keV) electrons with de Broglie wavelengths of 9 and 7 pm, respectively. The photon sidebands in the electron transverse momentum spectrum are detected in the convergent beam diffraction geometry using spatial filtering. As the coupling strength between the electrons and the light field increases, the sideband populations exhibit coherent, reversible oscillations among diffraction orders. The effect can serve as a coherent electron beam splitter or a phase plate in various types of electron microscopes.

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• Electron beams & optics
• Quantum description of light-matter interaction