Inelastic ponderomotive scattering of electrons at a high-intensity optical travelling wave in vacuum

In the early days of quantum mechanics Kapitza and Dirac predicted that matter waves would scatter off the optical intensity grating formed by two counter-propagating light waves [1]. This interaction, driven by the ponderomotive potential of the optical standing wave, was both studied theoretically and demonstrated experimentally for atoms [2] and electrons [3-5]. In the original version of the experiment [1,5], only the transverse momentum of particles was varied, but their energy and longitudinal momentum remained unchanged after the interaction. Here, we report on the generalization of the Kapitza-Dirac effect. We demonstrate that the energy of sub-relativistic electrons is strongly modulated on the few-femtosecond time scale via the interaction with a travelling wave created in vacuum by two colliding laser pulses at different frequencies. This effect extends the possibilities of temporal control of freely propagating particles with coherent light and can serve the attosecond ballistic bunching of electrons [6], or for the acceleration of neutral atoms or molecules by light.