Self-trapping of slow electrons in the energy domain

The interaction of light and swift electrons has enabled phase-coherent manipulation and acceleration of electron wavepackets. Here we investigate this interaction in a new regime where low-energy electrons (~20-200 eV) interact with a phase-matched light field. Our analytical and one-dimensional numerical study shows that slow electrons are subject to strong confinement in the energy domain due to the non-vanishing curvature of the electron dispersion. The spectral trap is tunable and an appropriate choice of light field parameters can reduce the interaction dynamics to only two energy states. The capacity to trap electrons expands the scope of electron beam physics, free-electron quantum optics and quantum simulators.