  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.
