  Strong interaction between light and matter waves, such as electron beams in
electron microscopes, has recently emerged as a new tool for understanding
entanglement. Here, we systematically investigate electron-light interactions
from first principles. We show that enhanced coupling can be achieved for
systems involving slow electron wavepackets interacting with plasmonic
nanoparticles, due to simultaneous classical recoil and quantum mechanical
photon absorption and emission processes. For slow electrons with longitudinal
broadenings longer than the dimensions of nanoparticles, phase-matching between
slow electrons and plasmonic oscillations is manifested as an additional degree
of freedom to control the strength of coupling. Our findings pave the way
towards a systematic and realistic understanding of electron-light interactions
beyond adiabatic approximations, and lay the ground for realization of
entangled electron-photon systems and Boson-sampling devices involving light
and matter waves.
