  We demonstrate the quantized transfer of photon energy and transverse
momentum to a high-coherence electron beam. In an ultrafast transmission
electron microscope, a three-dimensional phase modulation of the electron
wavefunction is induced by transmitting the beam through a laser-illuminated
thin graphite sheet. This all-optical free-electron phase space control results
in high-purity superpositions of linear momentum states, providing an
elementary component for optically programmable electron phase plates and beam
splitters.
