  Spontaneous processes triggered in a sample by free electrons are commonly
regarded as incoherent, and therefore unable to interfere with external light
sources. Here, we challenge this concept by showing through first-principles
theory that light and free-electron pulses can interfere when interacting with
a nanostructure, giving rise to a modulation in the spectral distribution of
the cathodoluminescence light emission that is strongly dependent on the
electron wave function. Specifically, for a temporally focused electron,
cathodoluminescence can be cancelled upon illumination with a spectrally
modulated dimmed laser that is phase-locked relative to the electron density
profile. We illustrate this idea with realistic simulations under attainable
conditions in currently available ultrafast electron microscopes. We further
argue that the interference between excitations produced by light and free
electrons opens a new window to manipulate the ultrafast materials response by
combining the spectral and temporal selectivity of the light with the atomic
resolution of electron beams.
