  Ultrafast electron-photon spectroscopy in electron microscopes commonly
requires ultrafast laser setups. Photoemission from an engineered electron
source is used to generate pulsed electrons, interacting with a sample that is
excited by the ultrafast laser pulse at a specified time delay. Thus,
developing an ultrafast electron microscope demands the exploitation of
extrinsic laser excitations and complex synchronization schemes. Here, we
present an inverse approach based on cathodoluminescence spectroscopy to
introduce internal radiation sources in an electron microscope. Our method is
based on a sequential interaction of the electron beam with an electron-driven
photon source (EDPHS) and the investigated sample. An electron-driven photon
source in an electron microscope generates phase-locked photons that are
mutually coherent with the near-field distribution of the swift electron. Due
to their different velocities, one can readily change the delay between the
photons and electrons arriving at the sample by changing the distance between
the EDPHS and the sample. We demonstrate the mutual coherence between the
radiations from the EDPHS and the sample by performing interferometry with a
combined system of an EDPHS and a WSe2 flake. We assert the mutual frequency
and momentum-dependent correlation of the EDPHS and sample radiation, and
determine experimentally the degree of mutual coherence of up to 27%. This
level of mutual coherence allows us to perform spectral interferometry with an
electron microscope. Our method has the advantage of being simple, compact and
operating with continuous electron beams. It will open the door to local
electron-photon correlation spectroscopy of quantum materials, single photon
systems, and coherent exciton-polaritonic samples with nanometric resolution.
