  Electron microscopy based on high-energy electrons allows nanoscopic
analytical imaging taking advantage of secondarily generated particles.
Especially for cathodoluminescence, the correlation between primary incident
electrons and emitted photons includes information on the entire interaction
process. However, electron-photon time correlation tracking the relaxation
dynamics of luminescent materials has so far not been achieved. In this work,
we propose time-correlated electron and photon counting microscopy, where
coincidence events of primary electrons and generated photons are counted after
interaction. The electron-photon time correlation enables extracting a unique
lifetime of the emitter independent of the photon state, accounting for
coherent and incoherent photon generation processes. We also introduce a
correlation factor and discuss the correlation between electrons and generated
coherent photons. Through momentum selection, we observe correlation changes
indicating the presence of pair correlation originated from the electron-photon
entanglement. The present work lays the foundation for developing
next-generation electron microscopy based on quantum correlation.
