  Coherent emission of light by free charged particles is ubiquitous in many
areas of physics and engineering, with the light's properties believed to be
successfully captured by classical electromagnetism in all relevant
experimental settings. The advent of interactions between light and free
quantum matter waves brought about fundamental questions regarding the role of
the particle wavefunction. Here we show that even in seemingly classical
experimental regimes, light emission is fundamentally tied to quantum
properties of the emitting particles, such as their quantum coherence and
correlations. By employing quantum electrodynamics, we unveil the role of the
particle's coherent momentum uncertainty, without which decoherence of light
becomes dominant. As an example, we consider Cherenkov radiation, envisioned
for almost a century as a shockwave of light. We find instead that the
shockwave's duration is fundamentally bound from below by the particle's
coherent momentum uncertainty due to the underlying entanglement between the
particle and light. This quantum optical paradigm opens new capabilities in
analytical electron microscopy, enabling the measurement of quantum
correlations of shaped electron wavepackets. Our findings also have
applications for Cherenkov detectors in particle physics. For example, by
measuring spectral photon autocorrelations, one can unveil the particle's
wavefunction size, shape and coherence. Such schemes are especially intriguing
for many high-energy particles, where other techniques are not available.
