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In this article, we present a unified reciprocal quantum electrodynamics (QED) formulation of free-electron and quantum–light interaction. For electron–light interactions, we bridge the underlying theories of photon-induced near-field electron microscopy, laser-induced particle accelerators, and radiation sources, such as quantum free electron laser, transition radiation and Smith-Purcell effect. We demonstrate an electron–photon spectral reciprocity relation between the electron energy loss/gain and the radiation spectra. This ‘acceleration/radiation correspondence’ (ARC) conserves the electron energy, and photon number exchanged, that is, ΔE/ℏω + Δν q = 0, and in the representation of a quantum electron wavepacket, displays explicit dependence on the history-dependent phase and shape of the wavepacket configuration. It originates from an interaction-induced quantum interference term that is usually ignored in Fermi’s golden rule analyses, but is kept in our combined quantum free electron–photon state formulation. We apply this formulation to both stimulated interaction and spontaneous emission of classical and quantum light by the quantum-featured electrons. The ‘spontaneous’ emissions of coherent states (‘classical’ light) are remarked and squeezed states of quantum light is shown to be enhanced with squeezing. This reciprocal QED formulation has promise for extensions to other fundamental research issues in quantum light and quantum matter interactions.

Beyond Fermi’s golden rule in free-electron quantum electrodynamics: acceleration/radiation correspondence