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It has been shown that the spontaneous emission rate of photons by freeelectrons, unlike stimulated emission, is independent of the shape ormodulation of the quantum electron wavefunction (QEW). Nevertheless, here weshow that the quantum state of the emitted photons is non-classical and doesdepend on the QEW shape. This non-classicality originates from the shapedependent off-diagonal terms of the photon density matrix. This is manifestedin the Wigner distribution function and would be observable experimentallythrough Homodyne detection techniques as a squeezing effect. Considering ascheme of electrons interaction with a single microcavity mode, we present aQED formulation of spontaneous emission by multiple modulated QEWs through abuild-up process. Our findings indicate that in the case of a density modulatedQEWs beam, the phase of the off-diagonal terms of the photon state emitted bythe modulated QEWs is the harbinger of bunched beam superradiance, where thespontaneous emission is proportional to N_e^2. This observation offers apotential for enhancement of other quantum electron interactions with quantumsystems by a modulated QEWs beam carrying coherence and quantum properties ofthe modulation.

Shape-Dependence of Spontaneous Photon Emission by Quantum Electron Wavepackets and the QED Origin of Bunched Electron Beam Superradiance