It has been shown that the spontaneous emission rate of photons by free electrons, unlike stimulated emission, is independent of the shape or modulation of the quantum electron wavefunction (QEW). Nevertheless, here we show that the quantum state of the emitted photons is non-classical and does depend on the QEW shape. This non-classicality originates from the shape dependent off-diagonal terms of the photon density matrix. This is manifested in the Wigner distribution function and would be observable experimentally through homodyne detection techniques as a squeezing effect. Considering a scheme of electrons interaction with a single microcavity mode, we present a QED formulation of spontaneous emission by multiple modulated QEWs through a build-up process. Our findings indicate that in the case of a density modulated QEWs beam, the phase of the off-diagonal terms of the photon state emitted by the modulated QEWs is the harbinger of bunched beam superradiance, where the spontaneous emission is proportional to N_e^2 . This observation offers a potential for enhancement of other quantum electron interactions with quantum systems by a modulated QEWs beam carrying coherence and quantum properties of the modulation.

中文翻译：

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异形量子电子波包的自发光子发射和束束电子束超辐射的 QED 起源。


已经表明，与受激发射不同，自由电子对光子的自发发射速率与量子电子波函数 （QEW） 的形状或调制无关。尽管如此，我们在这里表明发射光子的量子态是非经典的，并且确实取决于 QEW 形状。这种非经典性源于光子密度矩阵的形状相关非对角线项。这表现在 Wigner 分布函数中，并且可以通过零差检测技术作为挤压效应在实验中观察到。考虑到电子与单个微腔模式的相互作用方案，我们提出了一个通过构建过程由多个调制 QEW 自发发射的 QED 公式。我们的研究结果表明，在密度调制 QEW 光束的情况下，调制 QEW 发射的光子状态的非对角线项的相位是成束光束超辐射的预兆，其中自发发射与 N_e^2 成正比。这一观察结果为通过携带调制的相干性和量子特性的调制 QEWs 光束增强了其他量子电子与量子系统的相互作用提供了潜力。