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Photonic time-crystals (PTCs) are spatially-homogeneous media whoseelectromagnetic (EM) susceptibility varies periodically in time, causingtemporal reflections and refractions for any wave propagating within themedium. The time-reflected and time-refracted waves interfere, giving rise toFloquet modes with momentum bands separated by gaps (rather than energy bandsand gaps, as in photonic crystals). Here, we show that a free electron movingin a PTC spontaneously emits radiation, and, when associated with momentum-gapmodes, the radiation of the electron is exponentially amplified by themodulation of the refractive index. Moreover, under strong electron-photoncoupling, the quantum formulation reveals that the spontaneous emission intothe PTC bandgap experiences destructive quantum interference with the emissionof the electron into the PTC band modes, leading to suppression of theinterdependent emission. Free-electron physics in PTCs offers a new platformfor studying a plethora of exciting phenomena such as radiating dipoles movingat relativistic speeds and highly efficient quantum interactions with freeelectrons. Radiation emission in PTCs and its non-resonant nature hold thepromise for constructing new particle detectors with adjustable sensitivity andhighly tunable laser sources, ranging from terahertz to the x-ray regime,drawing their power from the modulation.

Light Emission by Free Electrons in Photonic Time-Crystals