Light Emission by Free Electrons in Photonic Time-Crystals

Photonic time-crystals (PTCs) are spatially-homogeneous media whose electromagnetic (EM) susceptibility varies periodically in time, causing temporal reflections and refractions for any wave propagating within the medium. The time-reflected and time-refracted waves interfere, giving rise to Floquet modes with momentum bands separated by gaps (rather than energy bands and gaps, as in photonic crystals). Here, we show that a free electron moving in a PTC spontaneously emits radiation, and, when associated with momentum-gap modes, the radiation of the electron is exponentially amplified by the modulation of the refractive index. Moreover, under strong electron-photon coupling, the quantum formulation reveals that the spontaneous emission into the PTC bandgap experiences destructive quantum interference with the emission of the electron into the PTC band modes, leading to suppression of the interdependent emission. Free-electron physics in PTCs offers a new platform for studying a plethora of exciting phenomena such as radiating dipoles moving at relativistic speeds and highly efficient quantum interactions with free electrons. Radiation emission in PTCs and its non-resonant nature hold the promise for constructing new particle detectors with adjustable sensitivity and highly tunable laser sources, ranging from terahertz to the x-ray regime, drawing their power from the modulation.