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Photonic time crystals – materials whose dielectric permittivity is modulated periodically in time – offer new concepts in light manipulation. We study theoretically the emission of light from a radiation source placed inside a photonic time crystal, and find that radiation corresponding to the momentum band gap is exponentially amplified, whether initiated by a macroscopic source, an atom, or by vacuum fluctuations, drawing the amplification energy from the modulation. The radiation linewidth becomes narrower with time, eventually shrinking to the middle of the bandgap, which enables to propose the concept of non-resonant tunable photonic time-crystal laser. Finally, we find that the spontaneous decay rate of an atom embedded in a photonic time-crystal vanishes at the band edge due to low density of photonic states.

Photonic time-crystals (PTCs) are spatially homogeneous media whose electromagnetic 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 momentum gaps (rather than energy bands and energy gaps, as in photonic crystals). Here, we present a study on the emission of radiation by free electrons in PTCs. We show that a free electron moving in a PTC spontaneously emits radiation, and when associated with momentum-gap modes, the electron emission process 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 platform for studying a plethora of exciting phenomena, such as radiating dipoles moving at relativistic speeds and highly efficient quantum interactions with free electrons.