Spontaneous emission decay and excitation in photonic temporal crystals

Over the last few decades, the prominent strategies for controlling spontaneous emission has been the use of resonant or space-periodic photonic structures. This approach, initially articulated by Purcell and later expanded by Bykov and Yablonovitch in the context of photonic crystals, leverages the spatial surroundings to modify the spontaneous emission decay rate of atoms or quantum emitters. However, the rise of time-varying photonics has compelled a reevaluation of the spontaneous emission process within dynamically changing environments, especially concerning photonic temporal crystals where optical properties undergo time-periodic modulation. Here, we apply classical light-matter interaction theory along with Floquet analysis to reveal a substantial enhancement in the spontaneous emission decay rate at the momentum gap frequency in photonic temporal crystals. This enhancement is attributed to time-periodicity-induced loss and gain mechanisms, as well as the non-orthogonality of Floquet eigenstates that are inherent to photonic temporal crystals. Intriguingly, our findings also suggest that photonic temporal crystals enable a non-equilibrium light-matter interaction process: the spontaneous excitation of an atom from its ground state to an excited state, accompanied by the concurrent emission of a photon, referred to as spontaneous emission excitation.