Classical–Quantum Correspondence in Photonic Temporal Crystals

In this work, we develop a quantum electrodynamical framework for photonic temporal crystals (PTCs), bridging classical momentum gaps and fully quantum phenomena within a single theoretical model.Building on previous studies of non-Hermitian band structures in time-periodically modulated media [1-4], we show that a PTC can be quantized through a Floquet Hamiltonian where the photonic modes form a synthetic lattice in momentum-Floquet space.A key insight is that the exponential field growth seen in classical PTCs corresponds, quantummechanically, to a localization-delocalization transition of photon wavefunctions.At critical momenta (i.e., the edges of the momentum gap), photon number states become delocalized, triggering exponential increases in photonic energy.Notably, when a two-level atom couples to these modes in a single-frequency cavity, conventional Rabi oscillations can be dramatically altered by the large continuum of Floquet-photonic states.Rather than exhibiting recurrent population exchange, the atomic state irreversibly decays into a half-and-half mixed state, even though there is only one nominal cavity resonance, illustrating how time-periodic modulation effectively expands the available photonic Hilbert space [4].These results highlight that, despite the overall Hamiltonian being Hermitian, classical pseudo-Hermitian features emerge through Floquet band folding and interplay with quantum light-matter interactions.Beyond clarifying the classical-quantum correspondence of PTCs, this framework opens avenues for exploring photon pair creation, squeezing, and tailored non-equilibrium light-matter interactions [4,5].