Quantum Theory of Photon Pair Creation in Photonic Time Crystals

Time-varying media offer a platform to realize novel and exotic wave effects, including photonic time crystals characterized by momentum band gaps with exponential wave amplification. Here we focus on the quantum electrodynamic properties of time-varying media, in particular, vacuum amplification and squeezing. For that purpose, we present a theory of photon pair generation in photonic time crystals that unveils the link between the classical and quantum electrodynamical properties of these systems: that is, a direct relation between reflectivity and pair generation through the squeezing parameter. By working within a Hermitian framework, we are able to characterize quantum pair generation processes in photonic time crystals, showing how momentum bandgaps result in an exponential enhancement of dynamical Casimir processes.