  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 electrodynamical
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 an Hermitian framework, we are able to characterize quantum pair
generation processes in photonic time crystals, showing how momentum bandgaps
result in a non-resonant exponential enhancement of dynamical Casimir
processes.
