Quantum Electrodynamics with Time-Varying Dielectrics
Fundamental advances in photonics and quantum optics have enabled the development of exotic meta-materials, epsilon-near-zero materials, atomic mirrors and photonic crystals which can form dielectric media with time-varying optical properties. We develop a general formalism to describe quantum electrodynamic (QED) effects in the presence of such time-varying dielectrics, following the Huttner-Barnett model for canonical quantization of electromagnetic fields in a dielectric medium. Considering a microscopic model for the dielectric as matter fields interacting with the electromagnetic environment, we allow for the possibility of dynamically varying the dielectric susceptibility and develop constraints on the temporal dependence of the susceptibility.
It is well known that the presence of a dielectric modifies the electromagnetic environment of an excited emitter, which in turn influences its emission rates. The Purcell effect is a consequence of this phenomenon. As an application of our time-varying Huttner-Barnett quantization scheme, we analyze the effect of temporally varying dielectric on the spontaneous emission rates of an excited two-level atom embedded in such a dielectric. Our results pave the way for investigating a wide range of QED phenomena in the presence of time-varying dielectrics.