Close encounters between periodic light and periodic arrays of quantum emitters

Periodically structured surfaces (metasurfaces), i.e., periodic light, have evolved as a powerful tool for manipulating electromagnetic fields both in classical and quantum regimes. However, no general approach for quantizing the electromagnetic fields and treating quantum light-matter interactions in such structures exists. Here, we construct an ab initio few-mode quantization scheme for metasurface resonances based on macroscopic quantum electrodynamics. We use our approach to propose a framework for strong light-matter coupling in which collective excitations of periodic arrays of quantum emitters are strongly coupled to the light modes supported by the metasurface, leading to the formation of crystal polaritons. As a proof-of-principle example of their potential, we show that interactions between crystal polaritons can lead to an efficient and directional generation of entangled photon pairs.