Cavity quantum electrodynamics in application to plasmonics and metamaterials

Frontier quantum engineering tasks require reliable control over light-matter interaction dynamics, which could be obtained by introducing electromagnetic structuring. Initiated by the Purcell's discovery of spontaneous emission acceleration in a cavity, the concept of electromagnetic modes' design have gained a considerable amount of attention due to development of photonic crystals, micro-resonators, plasmonic nanostructures and metamaterials. Those approaches, however, offer qualitatively different strategies for tailoring light-matter interactions and are based on either high quality factor modes shaping, near field control, or both. Remarkably, rigorous quantum mechanical description might address those processes in a different fashion. While traditional cavity quantum electrodynamics tools are commonly based on mode decomposition approach, few challenges rise once dispersive and lossy nanostructures, such as noble metals (plasmonic) antennas or metamaterials, are involved. The primary objective of this review is to introduce key methods and techniques while aiming to obtain comprehensive quantum mechanical description of spontaneous, stimulated and higher order emission and interaction processes, tailored by nanostructured material environment. The main challenge and the complexity here are set by the level of rigorousity, up to which materials should be treated. While relatively big nanostructured features (10. nm and larger) could be addressed by applying fluctuation-dissipation theorem and corresponding Green functions' analysis, smaller objects will require individual approach. Effects of material granularity, spatial dispersion, tunneling over small gaps, material memory and others will be reviewed. Quantum phenomena, inspired and tailored by nanostructured environment, plays a key role in development of quantum information devices and related technologies. Rigorous analysis is required for both examination of experimental observations and prediction of new effects.