Unconventional Light‐Matter Interactions Between Giant Atoms and Structured Baths with Next‐Nearest‐Neighbor Couplings

Abstract In this paper, the unconventional light‐matter interactions between giant atoms and structured baths (i.e., lattices) are studied with either Hermitian or non‐Hermitian next‐nearest‐neighbor coupling terms. Essentially different dynamics of the atoms and the propagating field in the Hermitian and non‐Hermitian cases is revealed, which can be further engineered by tuning parameters such as the atomic transition frequency and the (synthetic) magnetic field associated to the coupling terms. The next‐nearest‐neighbor couplings play an important role in controlling the emission direction and the field distribution in the lattice, thus providing opportunities for tailoring exotic dipole–dipole interactions. The results in this paper have potential applications in, e.g., engineering unconventional quantum networks and simulating quantum many‐body systems.