Strongly Confined Atomic Excitation Localization in a Weakly-Driven Atom-Waveguide Interface*

An atomic array coupled to a photonic crystal waveguide forms a strongly coupled quantum interface, exhibiting various intriguing collective features of quantum dynamics. Here we consider a homogeneous atomic array and theoretically investigate its steady-state distribution when the incident fields drive the atoms from both sides at asymmetric

angles. This effectively creates an interface shared by two zones of atoms under different driving angles. This setup introduces a competition between photon-mediated dipole-dipole interactions and the directionality of coupling, while differences of the travelling phases from the incident angles further influence the overall steady-state behavior. Under this asymmetric driving scheme, the presence of strongly confined excitation localization can be identified, where localization can occur either at the interface or at one of edges. Additionally, we examine the size effect on the atomic localization, deriving an empirical formula to predict parameter regimes that favor interfaced localization. We also consider a defect-driving scheme, where a third zone is created by undriven atoms under symmetric travelling phases. This results in strongly confined single-site excitation localization, which can be explained through analytical solutions under the reciprocal coupling. Finally, we propose several methods for precise control of multiple single-site localizations under the defect-driving scheme. Our results provide insights into driven-dissipative quantum systems with reciprocal couplings and pave the way for quantum simulation of exotic many-body states relevant to quantum information applications.