Plasmon-induced multipartite interactions and entanglement in quantum emitter hybrid systems

This study investigates multipartite entanglement in quantum emitter (QE) systems coupled to a two-dimensional hyperbolic surface (TDHS). Within the master equation framework, which distinguishes the contributions of surface plasmon field (SPF) with different spatial modes, we demonstrate that both the collective decay coefficients and the in-plane emission pattern of the emitters are strongly governed by the polarization of the transition dipole. Numerical analysis further reveals that the TDHS functions as a planar plasmonic waveguide supporting both reciprocal and nonreciprocal inter-emitter interactions. Building on these intriguing properties, we analyze the dynamics of spontaneously generated entanglement (SGE) in tripartite and quadripartite systems under various interaction configurations. Our results show that in certain two-dimensional geometries, strong nonreciprocal interactions enhance global entanglement compared with one-dimensional arrangements. Notably, the rhombic configuration supports destructive interference that suppresses on-site decay and drives the system into dark states with steady entanglement. Moreover, for systems initialized in mixed states, entanglement generation relies mainly on reciprocal interactions and shows only weak dependence on the interaction geometry. These findings provide a versatile route for engineering multipartite entanglement in TDHS-based plasmonic architectures, with promising applications in quantum information processing and integrated photonic devices.