From bound states to quantum spin models: chiral coherent dynamics in topological photonic rings.

Topological photonic systems offer a robust platform for guiding light in the presence of disorder, but their interplay with quantum emitters remains a frontier for realizing strongly correlated quantum states. Here, we explore a ring-shaped Su-Schrieffer-Heeger (SSH) photonic lattice interfaced with multiple quantum emitters to control topologically protected chiral quantum dynamics. Using a full microscopic model that includes cascaded Lindblad dynamics and chiral emitter-bath couplings, we reveal how the topology of the bath mediates nonreciprocal, long-range interactions between emitters. These interactions lead to rich many-body spin phenomena, including robust coherence, directional energy transfer, captured by an effective spin Hamiltonian derived from the system's topology. We show that topological bound states enable unidirectional emission, protect coherence against dissipation, and imprint nontrivial entanglement and mutual information patterns among the emitters. In particular, we showed that under circularly polarized excitation, the emitters not only inherit spin angular momentum from the field but also serve as transducers that coherently launch the spin-orbit-coupled topological photonic modes into the far field. Our results establish a direct bridge between topological photonic baths and emergent quantum magnetism, positioning this architecture as a promising testbed for studying chiral quantum optics, topologically protected entangled states, and long-range quantum coherence.