Emergent spin order and steady-state superradiance in one-dimensional baths

Abstract: Spontaneous collective decay in driven atomic ensembles can generate coherence far from equilibrium, as illustrated by superradiant lasers where decay into a single-mode cavity synchronizes atomic phases into a macroscopic dipole and yields superradiant emission of light with an ultranarrow spectrum. Whether similar ordering persists in multimode reservoirs with propagation and competing collective decay channels remains an open question. We address this problem by analyzing atoms coupled to one-dimensional electromagnetic baths through two models. The first is a ring cavity supporting two bright collective decay channels, and the second is a bidirectional waveguide where, in addition to competition between channels, propagation induces coherent dipole-dipole interactions. For suitable incoherent pumping strengths, the dynamics enters a synchronization window in which collective decay overcomes disordering processes, leading to spontaneous steady-state phase ordering and superradiant emission. We extract the thresholds marking the onset of synchronization and show that the maximum intensity scales quadratically in both models. The resulting order is not described by a single macroscopic dipole: in the ring cavity spontaneous chirality emerges at the level of individual trajectories, while the waveguide develops a local chirality with different orders dominating opposite ends of the atomic array. The analysis of the emitted light spectrum reveals a linewidth that seems to narrow with increased system size in the ring cavity, while narrowing in the waveguide remains inconclusive within accessible numerics. These results clarify how competition and propagation shape emergent order in one-dimensional reservoirs and identify regimes where steady-state superradiance may arise beyond the Dicke limit.