Emergence of stationary many-body entanglement in driven-dissipative Rydberg lattice gases

Non-equilibrium quantum dynamics represents an emerging paradigm for condensed matter physics, quantum information science, and statistical mechanics. Strongly interacting Rydberg atoms offer an attractive platform to study driven-dissipative dynamics of quantum spin models with long-range order. Here, we explore the conditions under which stationary many-body entanglement persists with near-unit fidelity and high scalability. In our approach, coherent many-body dynamics is driven by Rydberg-mediated laser transitions, while atoms at the lattice boundary reduce the entropy of the many-body state. Surprisingly, the many-body entanglement is established by continuously evolving a locally dissipative Rydberg system towards the steady-state, as with optical pumping. We characterize the dynamics of multipartite entanglement in a 1D lattice by way of quantum uncertainty relations, and demonstrate the long-range behavior of the stationary entanglement with finite-size scaling, reaching "hectapartite" entanglement under experimental conditions. Our work opens a route towards dissipative preparation of many-body entanglement with unprecedented scaling behavior.