Generating long-lived entangled states in multilevel atomic arrays with dipolar interactions*

We investigate the driven-dissipative dynamics of multilevel atoms in a 1D array interacting via photon-mediated dipole-dipole interactions. Contrary to two-level atoms, we find that multilevel atoms in the low excitation (weak drive) regime can become strongly entangled. These entangled states arise from the action of non-trivial effective many-body jump operators on the ground state manifold. We discuss the role played by elastic and inelastic interactions in generating entanglement as well as the long-lived nature of these states. Our predictions are testable in optical lattice and optical tweezer experiments using the ∼2.7μm transition from ³P₂ →³D₃ in ⁸⁷Sr.