Entanglement Generation in Weakly Driven Arrays of Multilevel Atoms via Dipolar Interactions

We investigate the driven-dissipative dynamics of multilevel atomic arrays interacting via dipolar interactions at subwavelength spacings. Unlike two-level atoms in the weakly excited regime, multilevel atoms can become strongly entangled. The entanglement manifests as the growth of spin waves in the ground-state manifold and survives after turning off the drive. We propose the $2.9\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{m}$ transition between ${^{3}P}_{2}\ensuremath{\leftrightarrow}{^{3}D}_{3}$ in $^{88}\mathrm{Sr}$ with 389 nm trapping light as a platform to test our predictions and explore many-body physics with light-matter interactions.