  We investigate the driven-dissipative dynamics of 1D and 2D arrays of
multilevel atoms interacting via dipole-dipole interactions and trapped at
subwavelength scales. Here we show that in the weakly driven low excitation
regime, multilevel atoms, in contrast to two-level atoms, can become strongly
entangled. The entanglement manifests as the growth of collective spin-waves in
the ground state manifold, and survives even after turning off the drive. We
propose to use the $\sim 2.9~\mu$m transition between $\rm ^3{\rm P}_2
\leftrightarrow \, ^3{\rm D}_3$ in $\rm ^{88}Sr$ with $\rm 389~nm$ trapping
light as an ideal experimental platform for validating our predictions and as a
novel quantum interface for the exploration of complex many-body phenomena
emerging from light-matter interactions.
