Population mixing due to dipole-dipole interactions in a 1D array of multilevel atoms

We examine theoretically how dipole-dipole interactions arising from multiple photon scattering lead to a modified distribution of ground state populations in a driven, ordered 1D array of multilevel atoms. Specifically, we devise a level configuration in which a ground-state population accumulated due solely to dipole-dipole interactions can be up to 20\% in regimes accessible to current experiments with neutral atom arrays. For much larger systems, the steady state can consist of an equal distribution of population across the ground state manifold. Our results illustrate how dipole-dipole interactions can be accentuated through interference, and regulated by the geometry of ordered atom arrays. More generally, control techniques for multilevel atoms that can be degraded by multiple scattering, such as optical pumping, will benefit from an improved understanding and control of dipole-dipole interactions available in ordered arrays.