Degenerate Zeeman Ground States in the Single-Excitation Regime

In this work, we demonstrate the importance of considering correlations between degenerate Zeeman sublevels that develop in dense atomic ensembles. In order to do this, we develop a set of equations capable of simulating large numbers of atoms while still incorporating correlations between degenerate Zeeman sublevels. This set of equations is exact in the single-photon limit, and may be interpreted as a generalization of the coupled harmonic oscillator equations typically used the literature. Using these equations, we demonstrate that in sufficiently dense systems, correlations between Zeeman sublevels can cause non-trivial differences in the photon scattering lineshape in arrays and clouds of atoms.