  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.
