  We theoretically and experimentally investigate nonlinear Zeeman effects
within a polarised single-photon source that uses a single 87Rb atom strongly
coupled to a high finesse optical cavity. The breakdown of the atomic hyperfine
structure in the D2 transition manifold for intermediate strength magnetic
fields is shown to result in asymmetric and, ultimately, inhibited operation of
the polarised atom-photon interface. The coherence of the system is considered
using Hong-Ou-Mandel interference of the emitted photons. This informs the next
steps to be taken and the modelling of future implementations, based on
feasible cavity designs operated in regimes minimising nonlinear Zeeman
effects, is presented and shown to provide improved performance.
