  We present the effects of resonator birefringence on the cavity-enhanced
interfacing of quantum states of light and matter, including the first
observation of single photons with a time-dependent polarisation state that
evolves within their coherence time. A theoretical model is introduced and
experimentally verified by the modified polarisation of temporally-long single
photons emitted from a $^{87}$Rb atom coupled to a high-finesse optical cavity
by a vacuum-stimulated Raman adiabatic passage (V-STIRAP) process. Further
theoretical investigation shows how a change in cavity birefringence can both
impact the atom-cavity coupling and engender starkly different polarisation
behaviour in the emitted photons. With polarisation a key resource for encoding
quantum states of light and modern micron-scale cavities particularly prone to
birefringence, the consideration of these effects is vital to the faithful
realisation of efficient and coherent emitter-photon interfaces for distributed
quantum networking and communications.
