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.
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