We investigate the interaction between single quantum emitters andnon-transversally polarised photons for which the electric field vectoramplitude has a significant component in the direction of propagation. Eventhough this situation seems to be at odds with the description of light as atransverse wave, it regularly occurs when interfacing or manipulating emitterswith non-paraxial, guided, or evanescent light. Here, we couple single rubidiumatoms to single photons which are confined in an optical microresonator bycontinuous total internal reflection. We experimentally show that thenon-transversal polarisation decisively alters the physics of stronglight--matter interaction. This effect has far-reaching and highly advantageousimplications, which, e.g., significantly advance the field of cavity quantumelectrodynamics with whispering-gallery-mode resonators. In particular, ourfinding allows us to experimentally realise a paradigmatic quantum system,which is ideally suited for basic studies and technological applications.
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