Scattering processes have played a crucial role in the development of quantum theory. In the field of optics, scattering phase shifts have been utilized to unveil interesting forms of light-matter interactions. Here, we investigate the mode-coupling phase of single photons to surface plasmon polaritons in a quantum plasmonic tritter. We observe that the coupling process induces a phase jump that occurs when photons scatter into surface plasmons and vice versa. This interesting coupling phase dynamics is of particular relevance for quantum plasmonic experiments. Furthermore, it is demonstrated that this photon-plasmon interaction can be modeled through a quantum-mechanical tritter. We show that the visibility of a double-slit and a triple-slit interference patterns are convenient observables to characterize the interaction at a slit and determine the coupling phase. Our accurate and simple model of the interaction, validated by simulations and experiments, has important implications not only for quantum plasmonic interference effects, but is also advantageous to classical applications.
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