| Summary: | <p>In this work I demonstrate the interference of three photons, a generalisation of the famous Hong Ou Mandel (HOM) interference. I show that three photon interference is governed by four parameters and measure three photon interference independent of two-photon interference. Surprisingly, even when the states of the photons are highly distinguishable they can still exhibit strong quantum interference, challenging our intuition formed by the double slit and HOM interference. This will be followed by a demonstration of four photon interference, where surprisingly we can still observe a fringe, when involved particles are pairwise orthogonal. To explain these effects, I will be presenting a new framework to describe multi-photon interference in terms of a graph-theoretical approach, which illustrates the origin of different orders of multi-photon interference. My work leads to a more general definition of what we regard as an interference fringe in multi-photon scattering. This study of multi-photon interference is followed by an interdisciplinary work between photonics and solid state physics in the newly developing field of topological photonics. Interference phenomena are inextricably tied to exchange symmetries of the particle. I realise a simulation of the Jackiw-Rossi model, as a localised topological mode in a photonic-crystal analogue of the 2D graphene lattice. These modes have previously been shown to obey non-abelian exchange statistics. I succeed in the experimental demonstration of a single such excitation and am able to study the detailed mode structure for the first time. The mode is a result of a topological defect and is as such protected against errors that do not change the topology of the system. Furthermore, I demonstrate adiabatic transport of the mode across the crystal lattice and show first attempts towards a demonstration of their non-abelian braiding statistics. To realise these experiments, I developed a new method based on a spatial light modulator to excite large modes in photonic crystals.</p>
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