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Between order and disorder: ultracold atoms in a quasicrystalline optical lattice 10.17863/CAM.44756 Sbroscia, Matteo Stefano 0000000241015984 Schneider, Ulrich Quasicrystals are long-range ordered and yet non-periodic. This interplay results in a wealth of intriguing physical phenomena, such as self-similarity, the inheritance of topological properties from higher dimensions, and the presence of non-trivial structure on all lengthscales. However, quasicrystalline materials are notoriously hard to synthesise, as defects and impurities may greatly alter their final microscopic composition. The field of quantum simulation with ultracold atoms offers a solution to this problem, namely the use of optical lattices – standing waves of light. Optical lattices are free of impurities and therefore ideally suited to study quasicrystals, enabling unprecedented access to observables that are unattainable in condensed matter systems. This study presents the first experimental realisation of a two-dimensional quasicrystalline potential for ultracold atoms, based on an eightfold symmetric optical lattice. Features pertaining to both ordered and disordered phases are observed, from sharp diffraction peaks in the matter-wave interference pattern, to a disorder-induced localised phase emerging at a critical lattice depth V_loc ~ 1.78 E_rec. The localised phase seems to be resilient against moderate interactions, which would make this the first experimental realisation of a 2D Bose glass. University of Cambridge 2019-11-30 Thesis Doctoral Doctor of Philosophy (PhD) en EPSRC https://www.repository.cam.ac.uk/handle/1810/297701 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/eb2d65a0-2502-4f4a-af43-53d220223e6d/download fa5b3e812c87da5445b85c01cff0ce37 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/23287a4c-38f2-41b6-8436-03b85d0b6568/download 87eda9de84448d1f82354d60eee3eb5f https://www.rioxx.net/licenses/all-rights-reserved/ All third party material has been explicitly noted in the thesis and referenced accordingly. Ultracold atoms Optical lattices Quasicrystals Aperiodic order