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Phase transitions in quasiperiodic and driven optical lattices 10.17863/CAM.69476 Carter, Edward Schneider, Ulrich 0000000343459498 Ultracold atoms in optical lattices are a versatile tool for precisely-controlled quantum simulation of a range of condensed matter phenomena. This thesis describes work to apply this tool in two areas: the simulation of quasicrystalline materials with a novel lattice geometry, and the use of Floquet driving to engineer behaviours qualitatively different from static systems. In particular I will present our work using periodic driving to make a continuous quantum phase transition become discontinuous, which to our knowledge has never been done before. Quasicrystals are a fascinating but still relatively under-explored class of materials existing as an intermediate between periodic and disordered systems. This makes them an ideal context for studying non-ergodic behaviour, especially with the tunable interactions allowed by ultracold atom physics. At the same time quasicrystals have an intriguing link to higher dimensions, so that a two-dimensional quasicrystal can be used to simulate systems with more than three spatial dimensions. I will describe two experiments performed by our group that use a quasicrystalline optical lattice to explore higher dimensions and non-ergodic states respectively, which we hope are a stepping stone towards future work with many-body localisation and higher-dimensional topological effects. The other part of the story is Floquet physics: the study of time-periodic Hamiltonians. Time dependence allows us to break many of the usual rules of quantum systems, adding a whole new set of control parameters and allowing qualitatively different behaviours. In this thesis I will discuss the application of Floquet driving to a periodic optical lattice and present our experimental observation of a discontinuous form of the well-known Mott insulator to superfluid quantum phase transition. While interesting in itself, we view this work too as a stepping stone towards Floquet engineering with the full optical quasicrystal. University of Cambridge 2020-11-27 Thesis Doctoral Doctor of Philosophy (PhD) eng https://www.repository.cam.ac.uk/handle/1810/322018 https://www.repository.cam.ac.uk/bitstreams/3e352a83-18f0-41f1-8065-eb3919277356/download 8fb06ae1151c28a6c1296d91b4a4bc99 https://www.repository.cam.ac.uk/bitstreams/9b16417d-9bc2-416b-b902-cd556d15a707/download 353adac0d1ebdfd65ab16480263c3c87 https://www.rioxx.net/licenses/all-rights-reserved/ Physics Ultracold atoms Optical lattices Quantum simulation Condensed matter Quasicrystals Floquet Quantum phase transitions Phase transitions