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Phase transitions in quasiperiodic and driven optical lattices



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Carter, Edward 


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.





Schneider, Ulrich


Physics, Ultracold atoms, Optical lattices, Quantum simulation, Condensed matter, Quasicrystals, Floquet, Quantum phase transitions, Phase transitions


Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge
EPSRC (1805225)