Negative temperature states of bosons in triangular and kagome lattices
This thesis reports on experiments using ultracold bosonic ³⁹K atoms to study quantum many-body states in frustrated lattices. For the first time, we load the atoms into the optical triangular and kagome lattices at negative temperature, where most atoms occupy the states with the highest energy. Due to geometric frustration, the highest energy states are Bloch states at the K and K′ points for the triangular lattice and the states in the flat band for the kagome lattice. We show that negative temperature states are stable on the experimental timescale. For the triangular lattice, we experimentally study the superfluid-to-Mott-insulator transition in 2D and extract the critical values of U/t for positive and negative temperatures. A Feshbach resonance provides another degree of freedom in addition to the lattice depth that can be used to check for universality of the extracted feature in terms of U/t. For the kagome lattice, the theoretical prediction of negative temperature states is a challenging problem. We theoretically investigate a class of states governed by a single macroscopic wavefunction. Among these, I describe how to generate the so-called three-colour states and how to uniformly sample such states using a Monte-Carlo method. The Gross-Pitaevskii equation provides another way to calculate the groundstates for the frustrated lattice and has the advantage of including the effects of both interaction and harmonic confinement. Although the resulting states from the calculation are not groundstates, they show a long-range triple-boson superfluid order. The last class of states considered is the Bose-Einstein distribution calculated from the band structure at zero interaction. The averaged time-of-flight images from these simulations are then compared with the results from the experiment. On the technical side, I describe an upgrade to the phase stabilisation setup, which is important for realising the kagome lattice. I explain the modulation technique which is used for precise lattice beam alignment. The effect of harmonic confinement on band gaps is also considered for lattice depth calibration. Lastly, I present the theory for lattice acceleration experiments which can be used to study Wilson lines and Euler class topology in the kagome lattice. Some preliminary experimental results are shown and compared with the simulation.
Quantum simulation, Ultracold atoms, Optical lattice, Triangular lattice, Kagome lattice, Negative temperature, Lattice acceleration
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