Bose-Hubbard physics in the kagome and triangular optical lattices at negative absolute temperature

Abstract

This thesis describes quantum many-body experiments with ultracold bosonic ³⁹K in the kagome and triangular optical lattices. These lattices display geometric frustration, which manifests itself in a degeneracy at the upper edge of the ground band manifold. In the case of the triangular lattice, the band structure features two inequivalent energy maxima; in the kagome lattice, the upper band is flat in the tight-binding limit. The flat band of the kagome lattice is predicted to host a range of exotic quantum phases and phenomena: for bosons, these include interaction-induced condensation and a state with three-boson superfluid order at finite temperature; for fermions, a spin liquid. I describe the design of the apparatus and some technical upgrades that were implemented. The kagome lattice is realised as an optical superlattice, where the phases of the two lattices are stabilised interferometrically. I also outline experimental progress towards the implementation of a quantum gas microscope, which will allow us to observe atoms in the kagome lattice with single-site resolution. We access the frustrated physics by creating states with negative absolute temperature, which preferentially occupy the upper band edge. This technique is applied to the triangular and kagome lattices for the first time. In the triangular lattice, we study the superfluid-to-Mott insulator transition at positive and negative temperatures, observing a dramatic reduction in the critical interaction strength at negative temperature. This is attributed to geometric frustration. Our efforts culminate in the preparation of a long-lived state at the upper band edge of the kagome lattice, where most atoms occupy the flat band. These experiments pave the way for the study of bosonic flat-band physics in the kagome lattice.