Many-body physics and topology in an optical kagome lattice

The kagome lattice hosts a rich band structure, featuring a flat band resulting from geometric frustration and non-Abelian topological charges at the band-touching points. The many-body physics in the flat band is complex and not fully understood: even for weakly interacting scalar bosons, condensation in the mean-field regime is predicted to be dictated by quantum geometry and an exotic state with three-boson order is expected at intermediate temperature. At the single particle level, topological charges are associated with the eigenstates’ frame rotations at band nodes; in lattices with three or more bands (such as the kagome lattice), they are non-Abelian, so that their ability to annihilate is path-dependent.  

We report on recent experiments investigating the bosonic phase diagram and the topology of the kagome optical lattice. We have prepared a long-lived state of ultracold bosons in the flat band by effectively inverting the sign of the tunnelling with a negative absolute temperature technique. We report on our latest measurements characterising this state with a variety of time-of-flight techniques. We also present measurements of frame charges using an interferometric protocol in which a single wave packet sequentially probes two band nodes along a chosen path, allowing the relative frame charges to be extracted. By tuning the lattice potential, we further demonstrate that the relative charges can be changed along this path by braiding nodes in momentum space.