Experiments with quantum gasses trapped in optical lattices, an analog of particles in a solid crystalline lattice, shed light on the behavior of condensed-matter systems, including solid-state materials. Studying non-equilibrium phenomena of quantum gasses in optical lattices provides a method to explore how a lattice’s energy band structure is augmented by inter-particle interactions (band renormalization). Separately, studying such phenomena provides a method to explore the geometric and topological structure of a lattice’s energy bands. These studies are aided by experimental probes that are unavailable to solid-state systems.

In the first part of my talk, I will describe our recent work towards understanding the effects of frustration in a system of bosonic atoms trapped in a unique lattice made of light – an optical kagome lattice. Here, we create a Bose-Einstein condensate, accelerate it, then trap it in the lattice. In doing so, we probe a special energy band of the lattice, which, in principle, should be dispersionless (flat, as a function of quasimomentum). However, our measurements show that interactions between atoms reintroduce band curvature by deforming the lattice away from the kagome geometry. In the second part of my talk, I will describe our current effort to understand the geometric and topological properties of energy bands, by exploring singularities at touching points between two bands.