Towards Bose condensation in the flat p-band of an optical honeycomb lattice

The orbital degree of freedom is important for understanding properties of condensed matter. In systems of atoms in optical lattices, many studies have been performed on the manifold of bands associated with the motional ground (lowest orbital) state of atoms in the wells – the so-called “s-bands”. The physics of higher orbital states in optical lattices have been studied theoretically for several lattice geometries, leading to the prediction of novel phases, such as complex Bose-Einstein condensates and topological semimetals. To date, experimental efforts on checkerboard and boron nitride lattices have already yielded fruitful results, including the observation of chiral superfluid and spontaneous time-reversal symmetry breaking, yet open questions remain. In this work, we present a way to prepare higher orbital states in a honeycomb lattice with arbitrary lattice translation. We study the dynamics of the system as atoms relax to the doubly degenerate energy minima in the lowest p-band of a honeycomb lattice, which is predicted to be exactly flat in the tight-binding limit. We propose an experimental scheme to observe Bose condensation in the lowest p-band, which could provide evidence on the effect of geometric frustration on band structure.