Quantum simulation with ultracold bosons in frustrated optical lattices*

We present results from our experiments using bosonic ³⁹K atoms in optical lattices as an analogue quantum simulator for the Bose-Hubbard model on the triangular and kagome lattices. Because these lattices are nonbipartite, they exhibit geometric frustration. This gives rise to two inequivalent band maxima in the triangular lattice and a flat band in the kagome lattice band structure. Since the effects of frustration are only seen at the top of the lowest set of touching bands, we prepare atoms at a negative absolute temperature such that these highest energy states are preferentially occupied. 

In the triangular lattice we have studied the bosonic superfluid to Mott insulator phase transition at negative temperature. We observed a marked difference in the critical interaction strength when compared to the positive temperature (unfrustrated) system and found dynamical signatures pointing towards an intervening chiral Mott insulator between the (chiral) superfluid and the Mott insulator. In the kagome lattice we have observed the melting of the Mott insulator into the flat band.