Negative absolute temperatures in a triangular optical lattice*

Negative absolute temperatures describe a situation where the entropy of a closed system reduces as the internal energy increases, and this leads to the peculiar situation that atoms in a band dominantly occupy the highest energy states in the band. Here we report the observation of negative absolute temperatures in a triangular optical lattice — a non-bipartite lattice where geometric frustration leads to two inequivalent maxima in the lowest band. This leads to strikingly different critical interaction strengths for the bosonic superfluid to Mott insulator transition at positive and negative absolute temperatures. We furthermore show for both cases how coherence emerges dynamically from a Mott insulator to a superfluid state, reminiscent of the Kibble-Zurek mechanism.