Simulations of atomic gases on frustrated optical lattices

We present results form quantum Monte Carlo simulations of ultra-cold bosonic atoms on frustrated optical lattices such as the triangular and the kagome lattice. For the triangular lattice case a supersolid state of matter emerges, resulting from a novel order-by-disorder effect in the quantum regime. On the kagome lattice no supersolid appears, instead the atoms form exotic valence-bond-solids with local bosonic resonances. The quantum melting of these solids into the superfluid takes place at weakly first-order quantum phase transitions. Relevant algorithmic improvements which allow for large-scale simulations of such systems are mentioned as well as possible experimental realizations of these scenarios based on current experimental advances in quantum optics. (C) 2007 Elsevier B.V. All rights reserved.