The inverted kagome lattice: frustrated bosons without superexchange

The route to quantum magnetism in ultracold atom systems is obstructed by the difficulties of reaching low enough temperatures of the order of the superexchange coupling $J$. The prospect of simulating the square lattice antiferromagnet, and its expected descendant, the $d$-wave superconductor arouse a lot of current interest. Here we want to show how a frustrated ``quantum magnet'' can be obtained with bosons in an inverted kagome lattice without the need for temperatures that are much smaller than the hopping $t$. We discuss a possible experimental setup and the rich zoo of phases which can be expected in this system: ranging from glassy arrangements of localized states over a coexisting density-wave--superfluid phase to the $\exp(3 i \varphi)$ condensate.