  We study theoretically the groundstates of two-dimensional Bose-Hubbard
models which are frustrated by gauge fields. Motivated by recent proposals for
the implementation of optically induced gauge potentials, we focus on the
situation in which the imposed gauge fields give rise to a pattern of staggered
fluxes, of magnitude $\alpha$ and alternating in sign along one of the
principal axes. For $\alpha=1/2$ this model is equivalent to the case of
uniform flux per plaquette $n_\phi=1/2$, which, in the hard-core limit,
realizes the "fully frustrated" spin-1/2 XY model. We show that the mean-field
groundstates of this frustrated Bose-Hubbard model typically break
translational symmetry. We introduce a general numerical technique to detect
broken symmetry condensates in exact diagonalization studies. Using this
technique we show that, for all cases studied, the groundstate of the
Bose-Hubbard model with staggered flux $\alpha$ is condensed, and we obtain
quantitative determinations of the condensate fraction. We discuss the
experimental consequences of our results. In particular, we explain the meaning
of gauge-invariance in ultracold atom systems subject to optically induced
gauge potentials, and show how the ability to imprint phase patterns prior to
expansion can allow very useful additional information to be extracted from
expansion images.
