  We perform variational Monte-Carlo calculations to show that bosons in a
rotating optical lattice will form analogs of fractional quantum Hall states
when the tunneling is sufficiently weak compared to the interactions and the
deviation of density from an integer is commensurate with the effective
magnetic field. We compare the energies of superfluid and correlated states to
one-another and to the energies found in full configuration-interaction
calculations on small systems. We look at overlaps between our variational
states and the exact ground-state, characterizing the ways in which fractional
quantum Hall effect correlations manifest themselves near the Mott insulating
state. We explore the experimental signatures of these states.
