  We study a model of a 2D ultracold atomic gas subject to an "optical flux
lattice": a laser configuration where Raman-dressed atoms experience a strong
artificial magnetic field. This leads to a bandstructure of narrow energy bands
with non-zero Chern numbers. We consider the case of two-level (spin-$1/2$)
fermionic atoms in this lattice, interacting via a repulsive $s$-wave contact
interaction. Atoms restricted to the lowest band are described by an effective
model of spinless fermions with interactions that couple states in a
momentum-dependent manner across the Brillouin zone; a consequence of the Raman
dressing of the two spin states. We present the results of detailed exact
diagonalization studies of the many-body states for a range of filling factors,
$\nu$. First, we present evidence for the existence of a phase with coupled
ferromagnetic--nematic ordering, which was previously suggested by a mean-field
analysis. Second, we present evidence indicating the presence of a
Laughlin-like fractional quantum Hall state occurring at filling factor $\nu =
1/3$. Finally, we observe a charge density wave state at $\nu=1/2$, which we
are able to cleanly distinguish from the Laughlin-like state by its
translational symmetry breaking and relatively small participation ratio.
