  We present a robust scheme by which fractional quantum Hall states of bosons
can be achieved for ultracold atomic gases. We describe a new form of optical
flux lattice, suitable for commonly used atomic species with groundstate
angular momentum $J_g = 1$, for which the lowest energy band is topological and
nearly dispersionless. Through exact diagonalization studies, we show that,
even for moderate interactions, the many-body groundstates consist of bosonic
fractional quantum Hall states, including the Laughlin state and the Moore-Read
(Pfaffian) state. Under realistic conditions, these phases are shown to have
energy gaps that are larger than temperature scales achievable in ultracold
gases.
