  We analyze a recently proposed method to create fractional quantum Hall (FQH)
states of atoms confined in optical lattices [A. S{\o}rensen {\it et al.},
Phys. Rev. Lett. {\bf 94} 086803 (2005)]. Extending the previous work, we
investigate conditions under which the FQH effect can be achieved for bosons on
a lattice with an effective magnetic field and finite onsite interaction.
Furthermore, we characterize the ground state in such systems by calculating
Chern numbers which can provide direct signatures of topological order and
explore regimes where the characterization in terms of wavefunction overlap
fails. We also discuss various issues which are relevant for the practical
realization of such FQH states with ultracold atoms in an optical lattice,
including the presence of the long-range dipole interaction which can improve
the energy gap and stabilize the ground state. We also investigate a new
detection technique based on Bragg spectroscopy to probe these system in an
experimental realization.
