  We show that topological phases with fractional excitations can occur in
two-dimensional ultracold dipolar gases on a particular class of optical
lattices. Due to the dipolar interaction and lattice confinement, a quantum
dimer model emerges naturally as the effective theory describing the low-energy
behaviors of these systems under well-controlled approximations. The desired
hierarchy of interaction energy scales is achieved by controlling the
anisotropy of the orbital dimers and the dipole moments of the particles.
Experimental realization and detection of various phases are discussed, as well
as the possible relevance for quantum computation.
