Topological Phases of Dipolar Particles in Elongated Wannier Orbitals

We show that topological phases with fractional excitations can occur in two-dimensional ultracold dipolar gases on a particular class of optical lattices. Because of 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 particles. Experimental realization and detection of various phases are discussed, as well as the possible relevance for quantum computation.