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We study the properties of dipolar fermions trapped in one-dimensionalbichromatic optical lattices and show the existence of fractional topologicalstates in the presence of strong dipole-dipole interactions. We find someinteresting connections between fractional topological states inone-dimensional superlattices and the fractional quantum Hall states: (i) theone-dimensional fractional topological states for systems at filling factor\nu=1/p have p-fold degeneracy, (ii) the quasihole excitations fulfill the samecounting rule as that of fractional quantum Hall states, and (iii) the totalChern number of p-fold degenerate states is a nonzero integer. The existence ofcrystalline order in our system is also consistent with the thin-torus limit ofthe fractional quantum Hall state on a torus. The possible experimentalrealization in cold atomic systems offers a new platform for the study offractional topological phases in one-dimensional superlattice systems.

Fractional topological states of dipolar fermions in one-dimensional optical superlattices