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Strongly correlated quantum systems can exhibit exotic behavior controlled bytopology. We predict that the \nu=1/2 fractional Chern insulator arisesnaturally in a two-dimensional array of driven, dipolar-interacting spins. As aspecific implementation, we analyze how to prepare and detect synthetic gaugepotentials for the rotational excitations of ultra-cold polar molecules trappedin a deep optical lattice. While the orbital motion of the molecules is pinned,at finite densities, the rotational excitations form a fractional Cherninsulator. We present a detailed experimental blueprint for KRb, anddemonstrate that the energetics are consistent with near-term capabilities.Prospects for the realization of such phases in solid-state dipolar systems arediscussed as are their possible applications.

Realizing Fractional Chern Insulators with Dipolar Spins