Realizing Fractional Chern Insulators with Dipolar Spins

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