N. Goldman, F. Gerbier, M. Lewenstein
We describe a scheme to engineer non-Abelian gauge potentials on a square optical lattice using laser-induced transitions. We emphasize the case of two-electron atoms, where the electronic ground state is laser coupled to a metastable state in a state-dependent optical lattice, and discuss how the nuclear spin can be viewed as a "flavor" quantum number undergoing non-Abelian tunneling along nearest-neighbor links. We show that this technique can be useful to simulate the equivalent of the Haldane quantum Hall model using cold atoms trapped in a square optical lattice, offering an interesting route to realize Chern insulators. The emblematic Haldane model is particularly suited to investigate the physics of topological insulators, but requires, in its original form, complex hopping terms beyond nearest-neighboring sites. This drawback inhibits a direct realization with cold atoms, using standard laser-induced tunneling techniques. We demonstrate that a simple mapping allows to express this model in terms of matrix hopping operators, that are defined on a standard square lattice. This mapping is investigated for two models that lead to anomalous quantum Hall phases. We discuss the practical implementation of such models using laser-induced tunneling methods.
View original:
http://arxiv.org/abs/1301.4959
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