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We show how spin-orbit coupling and Berry phase can appear in two-dimensionaloptical lattices by coupling atoms' internal degrees of freedom to radiation.The Rashba Hamiltonian, a standard description of spin-orbit coupling fortwo-dimensional electrons, is obtained for the atoms under certaincircumstances. We discuss the possibility of observing associated phenomena,such as the anomalous Hall and spin Hall effects, with cold atoms in opticallattices.Comment: 3 figure

Spin-Orbit Coupling and Berry Phase with Ultracold Atoms in 2D Optical Lattices