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