| We show that the dynamics of cold bosonic atoms in a 2D optical lattice produced by a bichromatic light-shift potential is described by a Bose-Hubbard model with an additional effective staggered magnetic field. Besides the known uniform superfluid and Mott insulating phases, the zero-temperature phase diagram exhibits a novel kind of finite-momentum superfluid phase, characterized by a quantized staggered rotational flux. An extension for fermionic atoms leads to an anisotropic Dirac spectrum and shows that this system can simulate graphene under uniaxial pressure. The obtained model is also related to the mean-field Hamiltonian first derived by Marston and Affleck in the context of the pi-staggered flux phase, proposed to describe the pseudogap phase of high-Tc superconductors. |
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