  We show that the dynamics of cold bosonic atoms in a two-dimensional square
optical lattice produced by a bichromatic light-shift potential is described by
a Bose-Hubbard model with an additional effective staggered magnetic field. In
addition to 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, which is
relevant to graphene and high-$T_c$ superconductors.
