Topological phases of two-component bosons in species-dependent artificial gauge potentials

We study bosonic atoms with two internal states in artificial gauge potentials whose strengths are different for the two components. A series of topological phases for such systems is proposed using the composite fermion theory and the parton construction. It is found in exact diagonalization that some of the proposed states may be realized for simple contact interaction between bosons. The ground states and low-energy excitations of these states are modeled using trial wave functions. The effective field theories for these states are also constructed and reveal some interesting properties.