Topological states of atoms in a spin-dependent optical potential

We investigate fermionic 6Li F = 1/2 atoms in a 2D spin-dependent optical lattice potential(SDOLP) generated by intersecting laser beams with a superposition of polarizations. For 6LiF = 1/2 the effective interaction of an atom with the electromagnetic field contains a scalar and avector (called as fictitious magnetic field, Bfic) potentials. The Li atoms behave as a quantum rotor(QR) with angular momentum given by the sum of the atomic rotational motion angular momentumand the hyperfine spin. We calculate the band structure of Li atoms in the SDOLP as a function ofthe laser intensity and an external magnetic field, perpendicular to the lattice plane, in a full band-structure calculation and also in a tight-binding approximation, and the Chern numbers of the SDOLP. We then introduce a blue-detuned potential, which introduces edges to the SDOLP, and thencalculate edge states and their spin and spin-current densities. We find both non-topological andtopological edge states for the Li atoms in this system.