SU(3) spin-orbit coupled fermions in an optical lattice

We propose a scheme to realize the SU(3) spin-orbit coupled three-component fermions in an one-dimensional optical lattice. The topological properties of the single-particle Hamiltonian are studied by calculating the Berry phase, winding number and edge state. We also investigate the effects of the interaction on the ground-state topology of the system, and characterize the interaction-induced topological phase transitions, using a state-of-the-art density-matrix renormalization-group numerical method. Finally, we show the typical features of the emerging quantum phases, and map out the many-body phase diagram between the interaction and the Zeeman field. Our results establish a way for exploring novel quantum physics induced by the SOC with SU(N) symmetry.