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We obtain the band structure of a particle moving in a magnetic spin texture, classified by its chirality and structure factor, in the presence of spin-orbit coupling. This rich interplay leads to a variety of novel topological phases characterized by the Berry curvature and their associated Chern numbers. We suggest methods of experimentally exploring these topological phases by Hall drift measurements of the Chern number and Berry phase interferometry to map the Berry curvature.
We study the Mott phase of three-component bosons, with one particle per site, in an optical lattice by mapping it onto an SU(3) spin model. In the simplest case of full SU(3) symmetry, one obtains a ferromagnetic Heisenberg model. Introducing an SU(
We discuss a general scheme for creating atomic spin-orbit coupling (SOC) such as the Rashba or Dresselhaus types using magnetic-field-gradient pulses. In contrast to conventional schemes based on adiabatic center-of-mass motion with atomic internal
We report the observation of tunable spin-orbit coupling (SOC) for ultracold $^{87}$Rb atoms in hyperfine spin-1 states. Different from most earlier experiments where atomic SOC of pseudo-spin-1/2 are synthesized with Raman coupling lasers, the schem
This review focuses on recent developments on studying synthetic spin-orbit (SO) coupling in ultracold atomic gases. Two types of SO coupling are discussed. One is Raman process induced coupling between spin and motion along one of the spatial direct
We propose an experimental scheme to simulate the fractionalization of particle number by using a one-dimensional spin-orbit coupled ultracold fermionic gas. The wanted spin-orbit coupling, a kink-like potential, and a conjugation-symmetry-breaking m