Engineering topological quantum order has become a major field of physics. Many advances have been made by synthesizing gauge fields in cold atomic systems. Here, we carry over these developments to other platforms which are extremely well suited for
quantum engineering, namely trapped ions and nano-trapped atoms. Since these systems are typically one-dimensional, the action of artificial magnetic fields has so far received little attention. However, exploiting the long-range nature of interactions, loops with non-vanishing magnetic fluxes become possible even in one-dimensional settings. This gives rise to intriguing phenomena, such as fractal energy spectra, flat bands with localized edge states, and topological many-body states. We elaborate on a simple scheme for generating the required artificial fluxes by periodically driving an XY spin chain. Concrete estimates demonstrating the experimental feasibility for trapped ions and atoms in waveguides are given.
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(
3) analog of spin-orbit coupling, additional spin-spin interactions are generated. We first consider the scenario of spin-dependent hopping phases, leading to Dzyaloshinskii-Moriya-type interactions. They result in the formation of spiral spin textures, which in one dimension can be understood by a local unitary transformation. Applying classical Monte Carlo simulations, we extend our study to two-dimensional systems, and systems with true spin-orbit coupling, involving spin-changing hoppings.
