Topological Phenomena in Trapped Ion Systems

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T. Shi and J. I. Cirac


DOI: 10.1103/PhysRevA.87.013606
PACS: 03.75.Hh, 37.10.Ty, 37.10.Vz, 05.30.Jp

We propose and analyze a scheme to observe topological phenomena with ions in microtraps. We consider a set of trapped ions forming a regular structure in two spatial dimensions and interacting with lasers. We find phonon bands with nontrivial topological properties, which are caused by the breaking of time-reversal symmetry induced by the lasers. We investigate the appearance of edge modes, as well as their robustness against perturbations. Long-range hopping of phonons caused by the Coulomb interaction gives rise to flat bands which, together with induced phonon-phonon interactions, can be used to produce and explore strongly correlated states. Furthermore, some of these ideas can also be implemented with cold atoms in optical lattices.