Quantum phases of trapped ions in an optical lattice

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We propose loading trapped ions into microtraps formed by an optical lattice. For harmonic microtraps, the Coulomb coupling of the spatial motions of neighboring ions can be used to construct a broad class of effective short-range Hamiltonians acting on an internal degree of freedom of the ions. For large anharmonicities, on the other hand, the spatial motion of the ions itself represents a spin-1/2 model with frustrated dipolar XY interactions. We illustrate the latter setup with three systems: the linear chain, the zigzag ladder and the triangular lattice. In the frustrated zigzag ladder with dipolar interactions we find chiral ordering beyond what was predicted previously for a next-nearest-neighbor model. In the frustrated anisotropic triangular lattice with nearest-neighbor interactions we find that the transition from the one-dimensional (1D) gapless spin-liquid phase to the 2D spiraling ordered phase passes through a gapped spin-liquid phase, similar to what has been predicted for the same model with Heisenberg interactions. Further, a second gapped spin-liquid phase marks the transition to the 2D Neel-ordered phase.
© IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. This work was supported by the European Union through the SCALA integrated project
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