Quantum Phases of Trapped Ions in an Optical Lattice

TL;DR

This paper explores how trapped ions in optical lattices can simulate various quantum spin models, revealing complex phases like chiral order and multiple spin-liquid states, advancing quantum simulation capabilities.

Contribution

It introduces a method to realize diverse quantum spin models with trapped ions in optical lattices, including frustrated and anisotropic systems, and predicts novel quantum phases.

Findings

Chiral ordering in zig-zag ladder with dipolar interactions.

Transition through gapped spin-liquid phases in triangular lattice.

Observation of multiple quantum phase transitions.

Abstract

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 zig-zag ladder, and the triangular lattice. In the frustrated zig-zag 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 gapless spin-liquid phase to the two-dimensional 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 two-dimensional Neel-ordered phase.