Programmable quantum simulations of spin systems with trapped ions

TLDR

Laser‑cooled trapped ions provide a clean platform for simulating interacting quantum spin models, with effective spins encoded in internal levels and measured via state‑dependent fluorescence, enabling studies of exotic quantum materials and systems beyond classical computational reach. This review surveys how trapped‑ion systems map to spin models, prepare complex equilibrium states, probe dynamical processes, and apply the platform to optimization and related tasks. By applying optical dipole forces with tailored laser spectra and patterns, the Coulomb interaction between ions is modulated to produce long‑range, tunable spin‑spin couplings that can be reconfigured, forming a prototypical quantum simulator.

Abstract

Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By applying optical fields that exert optical dipole forces on the ions, their Coulomb interaction can be modulated to produce long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields, in a prototypical example of a quantum simulator. Here we review the theoretical mapping of atomic ions to interacting spin systems, the preparation of complex equilibrium states, the study of dynamical processes in these many-body interacting quantum systems, and the use of this platform for optimization and other tasks. The use of such quantum simulators for studying spin models may inform our understanding of exotic quantum materials and shed light on the behavior of interacting quantum systems that cannot be modeled with conventional computers.