Creation of two-dimensional coulomb crystals of ions in oblate Paul traps for quantum simulations

TL;DR

This paper develops a theoretical framework for creating two-dimensional Coulomb crystals of ions in oblate Paul traps, enabling tunable quantum simulations of complex spin models and geometries.

Contribution

It introduces a novel trap design and analysis method for 2D ion crystals with adjustable interactions suitable for advanced quantum simulations.

Findings

Axial phonon modes enable programmable Ising interactions.

Interactions can be tuned from uniform to $r^{-3}$ decay.

The trap design supports complex geometries like triangular lattices.

Abstract

We develop the theory to describe the equilibrium ion positions and phonon modes for a trapped ion quantum simulator in an oblate Paul trap that creates two-dimensional Coulomb crystals in a triangular lattice. By coupling the internal states of the ions to laser beams propagating along the symmetry axis, we study the effective Ising spin-spin interactions that are mediated via the axial phonons and are less sensitive to ion micromotion. We find that the axial mode frequencies permit the programming of Ising interactions with inverse power law spin-spin couplings that can be tuned from uniform to $r^{-3}$ with DC voltages. Such a trap could allow for interesting new geometrical configurations for quantum simulations on moderately sized systems including frustrated magnetism on triangular lattices or Aharonov-Bohm effects on ion tunneling. The trap also incorporates periodic boundary conditions around loops which could be employed to examine time crystals.