Designing spin-spin interactions with one and two dimensional ion crystals in planar micro traps

TL;DR

This paper explores the design and feasibility of using magnetic field gradients in planar ion traps to induce and enhance spin-spin interactions for quantum simulation, including novel physics in 2D ion crystals.

Contribution

It extends previous proposals on magnetic gradient induced coupling to planar traps and analyzes the potential for resonant enhancement and 2D ion crystal interactions.

Findings

Planar ion traps can generate strong magnetic gradients for spin coupling.

Resonant enhancement of spin-spin interactions is feasible with chip devices.

Two-dimensional ion crystals exhibit interesting frustration effects.

Abstract

We discuss the experimental feasibility of quantum simulation with trapped ion crystals, using magnetic field gradients. We describe a micro structured planar ion trap, which contains a central wire loop generating a strong magnetic gradient of about 20 T/m in an ion crystal held about 160 \mu m above the surface. On the theoretical side, we extend a proposal about spin-spin interactions via magnetic gradient induced coupling (MAGIC) [Johanning, et al, J. Phys. B: At. Mol. Opt. Phys. 42 (2009) 154009]. We describe aspects where planar ion traps promise novel physics: Spin-spin coupling strengths of transversal eigenmodes exhibit significant advantages over the coupling schemes in longitudinal direction that have been previously investigated. With a chip device and a magnetic field coil with small inductance, a resonant enhancement of magnetic spin forces through the application of alternating magnetic field gradients is proposed. Such resonantly enhanced spin-spin coupling may be used, for instance, to create Schr\"odinger cat states. Finally we investigate magnetic gradient interactions in two-dimensional ion crystals, and discuss frustration effects in such two-dimensional arrangements.