Synthetic Gauge Fields for Vibrational Excitations of Trapped ions

TL;DR

This paper proposes a method to create synthetic gauge fields for vibrational excitations in trapped ion arrays, enabling the simulation of magnetic phenomena like the Aharonov-Bohm effect and topological edge states.

Contribution

It introduces a theoretical scheme to engineer gauge fields for phonons in microtrap arrays using frequency gradients and periodic driving, facilitating quantum simulation of topological effects.

Findings

Phonons can mimic charged particles in magnetic fields.

Microtrap arrays can realize Aharonov-Bohm effect.

Edge states of topological insulators can be observed.

Abstract

The vibrations of a collection of ions in a microtrap array can be described in terms of hopping phonons. We show theoretically that the vibrational couplings may be tailored by using a gradient of the microtrap frequencies, together with a periodic driving of the trapping potential. These ingredients allow us to induce effective gauge fields on the vibrational excitations, such that phonons mimic the behavior of charged particles in a magnetic field. In particular, microtrap arrays are ideally suited to realize the famous Aharonov-Bohm effect, and observe the paradigmatic edge states typical from quantum-Hall samples and topological insulators.