Synthetic Gauge Fields for Vibrational Excitations of Trapped ions

Understand

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.