Topological Phenomena in Trapped Ion Systems

TL;DR

This paper proposes a method to observe topological phenomena in trapped ion systems, revealing non-trivial phonon band structures, edge modes, and potential for exploring strongly correlated states.

Contribution

It introduces a scheme to realize and analyze topological phonon bands and edge states in trapped ion arrays with laser-induced symmetry breaking.

Findings

Identification of topological phonon bands in ion traps

Demonstration of robust edge modes against perturbations

Potential to explore strongly correlated states with long-range phonon interactions

Abstract

We propose and analyze a scheme to observe topological phenomena with ions in microtraps. We consider a set of trapped ions forming a regular structure in two spatial dimensions and interacting with lasers. We find phonon bands with non-trivial topological properties, which are caused by the breaking of time reversal symmetry induced by the lasers. We investigate the appearance of edge modes, as well as their robustness against perturbations. Long-range hopping of phonons caused by the Coulomb interaction gives rise to flat bands which, together with induced phonon-phonon interactions, can be used to produce and explore strongly correlated states. Furthermore, some of these ideas can also be implemented with cold atoms in optical lattices.