Experimental Proposal on Non-Abelian Aharonov-Bohm Caging Effect with a Single Trapped Ion

TL;DR

This paper proposes an experimental scheme using a single trapped ion to realize non-Abelian Aharonov-Bohm caging, enabling the study of localization phenomena and non-Abelian gauge fields in quantum systems.

Contribution

It introduces a novel method to synthesize non-Abelian gauge fields with a single trapped ion, expanding the experimental study of localization and non-Abelian physics.

Findings

Non-Abelian AB caging occurs under specific interference conditions.

Numerical simulations show localization depends on the interference matrix and initial state.

The scheme broadens experimental access to non-Abelian gauge phenomena.

Abstract

In the lattice system, when the synthetic flux reaches a $\pi$ phase along a closed loop under the synthetic gauge field, destructive interference occurs and gives rise to the localization phenomenon. This is known as the Aharonov-Bohm (AB) caging effect. It provides a powerful tool for the study of quantum transportation and dynamical effects. In the system where lattice sites possess internal structure and the underlying gauge field is non-Abelian, localization can also occur, forming the non-Abelian AB caging. Here, we propose an experimental scheme to synthesize non-Abelian gauge fields with a single trapped ion by coupling multiple internal levels and Fock states in its motion via laser fields. In contrast to the Abelian AB caging, we numerically observe that the non-Abelian AB caging occurs either when the interference matrix is nilpotent, or when the initial state is specifically set. Our experimental scheme broadens the study of localization phenomena and provides a novel tool for the study of non-Abelian physics.