Detecting unambiguously non-Abelian geometric phases with trapped ions

TL;DR

This paper proposes an experimentally feasible method using trapped ions to detect non-Abelian geometric phases, highlighting their noncommutative nature through population differences in atomic states.

Contribution

It introduces a novel scheme to observe non-Abelian geometric phases in trapped ions, emphasizing their noncommutative properties with current experimental capabilities.

Findings

Population differences reveal noncommutative non-Abelian phases

Scheme is feasible with current trapped ion technology

Distinct population outcomes for different path orderings

Abstract

We propose for the first time an experimentally feasible scheme to disclose the noncommutative effects induced by a light-induced non-Abelian gauge structure with trapped ions. Under an appropriate configuration, a true non-Abelian gauge potential naturally arises in connection with the geometric phase associated with two degenerated dark states in a four-state atomic system interacting with three pulsed laser fields. We show that the population in atomic state at the end of a composed path formed by two closed loops $C_1$ and $C_2$ in the parameter space can be significantly different from the composed counter-ordered path. This population difference is directly induced by the noncommutative feature of non-Abelian geometric phases and can be detected unambiguously with current technology.