Detecting unambiguously non-Abelian geometric phases with trapped ions

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.

6 pages

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• Jahn-Teller induced Berry phase in spin-orbit coupled Bose-Einstein condensates
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• Optical rotation of heavy hole spins by non-Abelian geometrical means
• Control of Tripod-Scheme Cold-Atom Wavepackets by Manipulating a non-Abelian Vector Potential
• Detecting non-Abelian geometric phase in circuit QED