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

References in corpus (6)

• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Spin Hall effects for cold atoms in a light induced gauge potential
• An experimental observation of geometric phases for mixed states using NMR interferometry
• Generalized Stern-Gerlach Effect for Chiral Molecules
• Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials
• Physical implementation of holonomic quantum computation in decoherence-free subspaces with trapped ions