Abstract
We propose 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 the atomic state at the end of a composed path formed by two closed loops C1 and C2 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.
Highlights
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
We analyze in detail why non-Abelian structures have not been observed in NMR experiments, and propose an experimentally feasible scheme to directly detect the observable effect induced by the noncommutative property of the non-Abelian gauge potentials in a trapped-ion system[24]
We show that a true nonAbelian 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
Summary
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. We analyze in detail why non-Abelian structures have not been observed in NMR experiments, and propose an experimentally feasible scheme to directly detect the observable effect induced by the noncommutative property of the non-Abelian gauge potentials in a trapped-ion system[24]. There always exist a pairwise degeneracy of states in the parameter space because the Hamiltonian is invariant under the operation S → −S, non-Abelian gauge structure may appear in the system.
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