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Deutsche Physikalische Gessellschaft IOP Institute of Physics

Detecting unambiguously non-Abelian geometric phases with trapped ions

Xin-Ding Zhang1, Z D Wang2, Liang-Bin Hu1, Zhi-Ming Zhang3 and Shi-Liang Zhu1,2,4

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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.


PACS

42.50.-p Quantum optics

03.65.Vf Phases: geometric; dynamic or topological

Subjects

Optics, quantum optics and lasers

Quantum information and quantum mechanics

Dates

Issue 4 (April 2008)

Received 5 October 2007

Published 15 April 2008



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