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arXiv:1301.5950

Reply to "Comment on 'Detecting Non-Abelian Geometric Phases with Three-Level Λ Atoms' "

Yan-Xiong Du, Xue, Z. Y., Zhang, X. D., Hui Yan

Published Jan 25, 2013• 0 citations
arXivHTMLPDF

Abstract

In this reply, we address the comment by Ericsson and Sjoqvist on our paper [Phys. Rev. A {\bf 84}, 034103 (2011)]. We point out that the zero gauge field is not the evidence of trivial geometric phase for a non-Abelian SU(2) gauge field. Furthermore, the recalculation shows that the non-Abelian geometric phase we proposed in the three-level $Λ$ system is indeed experimentally detectable.

DOI
10.48550/arxiv.1301.5950

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In this reply, we address the comment by Ericsson and Sjoqvist on our paper [Phys. Rev. A {\bf 84}, 034103 (2011)]. We point out that the zero gauge field is not the evidence of trivial geometric phase for a non-Abelian SU(2) gauge field. Furthermore, the recalculation shows that the non-Abelian geometric phase we proposed in the three-level ΛΛΛ system is indeed experimentally detectable.
In their recent paper, Yan-Xiong Du et al. [Phys. Rev. A 84, 034103 (2011)] claim to have found a non-Abelian adiabatic geometric phase associated with the energy eigenstates of a large-detuned three-level $\ensuremath{\Lambda}$ system. They further propose a test to detect the noncommutative feature of this geometric phase. On the contrary, we show that the non-Abelian geometric phase picked up by the energy eigenstates of a $\ensuremath{\Lambda}$ system is trivial in the adiabatic approximation, while, in the exact treatment of the time evolution, this phase is very small and cannot be separated from the non-Abelian dynamical phase acquired along the path in parameter space.
We show that a non-Abelian gauge potential in two nearly degenerated dressed states may be induced by two laser beams interacting with a three-level $\ensuremath{\Lambda}$ atomic system. We demonstrate that the populations of the atomic states at the end of a composed path formed by two closed loops are dependent on the order of those two loops, showing an unambiguous signature of the non-Abelian geometric phase. Through numerical calculations, we show that the non-Abelian feature of the geometric phases can be tested under realistic conditions.
In response to Hradil's Comment [preceding Comment, Phys. Rev. A 47, 4532 (1993)], we point out that his prescription for putting both the cosine and sine equal to zero when the data yield n3{\mathit{n}}_{3}n3​=n4{\mathit{n}}_{4}n4​ and n5{\mathit{n}}_{5}n5​=n6{\mathit{n}}_{6}n6​ can lead to meaningless results. Moreover, Hradil's Eq. (5) for obtaining D2{\mathit{D}}^{2}D2 from the measured variance leads to disagreement with experiment. Finally, it is possible to obtain a continuous spectrum of phases with our technique.