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Comment on `Detecting non-Abelian geometric phases with three-level $\Lambda$ systems' by Ericsson, Marie; Sjöqvist, Erik is a scholarly article available to read on EtoBox.

What is Comment on `Detecting non-Abelian geometric phases with three-level $\Lambda$ systems' about?

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 $\Lambda$ three-level system. They further propose a test to detect the non-commutative feature of this geometric phase. On the contrary, we show that the non-Abelian geometric phase picked up by the energy eigenstates of a $\Lambda$ 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.

Author

Ericsson, Marie; Sjöqvist, Erik

Published

2012

Language

EN