Comment on "detecting non-Abelian geometric phases with three-level Λ systems"

Abstract

In their recent paper, Yan-Xiong Du claim to have found a non-Abelian adiabatic geometric phase associated with the energy eigenstates of a large-detuned three-level Λ 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 Λ 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. © 2013 American Physical Society.