  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.

Quantum Physics