Comment on `Detecting non-Abelian geometric phases with three-level Λ systems'

• In their recent paper, Yan-Xiong Du {\it et al.} [Phys. Rev. A {\bf 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.

Subject headings

NATURVETENSKAP  -- Fysik -- Atom- och molekylfysik och optik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Atom and Molecular Physics and Optics (hsv//eng)

Keyword

Cold atoms

geometric phase

quantum computation

Fysik med inriktning mot atom- molekyl- och kondenserande materiens fysik

Physics with spec. in Atomic, Molecular and Condensed Matter Physics

Publication and Content Type

ref (subject category)

art (subject category)