Detecting non-Abelian geometric phases with three-level Λ systems

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 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.