Geometric Phase of Three-level Systems in Interferometry

Abstract

We present the first scheme for producing and measuring an Abelian geometric phase shift in a three-level system where states are invariant under a non-Abelian group. In contrast to existing experiments and proposals for experiments, based on U(1)-invariant states, our scheme geodesically evolves U(2)-invariant states in a four-dimensional SU(3)/U(2) space and is physically realized via a three-channel optical interferometer.

4 pages, 3 figures

References in corpus (2)

• A generalized Pancharatnam geometric phase formula for three level systems
• Representations of the Weyl group and Wigner functions for SU(3)

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