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.
@article{arxiv.quant-ph/0010068,
title = {Geometric Phase of Three-level Systems in Interferometry},
author = {Barry C. Sanders and Hubert de Guise and Stephen D. Bartlett and Weiping Zhang},
journal= {arXiv preprint arXiv:quant-ph/0010068},
year = {2007}
}