  Abelian and Non-Abelian evolution of a quantum system manifests differently
in the geometric phase acquired by the system under such evolutions. In this
work we develop and study, using dressed state techniques, an experimentally
realizable spin system which allows us to transit smoothly from non-Abelian to
Abelian evolutions by changing externally controllable parameters. The study
provides insights into the underlying physical phenomenon governing such a
transition allowing us greater control on phase generation in a quantum system.
The robustness of geometric phase against fluctuations of the external
parameters of the system has also been studied in this work. The noise analysis
has direct consequence on the present search for fault tolerant quantum gates
using geometric phase.
