A GENERALIZED PANCHARATNAM GEOMETRIC PHASE FORMULA FOR 3-LEVEL QUANTUM-SYSTEMS

We describe a recently developed generalization of the Poincare sphere method, to represent pure states of a three-level quantum system in a convenient geometrical manner, The construction depends on the proper ties of the group SU(3) and its generators in the defining representat ion, and uses geometrical objects and operations in an eight-dimension al real Euclidean space. This construction is then used to develop a g eneralization of the well known Pancharatnam geometric phase formula, for evolution of a three-level system along a geodesic triangle in sta te space.