A generalized Pancharatnam geometric phase formula for three level systems

Details A generalized Pancharatnam geometric phase formula for three level systems A generalized Pancharatnam geometric phase formula for three level systems

1996-05-29

arxiv.org/abs/quant-ph/9605042v1

J.Phys.A30:2417-2431,1997

Physics

Quantum Physics

12 pages, Revtex, one figure, epsf used for figure insertion

Scientific paper

10.1088/0305-4470/30/7/021

We describe a generalisation of the well known Pancharatnam geometric phase formula for two level systems, to evolution of a three-level system along a geodesic triangle in state space. This is achieved by using a recently developed generalisation 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 properties of the group $SU(3)\/$ and its generators in the defining representation, and uses geometrical objects and operations in an eight dimensional real Euclidean space. Implications for an n-level system are also discussed.

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