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A generalized Pancharatnam geometric phase formula for three level systems

Arvind·K. S. Mallesh·N. Mukunda
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Abstract

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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Arvind, K. S. Mallesh, N. Mukunda. 1996-05-29. A generalized Pancharatnam geometric phase formula for three level systems. https://doi.org/10.1088/0305-4470/30/7/021

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