A generalized Pancharatnam geometric phase formula for three-level quantum systems
- 7 April 1997
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 30 (7) , 2417-2431
- https://doi.org/10.1088/0305-4470/30/7/021
Abstract
We describe a recently developed generalization of the Poincaré 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. This construction is then used to develop a generalization of the well known Pancharatnam geometric phase formula, for evolution of a three-level system along a geodesic triangle in state space.Keywords
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