Geometric Phase in Quantum Mechanics is generally formulated entirely in terms of geometric structure of the Complex Hilbert Space. We will exploit this fact in case of mixed states for three level open systems undergoing depolarization using the eight dimensional Poincare sphere in the SU(2) Polarisation picture and non unit vector rays in H3 within the limit of pure state approach may be found to be in agreement with the Pancharatnam Phase, Berry Phase and Aharonov-Anandan Phase.

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Bloch-sphere representation of three-vertex geometric phases

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Annals of Physics

Geometric Phases forSU(3) Representations and Three Level Quantum Systems

G. Khanna, Shomeek Mukhopadhyay, R. Simon, Narasimhaiengar Mukunda

Published Jan 1, 1997• 78 citations

Publisher

DOI: 10.1006/aphy.1997.5601

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N

-state quantum system can be represented by $N\ensuremath{-}1$ spherical triangles on the Bloch sphere. The parameter dependence of the geometric phase was analyzed based on this picture. We found that the geometric phase exhibits rich nonlinear behavior in a high-dimensional Hilbert space.