Comprehensive Analysis of Geometric Phase for SU(3) Representations

TL;DR

This paper explores the geometric phase in quantum mechanics for SU(3) systems, analyzing mixed states and their relation to known phases like Berry and Pancharatnam, using geometric structures in high-dimensional spaces.

Contribution

It provides a comprehensive analysis of geometric phases in SU(3) representations, extending the understanding of phase behavior in three-level quantum systems.

Findings

Mixed states in SU(3) can be described using high-dimensional geometric structures.

The geometric phase for SU(3) systems aligns with known phases like Berry and Pancharatnam.

The analysis bridges pure and mixed state phases in three-level quantum systems.

Abstract

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.