Abstract

The geometric phase was discovered by Pancharatnam in 1956 and became a research topic of interest after Berry showed the same mathematical expression for phase in the context of evolution of quantum states. To this day it is used in optical phase elements for wavefront shaping and in quantum information, among many other areas. The mathematical description is often joined by a graphical description of the changes of state, for optics changes in polarization, where the states that are present in the evolution are connected by geodesics over the Poincare sphere. The mathematical approach correctly calculates the geometric phase, but the physical meaning does not seem clear.

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