Pancharatnam-Berry Phase in Quantum Optics: Relation to Bargmann Invariants and Geodesics.

A quantum system, when subjected to an adiabatic cyclic evolution of parameters governing its Hamiltonian, gains a phase factor known as the geometric phase. One of its most celebrated formulations in the regime of quantum optics is the Pancharatnam-Berry phase. It is said to be acquired by a beam of light undergoing an evolution of its polarization state. This article builds on the background and notion of the Pancharatnam-Berry phase in quantum optics. A convenient tool for visualizing the evolution of polarization states is the Poincaré sphere, which has been briefly discussed here. The close relation of the phase to a few other important concepts, such as Bargmann invariants and geodesics, has also been discussed in this article. [ABSTRACT FROM AUTHOR]