# Topological phase for spin-orbit transformations on a laser beam

## TL;DR

This paper explores the topological phase arising from SO(3) transformations in laser beams, demonstrating it experimentally through polarization and spatial mode manipulations, with implications for quantum and classical optics.

## Contribution

It provides the first experimental demonstration of the topological phase linked to SO(3) in laser beams, connecting quantum entanglement and classical light transformations.

## Key findings

- Topological phase confirmed via interferometry.
- Quantitative link between concurrence and fringe visibility.
- Applicable to both quantum and classical regimes.

## Abstract

We investigate the topological phase associated with the double connectedness of the SO(3) representation in terms of maximally entangled states. An experimental demonstration is provided in the context of polarization and spatial mode transformations of a laser beam carrying orbital angular momentum. The topological phase is evidenced through interferometric measurements and a quantitative relationship between the concurrence and the fringes visibility is derived. Both the quantum and the classical regimes were investigated.