# Braiding photonic topological zero modes

## TL;DR

This paper reports the first experimental measurement of the geometric phase resulting from braiding topological zero modes in a photonic system, demonstrating the potential of photonic lattices to study topological defects.

## Contribution

It introduces a novel experimental approach using 2D photonic waveguide arrays to measure braiding-induced geometric phases of topological zero modes.

## Key findings

- First measurement of braiding geometric phase in any system
- Use of tunable photonic waveguide arrays for topological studies
- Photonic lattices as a platform for topological defect research

## Abstract

A remarkable property of quantum mechanics in two-dimensional (2D) space is its ability to support "anyons," particles that are neither fermions nor bosons. Theory predicts that these exotic excitations can be realized as bound states confined near topological defects, like Majorana zero modes trapped in vortices in topological superconductors. Intriguingly, in the simplest cases the nontrivial phase that arises when such defects are "braided" around one another is not intrinsically quantum mechanical; rather, it can be viewed as a manifestation of the geometric (Pancharatnam-Berry) phase in wave mechanics, enabling the simulation of such phenomena in classical systems. Here we report the first experimental measurement in any system, quantum or classical, of the geometric phase due to such a braiding process. These measurements are obtained using an interferometer constructed from highly tunable 2D arrays of photonic waveguides. Our results introduce photonic lattices as a versatile playground for the experimental study of topological defects and their braiding, complementing ongoing efforts in solid-state systems and cold atomic gases.