# An SU(2) geometric phase induced by periodically driven Raman process in an ultracold dilute Bose gas

## TL;DR

This paper proposes a practical method to generate and observe a non-Abelian SU(2) geometric phase in ultracold Bose gases using a periodically driven Raman process, supported by Floquet theory analysis and simulation results.

## Contribution

It introduces a novel protocol for creating non-Abelian geometric phases in ultracold gases via Floquet-engineered Raman processes, with an experimental implementation proposal.

## Key findings

- Demonstration of non-Abelian gauge transformation properties
- Simulation of non-commuting SU(2) operators
- Proposal for experimental realization in ultracold gases

## Abstract

We propose a practical protocol to generate and observe a non-Abelian geometric phase using a periodically driven Raman process in the hyperfne ground state manifold of atoms in a dilute ultracold gas. Our analysis is based upon recent developments and application of Floquet theory to periodically driven quantum systems. The simulation results show the non-Abelian gauge transformation and the non-commuting property of the SU(2) transformation operators. Based on these results, we propose a possible experimental implementation with an ultracold dilute Bose gas.