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

Abstract

We propose a practical protocol to generate and observe a non-Abelian geometric phase using a periodically driven Raman process in the hyperfine 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. II. NON-ABELIAN GEOMETRIC PHASE IN A PERIODICALLY DRIVEN SYSTEMThe Floquet analysis of periodically driven quantum systems has been well studied. We consider a system based on the periodically driven systems studied in two recent papers [22,23]. Consider a spin-1/2 system whose Hamiltonian takes the form H(t, ωt + θ) =H(t)f (ωt + θ), arXiv:1907.10721v1 [quant-ph]