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Tripod-scheme cold atoms interacting with laser beams have attractedconsiderable interest for their role in synthesizing effective non-Abelianvector potentials. Such effective vector potentials can be exploited to realizean all-optical imprinting of geometric phases onto matter waves. By working oncarefully designed extensions of our previous work, we show that coherentlattice structure of cold-atom sub-wavepackets can be formed and that thenon-Abelian Aharonov-Bohm effect can be easily manifested via the translationalmotion of cold atoms. We also show that by changing the frame of reference,effects due to a non-Abelian vector potential may be connected with a simpledynamical phase effect, and that under certain conditions it can be understoodas an Abelian geometric phase in a different frame of reference. Results shouldhelp design better schemes for the control of cold-atom matter waves.

Control of Tripod-Scheme Cold-Atom Wavepackets by Manipulating a non-Abelian Vector Potential