  Tripod-scheme cold atoms interacting with laser beams have attracted
considerable interest for their role in synthesizing effective non-Abelian
vector potentials. Such effective vector potentials can be exploited to realize
an all-optical imprinting of geometric phases onto matter waves. By working on
carefully designed extensions of our previous work, we show that coherent
lattice structure of cold-atom sub-wavepackets can be formed and that the
non-Abelian Aharonov-Bohm effect can be easily manifested via the translational
motion 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 simple
dynamical phase effect, and that under certain conditions it can be understood
as an Abelian geometric phase in a different frame of reference. Results should
help design better schemes for the control of cold-atom matter waves.
