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

TL;DR

This paper demonstrates how to control and manipulate cold-atom wavepackets using non-Abelian vector potentials, revealing effects like lattice formation and the non-Abelian Aharonov-Bohm effect, with implications for quantum control schemes.

Contribution

It extends previous work to show formation of lattice structures and manifestation of the non-Abelian Aharonov-Bohm effect in cold atoms, linking non-Abelian effects to simpler phases via frame changes.

Findings

Formation of coherent lattice structures in cold-atom sub-wavepackets

Manifestation of non-Abelian Aharonov-Bohm effect through atomic motion

Connection between non-Abelian effects and Abelian phases in different frames

Abstract

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.