Cold-Atom Quantum Simulator for SU(2) Yang-Mills Lattice Gauge Theory

Non-Abelian gauge theories play an important role in the standard model of particle physics, and unfold a partially unexplored world of exciting physical phenomena. In this Letter, we suggest a realization of a non-Abelian lattice gauge theory—SU(2) Yang-Mills in ($1+1$) dimensions, using ultracold atoms. Remarkably, and in contrast to previous proposals, in our model gauge invariance is a direct consequence of angular momentum conservation and thus is fundamental and robust. Our proposal may serve as well as a starting point for higher-dimensional realizations.

Figure 1

A schematic representation of the required bosons (a), (b) and fermions (c), (d) superlattice structure; panel (e) shows schematically the combination of all the species to form the links-vertices structure. We have exaggerated the distance between the wells in order to make the structure more clear.