Baryon squishing in synthetic dimensions by effective $SU(M)$ gauge fields

TL;DR

This paper explores how synthetic dimensions and non-Abelian gauge fields in cold atomic systems can deform baryons into nonlocal 'squished' states, revealing new many-body phases and potential quantum simulation applications.

Contribution

It introduces a mapping of synthetic dimension systems to $SU(M)$ gauge theories, demonstrating nonlocal baryon deformation and potential for novel quantum phases.

Findings

Nonlocal 'squished' baryons formed by gauge fields and Zeeman effects.

Mapping of cold atom systems to $SU(M)$ gauge models.

Potential realization of $SU(M)$ random flux Hamiltonians.

Abstract

We investigate few body physics in a cold atomic system with synthetic dimensions (Celi et al., PRL 112, 043001 (2014)) which realizes a Hofstadter model with long-ranged interactions along the synthetic dimension. We show that the problem can be mapped to a system of particles (with $SU(M)$ symmetric interactions) which experience an $SU(M)$ Zeeman field at each lattice site {\em and} a non-Abelian $SU(M)$ gauge potential that affects their hopping from one site to another. This mapping brings out the possibility of generating {\em non-local} interactions (interaction between particles at different physical sites). It also shows that the non-Abelian gauge field, which induces a flavor-orbital coupling, mitigates the "baryon breaking" effects of the Zeeman field. For $M$ particles, the $SU(M)$ singlet baryon which is site localized, is "deformed" to be a nonlocal object ("squished" baryon) by the combination of the Zeeman and the non-Abelian gauge potential, an effect that we conclusively demonstrate by analytical arguments and exact (numerical) diagonalization studies. These results not only promise a rich phase diagram in the many body setting, but also suggests possibility of using cold atom systems to address problems that are inconceivable in traditional condensed matter systems. As an example, we show that the system can be adapted to realize Hamiltonians akin to the $SU(M)$ random flux model.