Dynamical Gauge Fields on Optical Lattices: A Lattice Gauge Theorist Point of View

TL;DR

This paper explores how optical lattices can be used to simulate lattice gauge theories by generating local invariance and link operators, aiming to bridge ultracold atom experiments with fundamental gauge theory phenomena.

Contribution

It proposes two strategies for mimicking lattice gauge theories in optical lattices, focusing on generating local invariance and composite operators with adjoint quantum numbers.

Findings

Potential methods to generate local gauge invariance in optical lattices

Link operators with adjoint quantum numbers can be realized in optical lattices

Framework for future experimental simulations of gauge theories

Abstract

Dynamical gauge fields are essential to capture the short and large distance behavior of gauge theories (confinement, mass gap, chiral symmetry breaking, asymptotic freedom). I propose two possible strategies to use optical lattices to mimic simulations performed in lattice gauge theory. I discuss how new developments in optical lattices could be used to generate local invariance and link composite operators with adjoint quantum numbers that could play a role similar to the link variables used in lattice gauge theory. This is a slightly expanded version of a poster presented at the KITP Conference: Frontiers of Ultracold Atoms and Molecules (Oct 11-15, 2010) that I plan to turn into a more comprehensive tutorial that could be used by members of the optical lattice and lattice gauge theory communities. Suggestions are welcome.