Quantum simulator of link models using spinor dipolar ultracold atoms

We propose a scheme for the quantum simulation of quantum link models in two-dimensional lattices. Our approach considers spinor dipolar gases on a suitably shaped lattice, where the dynamics of particles in the different hyperfine levels of the gas takes place in one-dimensional chains coupled by the dipolar interactions. We show that at least four levels are needed. The present scheme does not require any particular fine-tuning of the parameters. We perform the derivation of the parameters of the quantum link models by means of two different approaches, a non-perturbative one tied to angular momentum conservation, and a perturbative one. A comparison with other schemes for $(2+1)$-dimensional quantum link models present in literature is discussed. Finally, the extension to three-dimensional lattices is presented, and its subtleties are pointed out.