Quantum simulations of the Abelian Higgs model with a bosonic ladder

We propose to use a physical ladder of bosonic atoms to quantum simulate a lattice gauge theory called the Abelian Higgs model.
We use a spin-1 approximation where the 3 spin states are obtained with the three ways two bosons can be placed on a rung. Ladder structures can be realized experimentally, but generating attractive interactions among the nearest neighbor atoms is more challenging.
Recent work by J. Zeiher et al. (arXiv:1705.08372), shows that these interactions can be manufactured by using Rydberg's atoms.
A proof of principle would be to start with a single boson per rung which corresponds to the well studied case of the quantum (spin-1/2) Ising model in a transverse field. If relevant at the time of the conference, we comment on recent experimental progress to realize these ideas.