Abstract:

The lattice compact Abelian Higgs model is a non-perturbative regularized formulation of low-energy scalar quantum electrodynamics (sQED). I elaborate on the methods of simulating this model with configurable arrays of Rydberg atoms. Specifically, I show the mathematics for simulating a single-site spin-1 space using two or three Rydberg atoms. The target and simulators are compared using perturbative and numerical methods. The two-atom setup provides an easily controllable simulator of the single-site spin-1 space, while the three-atom setup involves solving nonlinear equations. Understanding these two setups is necessary, as we plan to simulate many-site spaces using these setups as the building blocks of larger Rydberg arrays.