Scalar Electrodynamics with Configurable Rydberg Atoms Arrays?*

We present a quantum Hamiltonian for scalar electrodynamics in one and two spatial dimensions where

the electric field Hilbert space is approximated by a spin-1 triplet.  We propose two different quantum

simulators for this model obtained by assembling arrays of Rydberg atoms with  ladder structures.

We compare observables associated with the real-time evolution of (small) systems for the simulators and the

target model. Discussions with the QuEra team regarding building the simulators using their  facilities have

started and we report on the progress of this enterprise at the time of the conference. We discuss

possible applications involving phase transitions and finite size scaling for this model and other models

based on quantum links.