Quantum Simulating 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.

Using numerical methods, we  compare observables associated with the real-time evolution and the phase diagram for the simulators and the target model. We discuss the progress of the experimental implementations at the time of the meeting.