Achieving the Continuum Limit of (1+1)D Lattice Quantum Electrodynamics in Cold-Atom Quantum Simulators

Advances in cold-atom simulators has allowed the implementation of a Z₂ lattice gauge theory in optical lattices where phenomena inherent of Quantum Electrodynamics (QED) can readily be observed. However a procedure for reliably taking the Z_N → U(1) limit necessary to recovery the continuum theory in quantum simulators has remained elusive. 

Here we propose such a scheme, encoding the Z_N  electric field in a plaquette consisting of N rydberg atoms each driven with a large, site-dependent detuning. By making the plaquette small enough, the gauge theory emerges as an effective model from the microscopic description. By exploiting the blockade mechanism both within and between plaquettes, both gauge and particle number breaking errors are heavily suppressed. 

The particle mass can be tuned by engineering a slight twist in every alternate plaquette while the electric field coupling can be changed by a simple modulation of the onsite detuning, allowing great flexibility to study confinement transitions in many regimes of the phase diagram. 

To benchmark our calculations we use the density matrix renormalization group to perform ground state calculations and quench dynamics. We investigate the accessibility of the continuum spectrum and the effect of charge-parity violation on preventing Coleman's phase transition when the topological θ-term is introduced. 

Our protocol can easily be realized in optical tweezer arrays and as a result of the scheme's scalability provides a systematic approach for extracting continuum data of abelian gauge theories from cold-atom quantum simulators.