Theoretical methods to design and test quantum simulators for the compact Abelian Higgs model

TL;DR

This paper proposes theoretical methods for designing and testing quantum simulators of the compact Abelian Higgs model using Rydberg atom arrays, enabling near-term quantum simulation of complex gauge theories.

Contribution

It introduces concrete proposals for using Rydberg atom configurations to simulate the Abelian Higgs model, including models with one and two spins, and compares them with existing approaches.

Findings

Two-atom Rydberg setup effectively simulates one-spin models.

Three-atom configurations involve solving nonlinear equations.

Proposals are feasible with current technology.

Abstract

The lattice compact Abelian Higgs model is a non-perturbative regularized formulation of low-energy scalar quantum electrodynamics. In 1+1 dimensions, this model can be quantum simulated using a ladder-shaped optical lattice with Rydberg-dressed atoms (Zhang et al., Phys. Rev. Lett. 121, 223201). In this setup, one spatial dimension is used to carry the angular momentum of the quantum rotors. One can use truncations corresponding to spin-2 and spin-1 to build local Hilbert spaces associated with the links of the lattice. We argue that ladder-shaped configurable arrays of Rydberg atoms can be used for the same purpose. We make concrete proposals involving two and three Rydberg atoms to build one local spin-1 space (a qutrit). We show that the building blocks of the Hamiltonian calculations are models with one and two spins. We compare target and simulators using perturbative and numerical methods. The two-atom setup provides an easily controllable simulator of the one-spin model while the three-atom setup involves solving nonlinear equations. This could be tested with current technology. We argue that near-term technology could be used to quantum simulate models with two or more spins.