Photon-mediated Stroboscopic Quantum Simulation of a $\mathbb{Z}_{2}$ Lattice Gauge Theory

TL;DR

This paper proposes a photon-mediated, stroboscopic approach to simulate a $ ext{Z}_2$ lattice gauge theory, enabling the realization of complex four-body interactions beyond 1+1 dimensions in quantum simulation.

Contribution

It introduces a novel method combining stroboscopic atomic control and photon-mediated interactions to simulate higher-dimensional lattice gauge theories.

Findings

Method enables simulation of four-body plaquette interactions.

Ground state preparation and Wilson loop measurement demonstrated.

Applicable to current atomic physics experimental setups.

Abstract

Quantum simulation of lattice gauge theories (LGTs), aiming at tackling non-perturbative particle and condensed matter physics, has recently received a lot of interest and attention, resulting in many theoretical proposals, as well as several experimental implementations. One of the current challenges is to go beyond 1+1 dimensions, where four-body (plaquette) interactions, not contained naturally in quantum simulating devices, appear. In this Letter, we propose a method to obtain them based on a combination of stroboscopic optical atomic control and the non-local photon-mediated interactions appearing in nanophotonic or cavity QED setups. We illustrate the method for a $\mathbb{Z}_{2}$ lattice Gauge theory. We also show how to prepare the ground state and measure Wilson loops using state-of-the-art techniques in atomic physics.