Photon-Mediated Stroboscopic Quantum Simulation of a Z2 Lattice Gauge Theory

Quantum simulation of lattice gauge theories, aiming at tackling nonperturbative 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 nonlocal photon-mediated interactions appearing in nanophotonic or cavity QED setups. We illustrate the method for a 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.