Floquet Engineering of a Dynamical <i>Z</i> ₂ Lattice Gauge Field with Ultracold Atoms

Abstract The Gauge field theory is a fundamental concept in modern physics, attracting many theoretical and experimental efforts towards its simulation. In this paper, we propose that a simple model, in which fermions coupled to a dynamical lattice gauge field, can be engineered via the Floquet approach. The model possesses both an independent Maxwell term and the local Z 2 gauge symmetry. Our proposal relies on a speciesdependent optical lattice, and can be achieved in one, two or three dimensions. By a unitary transformation, this model can be mapped into a non-interacting composite fermion system with fluctuating background charge. With the help of this composite fermion picture, two characteristic observations are predicted. One is the radio-frequency spectroscopy, which exhibits no dispersion in all parameter regimes. Second is the dynamical localization, which depends on the structure of the initial states.