Paper detail

Floquet Engineering of a Dynamical $Z_{2}$ Lattice Gauge Field with Ultracold Atoms

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 possess both a independent Maxwell term and the local $Z_{2}$ gauge symmetry. Our proposal relies on a species dependent optical lattice, and can be achieved in one, two or three dimension. By an unitary transformation, this model can be mapped into a non-interacting composite Fermion system with fluctuating back ground 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 the dynamical localization, which depends on the structure of the initial states.