  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.
