  In this letter we propose realistic schemes to realize topologically
nontrivial Floquet states by shaking optical lattices, using both one-dimension
lattice and two-dimensional honeycomb lattice as examples. The topological
phase in the two-dimensional model exhibits quantum anomalous Hall effect. The
transition between topological trivial and nontrivial states can be easily
controlled by shaking frequency and amplitude. Our schemes have two major
advantages. First, both the static Hamiltonian and the shaking scheme are
sufficiently simple to implement. Secondly, it requires relatively small
shaking amplitude and therefore heating can be minimized. These two advantages
make our scheme much more practical.
