  To realize band structures with non-trivial topological properties in an
optical lattice is an exciting topic in current studies on ultra cold atoms.
Here we point out that this lofty goal can be achieved by using a simple scheme
of shaking an optical lattice, which is directly applicable in current
experiments. The photon-assistant band hybridization leads to the production of
an effective spin-orbit coupling, in which the band index represents the
pseudospin. When this spin-orbit coupling has finite strengths along multiple
directions, non-trivial topological structures emerge in the Brillouin zone,
such as topological defects with a winding number 1 or 2 in a shaken square
lattice. The shaken lattice also allows one to study the transition between two
band structures with distinct topological properties.

Quantum Gases