  For cold atomic systems, varying the optical lattice potential periodically
provides a general and simple way to drive the system into phases with
nontrivial topology. Besides its simplicity, this driving approach, compared to
the usual driving approach by exerting an external electromagnetic field to the
static system, has the merit that it does not break the original static
system's time-reversal symmetry at any given time. Based on this approach, we
find that a trivial insulator with time-reversal symmetry can be driven into a
Floquet quantum spin Hall insulator. This novel state of matter can stably host
one or two pair of gapless helical states on the same boundary, which suggests
this state is not a simple analog of the quantum spin Hall insulator. The
effect of a time-reversal-symmetry-breaking periodic perturbation, the
stability of the novel states, and this new driving approach to a system
without time-reversal symmetry are discussed.
