  We investigate topological phases induced by a driven electric field coupled
to a dimer chain (a model for poly-acetylene) at high frequency regime. It is
shown how the topological invariant of the system can be controlled by the
field amplitude. Furthermore, in the presence of a time-periodic electric
field, the effect of the next-nearest neighbor hopping amplitudes on
topological properties is studied. Breaking of the inversion symmetry causes to
remove the degeneracy of zero edge states. The fractional Zak phase which is
now measurable by ultra-cold atoms in one dimensional optical lattice is also
calculated. For calculating modified band structure, we also develop a general
Floquet-Bloch approach for systems under application of a potential with
lattice and time translation invariance.
