  The Su-Schrieffer-Heeger model of polyacetylene is a paradigmatic Hamiltonian
exhibiting non-trivial edge states. By using Floquet theory we study how the
spectrum of this one-dimensional topological insulator is affected by a
time-dependent potential. In particular, we evidence the competition among
different photon-assisted processes and the native topology of the unperturbed
Hamiltonian to settle the resulting topology at different driving frequencies.
While some regions of the quasienergy spectrum develop new gaps hosting Floquet
edge states, the native gap can be dramatically reduced and the original edge
states may be destroyed or replaced by new Floquet edge states. Our study is
complemented by an analysis of Zak phase applied to the Floquet bands. Besides
serving as a simple example for understanding the physics of driven topological
phases, our results could find a promising test-ground in cold matter
experiments.

Mesoscale and Nanoscale Physics;Quantum Gases