  The bulk-edge correspondence guarantees that the interface between two
topologically distinct insulators supports at least one topological edge state
that is robust against static perturbations. Here, we address the question of
how dynamic perturbations of the interface affect the robustness of edge
states. We illuminate the limits of topological protection for Floquet systems
in the special case of a static bulk. We use two independent dynamic quantum
simulators based on coupled plasmonic and dielectric photonic waveguides to
implement the topological Su-Schriefer-Heeger model with convenient control of
the full space- and time-dependence of the Hamiltonian. Local time periodic
driving of the interface does not change the topological character of the
system but nonetheless leads to dramatic changes of the edge state, which
becomes rapidly depopulated in a certain frequency window. A theoretical
Floquet analysis shows that the coupling of Floquet replicas to the bulk bands
is responsible for this effect. Additionally, we determine the depopulation
rate of the edge state and compare it to numerical simulations.
