  Here we provide a picture of transport in quantum well heterostructures with
a periodic driving field in terms of a probabilistic occupation of the
topologically protected edge states in the system. This is done by generalizing
methods from the field of photon assisted tunneling. We show that the time
dependent field {\it dresses} the underlying Hamiltonian of the heterostructure
and splits the system into side-bands. Each of these sidebands is occupied with
a certain probability which depends on the drive frequency and strength. This
leads to a reduction in the topological transport signatures of the system
because of the probability to absorb/emit a photon. Therefore when the voltage
is tuned to the bulk gap the conductance is smaller then the expected $2e^2/h$.
We refer to this as photon inhibited topological transport. Nevertheless, the
edge modes reveal their topological origin in the robustness of the edge
conductance to disorder and changes in model parameters. In this work the
analogy with photon assisted tunneling allows us to interpret the calculated
conductivity and explain the sum rule observed by previous authors
