  We consider the fate of a helical edge state of a spin Hall insulator and its
topological transition in presence of a circularly polarized light when coupled
to various forms of environments. A Lindblad type equation is developed to
determine the fermion occupation of the Floquet bands. We find by using
analytical and numerical methods that non-secular terms, corresponding to
2-photon transitions, lead to a mixing of the band occupations, hence the light
induced photocurrent is in general not perfectly quantized in the presence of
finite coupling to the environment, although deviations are small in the
adiabatic limit. Sharp crossovers are identified at frequencies $\Omega$ and
$\frac{1}{2}\Omega$ ($\Omega$ is the strength of light-matter coupling) with
the former resembling to a phase transition.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics