  Floquet theory has spawned many exciting possibilities for electronic
structure control with light with enormous potential for future applications.
The experimental realization in solids, however, largely remains pending. In
particular, the influence of scattering on the formation of Floquet-Bloch
states remains poorly understood. Here we combine time- and angle-resolved
photoemission spectroscopy with time-dependent density functional theory and a
two-level model with relaxation to investigate the survival of Floquet-Bloch
states in the presence of scattering. We find that Floquet-Bloch states will be
destroyed if scattering -- activated by electronic excitations -- prevents the
Bloch electrons from following the driving field coherently. The two-level
model also shows that Floquet-Bloch states reappear at high field intensities
where energy exchange with the driving field dominates over energy dissipation
to the bath. Our results clearly indicate the importance of long scattering
times combined with strong driving fields for the successful realization of
various Floquet phenomena.
