Subcycle Formation of Floquet-Bloch Bands

Floquet-Bloch states can form in solids under periodic driving of electrons. We capture their ultrafast buildup with angle-resolved photoemission spectroscopy and subcycle time resolution. For this, we drive the Dirac surface state of a topological insulator with intense mid-infrared fields. Starting with strong intraband currents, Floquet sidebands build up in a single optical cycle. Intraband acceleration simultaneously proceeds in multiple sidebands until high-energy electrons scatter into bulk states and dissipation destroys the Floquet bands. A full quantum theory describes the simultaneous occurrence of Floquet states with intraband and interband dynamics. Our results shed new light on the dynamics of Floquet states and suggest that optical band-structure engineering is possible within a single oscillation cycle of the carrier field of light.