  Recent advances in the field of condensed-matter physics have unlocked the
potential to realize and control emergent material phases that do not exist in
thermal equilibrium. One of the most promising concepts in this regard is
Floquet engineering, the coherent dressing of matter via time-periodic
perturbations. However, the broad applicability of Floquet engineering to
quantum materials is still unclear. For the paradigmatic case of monolayer
graphene, the theoretically predicted Floquet-induced effects, despite a
seminal report of the light-induced anomalous Hall effect, have been put into
question. Here, we overcome this problem by using electronic structure
measurements to provide direct experimental evidence of Floquet engineering in
graphene. We report light-matter-dressed Dirac bands by measuring the
contribution of Floquet sidebands, Volkov sidebands, and their quantum path
interference to graphene's photoemission spectral function. Our results finally
demonstrate that Floquet engineering in graphene is possible, paving the way
for the experimental realization of the many theoretical proposals on
Floquet-engineered band structures and topological phases.
