Coherent dynamics of Floquet-Bloch states in monolayer W S 2 reveals fast adiabatic switching

Floquet engineering offers a path to optically controlled materials, but experimental implementations have frequently relied on femtosecond pulses to achieve the high peak fields required to maximize light-matter interactions and obtain a measurable response. The Floquet formalism, however, is based on a continuous, periodic drive. Here we use femtosecond laser pulses to drive the optical Stark effect, a simple realization of Floquet engineering, in monolayer $\mathrm{W}{\mathrm{S}}_{2}$. By monitoring the coherent evolution of the free-induction decay, we show that the system evolves adiabatically, and that the finite duration of the pulses does not introduce any effects beyond Floquet theory. Furthermore, we demonstrate that the induced energy shift follows a linear dependence on instantaneous intensity, even for ultrafast driving fields of fewer than 15 optical cycles.