Floquet engineering in the presence of optically excited carriers

Floquet engineering provides an optical means to manipulate electronic bandstructures, however, carriers excited by the pump field can lead to an effective heating, and can obscure measurement of the band changes. Here, we use multidimensional coherent spectroscopy to create a coherent ensemble of excitons in monolayer ${\mathrm{WS}}_{2}$ and measure the evolution of the coherence throughout the duration of the Floquet pump pulses with constant fluence but varying pulse duration. Changes to the amplitude of the macroscopic coherence quantifies the additional broadening introduced by interactions with carriers excited via two-photon absorption of the red-detuned pump. At the same time, the evolution of the average phase allows the instantaneous changes to the bandstructure to be quantified, which is demonstrated to be independent of the additional broadening. This approach to measuring the evolution of Floquet-Bloch states demonstrates a means to quantify effective heating and nonadiabaticity caused by excited carriers, while at the same time resolving the coherent evolution of the bandstructure.