Coherent optical manipulation of electronic bandstructures via Floquet Engineering is a promising means to control quantum systems on an ultrafast time scale. However, the ultrafast switching on/off of the driving field comes with questions regarding the limits of the Floquet formalism (which is defined for an infinite periodic drive) through the switching process and to what extent the transient changes can be driven adiabatically. Experimentally addressing these questions has been difficult, in large part due to the absence of an established technique to measure coherent dynamics through the duration of the pulse. Here, using multidimensional coherent spectroscopy we explicitly excite, control, and probe a coherent superposition of excitons in the K and K' valleys in monolayer WS2. With a circularly polarized, red-detuned pump pulse, the degeneracy of the K and K' excitons can be lifted, and the phase of the coherence rotated. We directly measure phase rotations greater than π during the 100 fs driving pulse and show that this can be described by a combination of the AC-Stark shift of excitons in one valley and the Bloch-Siegert shift of excitons in the opposite valley. Despite showing a smooth evolution of the phase that directly follows the intensity envelope of the nonresonant pump pulse, the process is not perfectly adiabatic. By measuring the magnitude of the macroscopic coherence as it evolves before, during, and after the nonresonant pump pulse we show that there is additional decoherence caused by power broadening in the presence of the nonresonant pump. This nonadiabaticity arises as a result of interactions with the otherwise adiabatic Floquet states and may be a problem for many applications, such as manipulating qubits in quantum information processing; however, these measurements also suggest ways such effects can be minimized or eliminated.
Keywords: AC-Stark effect; Floquet engineering; adiabatic control; coherent phase control; decoherence; monolayer WS2; multidimensional coherent spectroscopy.