Effects of Floquet Engineering on the Coherent Exciton Dynamics in Monolayer WS₂

Coherent optical manipulation of electronic bandstructuresviaFloquet Engineering is a promising means to control quantum systemson an ultrafast time scale. However, the ultrafast switching on/offof the driving field comes with questions regarding the limits ofthe Floquet formalism (which is defined for an infinite periodic drive)through the switching process and to what extent the transient changescan be driven adiabatically. Experimentally addressing these questionshas been difficult, in large part due to the absence of an establishedtechnique to measure coherent dynamics through the duration of thepulse. Here, using multidimensional coherent spectroscopy we explicitlyexcite, control, and probe a coherent superposition of excitons inthe K and K & PRIME; valleys in monolayerWS(2). With a circularly polarized, red-detuned pump pulse,the degeneracy of the K and K & PRIME;excitons can be lifted, and the phase of the coherence rotated. Wedirectly measure phase rotations greater than & pi; during the 100fs driving pulse and show that this can be described by a combinationof the AC-Stark shift of excitons in one valley and the Bloch-Siegertshift of excitons in the opposite valley. Despite showing a smoothevolution of the phase that directly follows the intensity envelopeof the nonresonant pump pulse, the process is not perfectly adiabatic.By measuring the magnitude of the macroscopic coherence as it evolvesbefore, during, and after the nonresonant pump pulse we show thatthere is additional decoherence caused by power broadening in thepresence of the nonresonant pump. This nonadiabaticity arises as aresult of interactions with the otherwise adiabatic Floquet statesand may be a problem for many applications, such as manipulating qubitsin quantum information processing; however, these measurements alsosuggest ways such effects can be minimized or eliminated.