Semiconductor Bloch equation analysis of optical Stark and Bloch-Siegert shifts in monolayerWSe(2) and MoS2

We report on the theoretical and experimental investigation of valley-selective optical Stark and Bloch-Siegert shifts of exciton resonances in monolayers WSe2 and MoS2 induced by strong circularly polarized nonresonant optical fields. We predict and observe transient shifts of both 1sA and 1sB exciton transitions in the linear interaction regime. The theoretical description is based on semiconductor Bloch equations. The solutions of the equations are obtained with a modified perturbation technique, which takes into account many-body Coulomb interaction effects. These solutions allow to explain the polarization dependence of the shifts and calculate their values analytically. We found experimentally the limits of the applicability of the theoretical description by observing the transient exciton spectra change at high field amplitudes of the driving wave.