Berry phases of quantum trajectories of optically excited electron-hole pairs in semiconductors under strong terahertz fields

The quantum evolution of particles under strong fields can be essentially captured by a small number of quantum trajectories that satisfy the stationary phase condition of the Dirac-Feynmann path integral. The quantum trajectories are a key concept in understanding extreme nonlinear optical phenomena, such as high-order harmonic generation (HHG) and high-order terahertz sideband generation (HSG). In contrast to HHG in atoms and molecules, HSG in semiconductors can have interesting effects due to nontrivial 'vacuum' states of band materials. We find that, in a semiconductor with non-vanishing Berry curvature in its energy bands, the cyclic quantum trajectories of an electron-hole pair under a strong elliptically polarized terahertz field can accumulate a Berry phase. Taking monolayer MoS2 as a model system, we show that the Berry phase appears as a Faraday rotation angle in the pulse emission from the material under short-pulse excitation. This finding reveals an interesting transport effect in the extreme nonlinear optics regime.