In recent years the physics of two-dimensional semiconductors was revived by the discovery of the class of transition metal dichalcogenides. In these systems excitons dominate the optical response in the visible range and open many perspectives for nonlinear spectroscopy. To describe the coherence and polarization dynamics of excitons after ultrafast excitation in these systems, we employ the Bloch equation model of a two-level system extended by a local field describing the exciton-exciton interaction. We calculate four-wave mixing signals and analyze the dependence of the temporal and spectral signals as a function of the delay between the exciting pulses. Exact analytical results obtained for the case of ultrafast ($delta$-shaped) pulses are compared to numerical solutions obtained for finite pulse durations. If two pulses are used to generate the nonlinear signal, characteristic spectral line splittings are restricted to short delays. When considering a three-pulse excitation the line splittings, induced by the local field effect, persist for long delays. All of the found features are instructively explained within the Bloch vector picture and we show how the exciton occupation dynamics govern the different four-wave mixing signals.
Download