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

Influence of local fields on the dynamics of four-wave mixing signals from 2D semiconductor systems