  We performed ultrafast degenerate pump-probe spectroscopy on monolayer WSe2
near its exciton resonance. The observed differential reflectance signals
exhibit signatures of strong many-body interactions including the
exciton-exciton interaction and free carrier induced band gap renormalization.
The exciton-exciton interaction results in a resonance blue shift which lasts
for the exciton lifetime (several ps), while the band gap renormalization
manifests as a resonance red shift with several tens ps lifetime. Our model
based on the many-body interactions for the nonlinear optical susceptibility
fits well the experimental observations. The power dependence of the spectra
shows that with the increase of pump power, the exciton population increases
linearly and then saturates, while the free carrier density increases
superlinearly, implying that exciton Auger recombination could be the origin of
these free carriers. Our model demonstrates a simple but efficient method for
quantitatively analyzing the spectra, and indicates the important role of
Coulomb interactions in nonlinear optical responses of such 2D materials.
