  We study the coherent light-matter interactions of GaAs quantum wells
associated with excitons, biexcitons and many-body effects. For most
polarization configurations, excitonic features dominate the phase-resolved
two-dimensional Fourier-transform (2DFT) spectra and have dispersive
lineshapes, indicating the presence of many-body interactions. For cross-linear
excitation, excitonic features become weak and absorptive due to the strong
suppression of many-body effects; a result that can not be directly determined
in transient four-wave mixing experiments. The biexcitonic features do not
weaken for cross-polarized excitation and thus are more important.
