We present a collection of zero-, one- and two-quantum two-dimensional coherent spectra of excitons and trions in a CdTe/(Cd,Mg)Te quantum well. The set of spectra provides a unique and comprehensive picture of the exciton and trion nonlinear optical
response. Exciton-exciton and exciton-trion coherent coupling is manifest as distinct peaks in the spectra, whereas signatures of trion-trion interactions are absent. Excellent agreement using density matrix calculations is obtained, which highlights the essential role of many-body effects on coherent interactions in the quantum well.
