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.
We report the observation of double-quantum coherence signals in a gas of potassium atoms at twice the frequency of the one-quantum coherences. Since a single atom does not have a state at the corresponding energy, this observation must be attributed
to a collective resonance involving multiple atoms. These resonances are induced by weak inter-atomic dipole-dipole interactions, which means that the atoms cannot be treated in isolation, even at a low density of $10^{12}$ cm$^{-3}$.
We present experimental coherent two-dimensional Fourier transform spectra of the exciton resonances in semiconductor quantum wells for a pulse sequence that isolates two-quantum coherences. By measuring the real part of the spectra, we can determine
that the spectra are dominated by two quantum coherences due to many-body interactions, not bound biexcitons. Simulations performed using dynamics controlled truncation agree well with the experiments.
