Book excerpt: Research on this program has focused on the study and application of the nonlinear response of GaAs and GaAs heterostructures. The work has resulted in the demonstration that the primary nonlinear optical response in GaAs is in fact not due to static interactions in the Hamiltonian (e.g., Coulomb, exchange, etc.), but rather due to strong dynamic exciton-exciton interactions, similar to resonance collisional broadening in dense gases. This so called excitation induced dephasing contribution has been shown to be a primary contributor to the observed polarization dependences of the nonlinear response which were not accounted for by the earlier theory. Other work on this project has focused on the detection and characterization of quantum coherences, notably the two photon induced coherence associated with the biexciton and the Raman coherence associated with the heavy hole light hole interaction. Measurements have shown the ultrafast two photon oscillation of the two photon coherence and the unexpectedly fast relaxation of the Raman coherence. The measurements provide insight into the nature of relaxation. Related w9rk has shown new behavior regarding exciton transport including magnetic field induced freezeout and, in high quality material, ballistic transport. Quantum wells, excitons, nonlinear spectroscopy.