The interplay between disorder and Coulomb interactions ubiquitously affects the properties of condensed matter
systems. We examine its role in the nonlinear optical response of semiconductor quantum wells. In particular, we
investigate the coherent coupling strength between exciton resonances that are spectrally split by interface fluctuations.
Previous studies yielded conflicting results. In light of rising interest in semiconductor devices that rely on spatial and/or
temporal coherence, we revisit this problem by applying a newly developed spectroscopy method: electronic two-dimensional
Fourier transform spectroscopy (2DFTS). 2DFTS is a powerful technique for revealing the presence of
coupling and for distinguishing the (coherent or incoherent) nature of such coupling, especially in complex systems with
several spectrally overlapping resonances. Even the most basic information about such complex systems, including the
homogeneous and inhomogeneous linewidths of various resonances, cannot be extracted reliably using conventional
spectroscopic tools. In these new 2DFTS measurements, we did not observe any clear cross peaks corresponding to
coherent couplings between either heavy-hole or light-hole excitons. These measurements allow us to place a
quantitative upper bound on the possible coupling strength in this prototypical system. A modified mean-field theory
reveals a simple yet important relation that determines how the coherent coupling strength depends on the disorder
correlation length and Coulomb interaction length.