Optical signatures of energy-level statistics in a disordered quantum system

Time-resolved measurements of the resonant Rayleigh scattering from quantum well excitons are shown to provide information on the energy-level statistics of the localized exciton states. The signal transients are reproduced by a microscopic quantum model of the exciton two-dimensional motion in presence of spatially correlated disorder. This model allows quantitative determination of the average energy separation between the localized states. Here this quantity turns out to be only a few times smaller than the average disorder amplitude, proving that spatial correlation and quantum mechanics are equally important in the description of the exciton localization process.