Time-resolved Rayleigh scattering of excitons: Evidence for level repulsion in a disordered system

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Abstract
The theory of resonant Rayleigh scattering of light by excitons in a disordered quantum structure is presented. Disorder is modeled by a random Gauss distributed potential with finite correlation length in space. The time dependent scattered signal under pulsed excitation is studied by solving the Schrödinger equation for the exciton center-of-mass motion. The key quantity turns out to be the distribution of energy level distances weighted by the optical matrix elements. The limit of classical center-of-mass motion is derived analytically, while large-scale simulations are performed for the general case. The results show that the quantum-mechanical nature of the exciton motion is responsible for an oscillating behavior of the time dependent intensity. The oscillations originate from an interplay between the quantum-mechanical energy-level repulsion and the correlation induced by the finite correlation length of the disorder.