Memory and correlation effects in the exciton-phonon kinetics

The interaction between excitonic and phonon modes in semiconductor nanostructures leads to both relaxation of the excitonic population as well as to pure dephasing of the optical polarization. In small quantum dots, where the interstate relaxation is tiny, clear signatures of pure dephasing effects have been measured, see e.g. the extensive work done in [1] and [2]. In this case, an accurate theoretical modeling is possible in the framework of an extended version of the Independent Boson Model [3]. In quantum wells (QW), disorder-localized exciton states have significant spatial overlap and can be spectrally rather close, thus a combination of population relaxation and pure dephasing is expected. However, as a consequence of the so-called Markov approximation, the absorption spectrum of a QW results to be a superposition of Lorentzian peaks, thus accounting for population relaxation only. We improve on this situation by going beyond the Markov approximation in the solution of a 2nd Born density-matrix theory for excitons and acoustic phonons in disordered QW. We start here with the same model which was used in [4]: center-of-mass (COM) excitons are created in disorder eigenstates |α〉 of the QW by B α and are coupled to longitudinal acoustic phonons (a † q creates a bulk like phonon state |q〉) via deformation potential interaction: