Excitonic approach to the ultrafast optical response of semiconductor quantum wells

Abstract

We use a basis of bound and unbound excitons to study the coherent dynamics of optically excited excitons in a semiconductor quantum well. We derive a set of excitonic dynamic equations for quantum wells that includes the influence of phase-space filling and the exchange interaction. We calculate the nonlinear absorption for excitation by a short pulse resonant on the $1s$ exciton, and show that the $1s$ excitonic peak is reduced and blueshifted as the exciton density increases. By examining the dynamics of the populations in the different excitonic states, we show that at moderate densities $(n=1.3\ifmmode\times\else\texttimes\fi{}{10}^{10}\text{ }{\text{cm}}^{\ensuremath{-}2})$ the absorption near the $1s$ peak is well described using only the $1s$ excitonic state but that at higher densities $(n=5.0\ifmmode\times\else\texttimes\fi{}{10}^{10}\text{ }{\text{cm}}^{\ensuremath{-}2})$ the other excitons---both optically active and optically inactive---play a significant role. For moderate densities, we derive analytical expressions to describe the density-dependent blueshift and bleaching of the $1s$ excitonic resonance. Finally, we discuss the potential advantages of this formalism for the investigation of both interband and intraband dynamics in quantum wells.