Monitoring the buildup of the quantum dot polaron: Pump-probe and four-wave mixing spectra from excitons and biexcitons in semiconductor quantum dots

Abstract

Pump-probe (PP) and four-wave mixing (FWM) signals from a single quantum dot are presented which are based on a four-level quantum dot model, accounting for the fine structure splitting as well as for the biexciton binding and phonon-induced pure dephasing. We have derived closed form analytical expressions for the PP and FWM polarization components in the time domain after excitation with a pair of ultrafast laser pulses. The solutions are exact within this model. We discuss the dependence of the signals on the polarization of the exciting pulses. We show that for PP spectra after excitation with collinearly polarized pulses and for FWM spectra after cocircular excitation changes in the line shape are entirely due to the polaron formation leading to a fixed shape when this process is completed. For PP spectra after cocircular excitation and FWM spectra after collinear excitation in general periodic modulations of the shape are superimposed which persist even on long time scales and reflect quantum beats due to the fine structure splitting or the biexciton binding energy.