Coupled electron-nuclear spin dynamics in quantum dots: A graded box model approach

The dynamics of electron and nuclear spin polarization in an ensemble of singly negatively charged quantum dots subject to optical excitation is theoretically studied using a graded box model, in which the electron density is approximated by a sequence of steps. The model is numerically implemented for a limited number of nuclei (up to N = 192) with spins I = 1/2 or I = 3/2. The polarization dynamics is found to depend strongly on the polarized excitation protocol. For excitation by periodic laser pulses, the electron-nuclear spin dynamics evolves coherently and gives rise to a recurrence effect in the electron spin dynamics as well as to a decelerated nuclear polarization. The validity of the model is justified by comparison with experimental data on the electron spin polarization in (In, Ga)As/GaAs quantum dots.