Spectral properties and control of an exciton trapped in a multi-layered quantum dot

The spectral properties of one exciton trapped in a self-assembled multi-layered quantum dot is obtained using a high precision variational numerical method. The exciton Hamiltonian includes the effect of the polarization charges, induced by the presence of the exciton in the quantum dot, at the material interfaces. The method allows to implement rather easily the matching conditions at the interfaces of the hetero-structure. The numerical method also provides accurate approximate eigenfunctions that enable the study of the separability of the exciton eigenfunction in electron and hole states. The separability, or the entanglement content, of the total wave function allows a better understanding of the spectral properties of the exciton and, in particular, shed some light about when the perturbation theory calculation of the spectrum is fairly correct or not. Finally, using the approximate spectrum and eigenfunctions, the controlled time evolution of the exciton wave function is analyzed when an external driving field is applied to the system. It is found that it is possible to obtain pico and sub-picoseconds controlled oscillations between two particular states of the exciton with a rather low leakage of probability to other exciton states, and with a simple pulse shape.