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The spectral properties of one exciton trapped in a self-assembledmulti-layered quantum dot is obtained using a high precision variationalnumerical method. The exciton Hamiltonian includes the effect of thepolarization charges, induced by the presence of the exciton in the quantumdot, at the material interfaces. The method allows to implement rather easilythe matching conditions at the interfaces of the hetero-structure. Thenumerical method also provides accurate approximate eigenfunctions that enablethe study of the separability of the exciton eigenfunction in electron and holestates. The separability, or the entanglement content, of the total wavefunction allows a better understanding of the spectral properties of theexciton and, in particular, shed some light about when the perturbation theorycalculation of the spectrum is fairly correct or not. Finally, using theapproximate spectrum and eigenfunctions, the controlled time evolution of theexciton wave function is analyzed when an external driving field is applied tothe system. It is found that it is possible to obtain pico and sub-picosecondscontrolled oscillations between two particular states of the exciton with arather low leakage of probability to other exciton states, and with a simplepulse shape.

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