It is demonstrated how the exciton and the biexciton state of a quantum dot can be prepared with high fidelity on a picosecond time-scale by driving the dot with a strong laser pulse that is tuned above the exciton resonance for exciton preparation and in resonance with the exciton transition for biexciton preparation. The proposed schemes make use of the phonon-induced relaxation towards photon dressed states in optically driven quantum dots and combine the simplicity of Rabi flopping with the robustness of adiabatic rapid passage schemes. Our protocols allow for an on-demand, fast and almost perfect state preparation even at strong carrier-phonon interaction where other schemes fail. In fact, the performance of the presented protocols is shown to be the better the stronger the carrier-phonon interaction is.
