We report the sub-picosecond initialization of a single heavy hole spin in a self-assembled quantum dot with >98.5 % fidelity and without external magnetic field. Using an optically adressable charge and spin storage device we tailor the relative electron and hole tunneling escape timescales from the dot and simultaneously achieve high-fidelity initialization, long hole storage times and high efficiency readout via a photocurrent signal. We measure electric field-dependent Rabi oscillations of the neutral and charged exciton transitions in the ultrafast tunneling regime and demonstrate that tunneling induced dephasing (TID) of excitonic Rabi rotations is the major source for the intensity damping of Rabi oscillations in the low Rabi frequency, low temperature regime. Our results are in very good quantitative agreement with quantum-optical simulations revealing that TID can be used to precisely measure tunneling escape times and extract changes in the Coulomb binding energies for different charge configurations of the quantum dot. Finally, we demonstrate that for sub-picosecond electron tunneling escape TID of a coherently driven exciton transition facilitates ultrafast hole spin initialization with near-unity fidelity.
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