  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.
