Feedback control of nuclear spin bath of a single hole spin in a quantum dot

For a III-V semiconductor quantum dot charged with a single hole, we investigate the feedback control of the nuclear spin bath through dynamical nuclear spin polarization. The scheme utilizes the hole-nuclear flip-flop by their anisotropic hyperfine interaction, where the flip direction of the nuclear spin can be conditioned on the sign of the overall hyperfine field through initialization processes that do not involve explicit measurement. We show that a negative feedback can be implemented to suppress the statistical fluctuations of the nuclear hyperfine field for enhancing the coherence time of the hole spin qubit. Positive feedback can prepare the nuclear spin ensemble into states where the nuclear hyperfine field distribution has two well separated peaks, realizing a quantum heat bath that cannot be described by a single effective temperature.