  In many electron spin qubit systems coherent control is impaired by the
fluctuating nuclear spin bath of the host material. Previous experiments have
shown dynamic nuclear polarization with feedback to significantly prolong the
inhomogeneous dephasing time $T_2^*$ by narrowing the distribution of nuclear
Overhauser field fluctuations. We present a model relating the achievable
narrowing of the Overhauser field to both the pump rate and the noise magnitude
and find reasonable agreement with experimental data. It shows that former
experiments on gated GaAs quantum dots were limited by the pump rate of the
pumping mechanism used. Here we propose an alternative feedback scheme using
electron dipole spin resonance. Sequentially applying two ac electric fields
with frequencies slightly detuned from the desired Larmor frequency results in
a pump curve with a stable fixed point. Our model predicts that $T_2^*$ values
on the order of microseconds can be achieved.
