  We analyze the polarization of nuclear spins in a quantum dot induced by a
single-electron spin that is electrically driven to perform coherent Rabi
oscillations. We derive the associated nuclear-spin polarization rate and
analyze its dependence on the accessible control parameters, especially the
detuning of the driving frequency from the electron Larmor frequency. The
arising nuclear-spin polarization is related to the Hartmann-Hahn effect known
from the NMR literature with two important differences. First, in quantum dots
one typically uses a micro magnet, leading to a small deflection of the
quantization axes of the electron and nuclear spins. Second, the electric
driving wiggles the electron with respect to the atomic lattice. The two
effects, absent in the traditional Hartmann-Hahn scenario, give rise to two
mechanisms of nuclear-spin polarization in gated quantum dots. The arising
nuclear-spin polarization is a resonance phenomenon, achieving maximal
efficiency at the resonance of the electron Rabi and nuclear Larmor frequency
(typically a few or a few tens of MHz). As a function of the driving frequency,
the polarization rate can develop sharp peaks and reach large values at them.
Since the nuclear polarization is experimentally detected as changes of the
electron Larmor frequency, we often convert the former to the latter in our
formulas and figures. In these units, the polarization can reach hundreds of
MHz/s in GaAs quantum dots and at least tens of kHz/s in Si quantum dots. We
analyze possibilities to exploit the resonant polarization effects for
achieving large nuclear polarization and for stabilizing the Overhauser field
through feedback.
