Dynamics of Overhauser Field under nuclear spin diffusion in a quantum dot

The coherence of electron spin can be significantly enhanced by locking the
Overhauser field from nuclear spins using the nuclear spin preparation. We
propose a theoretical model to calculate the long time dynamics of the
Overhauser field under intrinsic nuclear spin diffusion in a quantum dot. We
obtain a simplified diffusion equation that can be numerically solved and show
quantitatively how the Knight shift and the electron-mediated nuclear spin
flip-flop affect the nuclear spin diffusion. The results explain several recent
experimental observations, where the decay time of Overhauser field is measured
under different configurations, including variation of the external magnetic
field, the electron spin configuration in a double dot, and the initial nuclear
spin polarization rate.