Dynamics of the Overhauser field under nuclear spin diffusion in a quantum dot

The coherence of electron spins can be enhanced significantly by preparing the nuclear spin polarizations to generate an Overh auser field with small fluctuations. We propose a theoretical model for calculating the long time dynamics of the prepared Overhauser field under nuclear spin diffusion in a quantum dot.We obtained a simplified diffusion equation that can be numerically s o lved, and we show quantitatively how the Knight shift and the electronmediated nuclear spin flip-flops affect the nuclear spin diffusion. The results explain several recent experimental observations, where the measured decay time of the Overhauser field i s dependent on the external magnetic field, electron spin state in double quantum dots and initial nuclear spin polarization rate.