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

## TL;DR

This paper presents a theoretical model for the long-term dynamics of the Overhauser field in quantum dots, accounting for nuclear spin diffusion and related effects, explaining recent experimental observations.

## Contribution

It introduces a simplified diffusion equation model that incorporates Knight shift and electron-mediated flip-flops, advancing understanding of nuclear spin behavior in quantum dots.

## Key findings

- Quantitative explanation of Overhauser field decay times
- Impact of magnetic field and electron configuration on nuclear spin diffusion
- Correlation with recent experimental measurements

## Abstract

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.