The limiting nuclear polarization in a quantum dot under optical electron-spin orientation and applicability of the box-model of the electron-nuclear dynamics

TL;DR

This paper derives an exact expression for the maximum nuclear polarization in a quantum dot and demonstrates that the simplified box-model effectively describes electron-nuclear spin dynamics over hundreds of optical cycles.

Contribution

The authors provide an exact formula for nuclear polarization limits and justify the use of the box-model for short-term spin dynamics in quantum dots.

Findings

Limiting nuclear polarization grows slowly with more nuclear groups.

The box-model is valid for describing dynamics over hundreds of optical periods.

Refinement of the model shows minimal impact on polarization within certain timescales.

Abstract

For the model Hamiltonian describing the electron-nuclear dynamics of a quantum dot, we obtained an exact expression for the limiting nuclear polarization as a function of the number of groups of equivalent nuclei. It is shown that the refinement of the model Hamiltonian by increasing the number of the groups results in a slow growth of the limiting nuclear polarization. This allowed us to put forward arguments in favor of applicability of the box-model (with all the nuclei being equivalent) for description of the electron-nuclear spin dynamics within the time intervals of around hundreds of periods of the optical orientation.