Quantum Description of Nuclear Spin Cooling in a Quantum Dot

TL;DR

This paper presents a theoretical model for nuclear spin cooling in quantum dots, demonstrating that polarization levels above 90% are achievable rapidly by overcoming dark state limitations through inhomogeneous Knight fields and wave function shifts.

Contribution

It introduces a master equation approach that accounts for nuclear spin coherences and dark states, showing how to surpass dark state limitations in nuclear spin cooling.

Findings

Polarizations over 90% achievable within milliseconds.

Inhomogeneous Knight fields mitigate dark state effects.

Small shifts in electron wave function enable enhanced cooling.

Abstract

We study theoretically the cooling of an ensemble of nuclear spins coupled to the spin of a localized electron in a quantum dot. We obtain a master equation for the state of the nuclear spins interacting with a sequence of polarized electrons that allows us to study quantitatively the cooling process including the effect of nuclear spin coherences, which can lead to ``dark states'' of the nuclear system in which further cooling is inhibited. We show that the inhomogeneous Knight field mitigates this effect strongly and that the remaining dark state limitations can be overcome by very few shifts of the electron wave function, allowing for cooling far beyond the dark state limit. Numerical integration of the master equation indicates, that polarizations larger than 90% can be achieved within a millisecond timescale.