Preparation of Non-equilibrium Nuclear Spin States in Double Quantum Dots

TL;DR

This paper provides a detailed theoretical analysis of nuclear spin polarization dynamics in double quantum dots, revealing stable and unstable states and aligning with experimental observations.

Contribution

It introduces a new numerical method for simulating semiclassical central-spin problems and extends understanding of nuclear spin state preparation in quantum dots.

Findings

Large difference in Overhauser fields can be stabilized.

Dark states form and are stable configurations.

Elimination of the difference field is unstable without noise.

Abstract

We theoretically study the dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. In our prior work [Phys. Rev. Lett. 104, 226807 (2010)] we identified three regimes of long-term dynamics, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. In particular, when the dots are different sizes we found that the Overhauser field becomes larger in the smaller dot. Here we present a detailed theoretical analysis of these problems including a model of the polarization dynamics and the development of a new numerical method to efficiently simulate semiclassical central-spin problems. When nuclear spin noise is included, the results agree with our prior work indicating that large difference fields and dark states are stable configurations, while the elimination of the difference field is unstable; however, in the absence of noise we find all three steady states are achieved depending on parameters. These results are in good agreement with dynamic nuclear polarization experiments in double quantum dots.