Nuclear Spin Noise in the Central Spin Model

TL;DR

This paper provides an analytical study of nuclear spin noise in quantum dots using the central spin model, revealing a two-peak spectrum structure influenced by hyperfine interactions and magnetic fields.

Contribution

It introduces an analytical solution within the box model approximation for nuclear spin noise, validated by numerical simulations, and characterizes the spectral features under high magnetic fields.

Findings

Nuclear spin noise spectra exhibit a two-peak structure at high magnetic fields.

The shape of the spectrum is governed by the distribution of hyperfine constants.

Analytical results agree well with numerical simulations.

Abstract

We study theoretically the spin fluctuations of nuclei in quantum dots. We employ the central spin model which accounts for the hyperfine interaction of the nuclei with the electron spin. We present an analytical solution in the frame of the box model approximation where all hyperfine coupling constants are assumed to be equal. These results are in good agreement with numerical simulations. We demonstrate that in rather high magnetic field the nuclear spin noise spectra has a two-peak structure centered at the nuclear Zeeman frequency with the shape of the spectrum controlled by the distribution of the hyperfine constants.