# Spectrum of the Nuclear Environment for GaAs Spin Qubits

## TL;DR

This study characterizes the spectral properties of the nuclear spin environment in GaAs spin qubits over a wide frequency range, revealing a classical diffusion model and the effects of magnetic field and dynamical decoupling.

## Contribution

It provides a detailed spectral analysis of Overhauser noise in GaAs qubits across six orders of magnitude in frequency, incorporating magnetic field effects and dynamical decoupling regimes.

## Key findings

- Overhauser noise spectrum matches a classical diffusion model from 1 mHz to 1 kHz.
- Increasing magnetic field suppresses spin diffusion and reduces spectral content.
- Dynamical decoupling reveals a crossover from transverse to longitudinal Overhauser fluctuations.

## Abstract

Using a singlet-triplet spin qubit as a sensitive spectrometer of the GaAs nuclear spin bath, we demonstrate that the spectrum of Overhauser noise agrees with a classical spin diffusion model over six orders of magnitude in frequency, from 1 mHz to 1 kHz, is flat below 10 mHz, and falls as $1/f^2$ for frequency $f \! \gtrsim \! 1$ Hz. Increasing the applied magnetic field from 0.1 T to 0.75 T suppresses electron-mediated spin diffusion, which decreases spectral content in the $1/f^2$ region and lowers the saturation frequency, each by an order of magnitude, consistent with a numerical model. Spectral content at megahertz frequencies is accessed using dynamical decoupling, which shows a crossover from the few-pulse regime ($\lesssim \! 16$ $\pi$-pulses), where transverse Overhauser fluctuations dominate dephasing, to the many-pulse regime ($\gtrsim \! 32$ $\pi$-pulses), where longitudinal Overhauser fluctuations with a $1/f$ spectrum dominate.