# Fourth-order spin correlation function in the extended central spin model

## TL;DR

This paper investigates the fourth-order spin correlation function in the extended central spin model using quantum and classical approaches, revealing how quadrupolar interactions influence long-time electron spin dynamics in quantum dots.

## Contribution

It introduces a quantum mechanical method to analyze the bispectrum of spin noise and compares it with classical simulations, highlighting the effects of quadrupolar interactions.

## Key findings

- Quantum and classical spectra converge for large bath sizes.
- Broadening of the bispectrum indicates quadrupolar interaction strength.
- Increasing magnetic field narrows the bispectrum, reducing quadrupolar effects.

## Abstract

Spin noise spectroscopy has developed into a very powerful tool to access the electron spin dynamics. While the spin-noise power spectrum in an ensemble of quantum dots in a magnetic field is essentially understood, we argue that the investigation of the higher order cumulants promises to provide additional information not accessible by the conventional power noise spectrum. We present a quantum mechanical approach to the correlation function of the spin-noise power operators at two different frequencies for small spin bath sizes and compare the results with a simulation obtained from the classical spin dynamics for large number of nuclear spins. This bispectrum is defined as a two-dimensional frequency cut in the parameter space of the fourth-order spin correlation function. It reveals information on the influence of the nuclear-electric quadrupolar interactions on the long-time electron spin dynamics dominated by a magnetic field. For large bath sizes and spin lengths the quantum mechanical spectra converge to those of the classical simulations. The broadening of the bispectrum across the diagonal in the frequency space is a direct measure of the quadrupolar interaction strength. A narrowing is found with increasing magnetic field indicating a suppression of the influence of quadrupolar interactions in favor of the nuclear Zeeman effect.