Non-Markovian dynamics of a localized electron spin due to the hyperfine interaction

TL;DR

This paper reviews a theoretical study on the complex non-Markovian dynamics of a localized electron spin interacting with nuclear spins, highlighting a critical crossover in long-term behavior and proposing a measurement scheme.

Contribution

It provides a perturbative analysis valid for various nuclear polarizations and spins, revealing rich dynamical regimes and a critical crossover in spin behavior.

Findings

Electron spin exhibits exponential, non-exponential decay, and oscillations.

A critical crossover in long-time dynamics depends on wave function shape and dimensionality.

Proposes a spin-echo technique to measure the predicted dynamics.

Abstract

We review our theoretical work on the dynamics of a localized electron spin interacting with an environment of nuclear spins. Our perturbative calculation is valid for arbitrary polarization p of the nuclear spin system and arbitrary nuclear spin I in a sufficiently large magnetic field. In general, the electron spin shows rich dynamics, described by a sum of contributions with exponential decay, non-exponential decay, and undamped oscillations. We have found an abrupt crossover in the long-time spin dynamics at a critical shape and dimensionality of the electron envelope wave function. We conclude with a discussion of our proposed scheme to measure the relevant dynamics using a standard spin-echo technique.