Quantum versus classical hyperfine-induced dynamics in a quantum dot

TL;DR

This paper compares quantum and classical models of electron spin dynamics in quantum dots influenced by hyperfine interactions, highlighting their agreement at zero magnetic field and divergence over time at finite fields.

Contribution

It provides a detailed comparison between mean-field and exact quantum evolution of electron spins in quantum dots under hyperfine interactions, especially in the case of uniform coupling.

Findings

Quantum and classical dynamics agree at zero magnetic field.

Differences emerge at finite magnetic fields after a critical time.

Quantum evolution diverges from mean-field predictions over time.

Abstract

In this article we analyze spin dynamics for electrons confined to semiconductor quantum dots due to the contact hyperfine interaction. We compare mean-field (classical) evolution of an electron spin in the presence of a nuclear field with the exact quantum evolution for the special case of uniform hyperfine coupling constants. We find that (in this special case) the zero-magnetic-field dynamics due to the mean-field approximation and quantum evolution are similar. However, in a finite magnetic field, the quantum and classical solutions agree only up to a certain time scale t<\tau_c, after which they differ markedly.