Dynamics and decoherence in the central spin model using exact methods

TL;DR

This paper uses exact integrable methods to analyze the dynamics and decoherence of a central spin qubit interacting with a nuclear spin bath, revealing frequency contributions, decay times, and a new low-frequency scale.

Contribution

It introduces an exact analytical approach to study qubit decoherence in the central spin model, providing insights into frequency broadening and low-frequency dynamics.

Findings

Main frequency contributions can be predicted analytically.

Decoherence decay times are estimated from the frequency broadening.

A new low-frequency time scale appears for small bath polarization.

Abstract

The dynamics and decoherence of an electronic spin-1/2 qubit coupled to a bath of nuclear spins via hyperfine interactions in a quantum dot is studied. We show how exact results from the integrable solution can be used to understand the dynamic behavior of the qubit. It is possible to predict the main frequency contributions and their broadening for relatively general initial states analytically, leading to an estimate of the corresponding decay times. Furthermore, for a small bath polarization, a new low-frequency time scale is observed.