Persisting correlations of a central spin coupled to large spin baths

TL;DR

This paper rigorously analyzes the central spin model, demonstrating conditions under which the central spin's magnetization persists despite coupling to a large spin bath, highlighting the impact of weakly coupled spins.

Contribution

It provides mathematically rigorous bounds for the persistent magnetization of a central spin in large spin baths, including the limit of infinite bath size and the effect of weakly coupled spins.

Findings

Magnetization persists in the large bath limit under certain conditions.

Only when nearly all bath spins are weakly coupled does magnetization vanish.

The results apply with and without an external magnetic field.

Abstract

The decohering environment of a quantum bit is often described by the coupling to a large bath of spins. The quantum bit itself can be seen as a spin $S=1/2$ which is commonly called the central spin. The resulting central spin model describes an important mechanism of decoherence. We provide mathematically rigorous bounds for a persisting magnetization of the central spin in this model with and without magnetic field. In particular, we show that there is a well defined limit of infinite number of bath spins. Only if the fraction of very weakly coupled bath spins tends to 100\% does no magnetization persist.