Spin- and entanglement-dynamics in the central spin model with homogeneous couplings

TL;DR

This paper provides an exact analysis of the time-dependent dynamics and entanglement of a central spin coupled homogeneously to a bath, revealing diverse behaviors based on initial bath states and implications for decoherence.

Contribution

It offers an exact solution for the central spin model with homogeneous couplings, exploring how initial bath states influence decoherence and entanglement dynamics.

Findings

Central spin polarization decays to zero for unpolarized unentangled baths in the thermodynamic limit.

Entanglement entropy reaches maximum when the bath is initially unpolarized and unentangled.

Persistent oscillations occur when the bath starts in an eigenstate of total spin.

Abstract

We calculate exactly the time-dependent reduced density matrix for the central spin in the central-spin model with homogeneous Heisenberg couplings. Therefrom, the dynamics and the entanglement entropy of the central spin are obtained. A rich variety of behaviors is found, depending on the initial state of the bath spins. For an initially unpolarized unentangled bath, the polarization of the central spin decays to zero in the thermodynamic limit, while its entanglement entropy becomes maximal. On the other hand, if the unpolarized environment is initially in an eigenstate of the total bath spin, the central spin and the entanglement entropy exhibit persistent monochromatic large-amplitude oscillations. This raises the question to what extent entanglement of the bath spins prevents decoherence of the central spin.