Dynamics of entanglement creation between two spins coupled to a chain

TL;DR

This paper investigates how entanglement between two spins can be generated and evolves over time when they are coupled to a common thermal spin chain reservoir, considering different initial states and distances.

Contribution

It introduces a model of entanglement dynamics with a spin chain reservoir mapped to oscillators, analyzing the effects of initial states and spatial separation.

Findings

Entanglement can be generated via a common spin chain reservoir.

The dynamics depend on initial states and the distance between spins.

Entanglement evolution is characterized for transient times.

Abstract

We study the dynamics of entanglement between two spins which is created by the coupling to a common thermal reservoir. The reservoir is a spin-$\frac{1}{2}$ Ising transverse field chain thermally excited, the two defect spins couple to two spins of the chain which can be at a macroscopic distance. In the weak-coupling and low-temperature limit the spin chain is mapped onto a bath of linearly interacting oscillators using the Holstein-Primakoff transformation. We analyse the time evolution of the density matrix of the two defect spins for transient times and deduce the entanglement which is generated by the common reservoir. We discuss several scenarios for different initial states of the two spins and for varying distances.