Two-spin entanglement induced by electron scattering in nanostructures

TL;DR

This paper models how electron scattering in nanostructures can generate entanglement between two magnetic impurities, providing analytical solutions and exploring deterministic and probabilistic entanglement mechanisms.

Contribution

It introduces a weak coupling approximation for analytical solutions and compares these with exact numerical results in a two-impurity entanglement model.

Findings

Entanglement can be generated deterministically and probabilistically.

Analytical solutions match well with numerical results.

The model elucidates the role of scattering in impurity entanglement.

Abstract

We present a model where two magnetic impurities in a discrete tight-binding ring become entangled because of scattering processes associated to the injection of a conduction electron. We introduce a weak coupling approximation that allows us to solve the problem in a analytical way and compare the theory with the exact numerical results. We obtain the generation of entanglement both in a deterministic way and in a probabilistic one. The first case is intrinsically related to the structure of the two-impurity reduced density matrix, while the second one occurs when a projection on the electron state is performed.