Local and nonlocal entanglement for quasiparticle pairs induced by Andreev reflection

TL;DR

This paper theoretically analyzes how local and nonlocal entanglement of quasiparticle pairs, induced by Andreev reflections at superconductor-normal interfaces, can be quantified and detected through concurrence and Bell inequality violations.

Contribution

It introduces a method to quantify and detect local and nonlocal entanglement via concurrence and Bell inequality violations based on reflection eigenvalues.

Findings

Both local and nonlocal entanglement can be quantified by concurrence.

Entanglement can be detected from Bell inequality violations of spin current correlators.

A one-to-one correspondence exists between concurrence and Bell-CHSH parameter in the tunneling limit.

Abstract

We investigate local and nonlocal entanglement of particle pairs induced by direct and crossed Andreev reflections at the interfaces between a superconductor and two normal conductors. It is shown theoretically that both local and nonlocal entanglement can be quantified by concurrence and detected from the violation of a Bell inequality of spin current correlators, which are determined only by normal reflection and Andreev reflection eigenvalues. There exists a one-to-one correspondence between the concurrence and the maximal Bell-CHSH parameter in the tunneling limit.