Entanglement detection from conductance measurements in carbon nanotube Cooper pair splitters

TL;DR

This paper proposes a method to detect entanglement in Cooper pairs split in carbon nanotubes using conductance measurements influenced by spin-orbit interaction and magnetic field tuning, enabling Bell inequality tests without complex noise analysis.

Contribution

It introduces a practical entanglement detection scheme based on conductance measurements that does not require full spin-orbit knowledge or noise measurements, and is robust to imperfections.

Findings

Entanglement detection via Bell inequality violation is feasible with current technology.

Spin filtering axes can be tuned by magnetic fields to test entanglement.

The method is robust against disorder and imperfect splitting efficiency.

Abstract

Spin-orbit interaction provides a spin filtering effect in carbon nanotube based Cooper pair splitters that allows us to determine spin correlators directly from current measurements. The spin filtering axes are tunable by a global external magnetic field. By a bending of the nanotube the filtering axes on both sides of the Cooper pair splitter become sufficiently different that a test of entanglement of the injected Cooper pairs through the Bell inequality can be implemented. This implementation does not require noise measurements, supports imperfect splitting efficiency and disorder, and does not demand a full knowledge of the spin-orbit strength. Using a microscopic calculation we demonstrate that entanglement detection by violation of the Bell inequality is within the reach of current experimental setups.