Entanglement of Nambu Spinors and Bell Inequality Test Without Beam Splitters

TL;DR

This paper proposes a novel method to detect electronic entanglement in quantum Hall edge states using Nambu spinors, eliminating the need for beam splitters and enabling Bell inequality tests through charge-current measurements.

Contribution

It introduces a new approach to generate and detect electron-hole entanglement in solid-state systems without beam splitters, using Nambu spinors and charge noise measurements.

Findings

Bell inequality violation occurs in a large parameter region.

Charge-current measurement can reveal spinor correlations.

Method is compatible with existing experimental setups.

Abstract

The identification of electronic entanglement in solids remains elusive so far, which is owed to the difficulty of implementing spinor-selective beam splitters with tunable polarization direction. Here, we propose to overcome this obstacle by producing and detecting a particular type of entanglement encoded in the Nambu spinor or electron-hole components of quasiparticles excited in quantum Hall edge states. Due to the opposite charge of electrons and holes, the detection of the Nambu spinor translates into a charge-current measurement, which eliminates the need for beam splitters and assures a high detection rate. Conveniently, the spinor correlation function at fixed effective polarizations derives from a single current-noise measurement, with the polarization directions of the detector easily adjusted by coupling the edge states to a voltage gate and a superconductor, both having been realized in experiments. We show that the violation of Bell inequality occurs in a large parameter region. Our work opens a new route for probing quasiparticle entanglement in solid-state physics exempt from traditional beam splitters.