Shot noise for entangled and spin-polarized electrons

TL;DR

This paper reviews recent research on shot noise in entangled and spin-polarized electrons within mesoscopic systems, highlighting novel setups, calculations, and the effects of Rashba spin-orbit interaction on noise behaviors.

Contribution

It introduces new proposals for electron entanglers, analyzes shot noise in various geometries, and explores the impact of Rashba spin-orbit interaction on noise characteristics.

Findings

Entangled electron pairs show continuous bunching and antibunching depending on Rashba angle.

Shot noise exhibits oscillations as a function of Rashba phase for spin-polarized currents.

Unentangled triplets and entangled pairs have distinguishable shot noise signatures.

Abstract

We review our recent contributions on shot noise for entangled electrons and spin-polarized currents in novel mesoscopic geometries. We first discuss some of our recent proposals for electron entanglers involving a superconductor coupled to a double dot in the Coulomb blockade regime, a superconductor tunnel-coupled to Luttinger-liquid leads, and a triple-dot setup coupled to Fermi leads. We calculate current and shot noise for spin-polarized currents and entangled/unentangled electron pairs in a beam-splitter geometry with a \textit{local} Rashba spin-orbit (s-o) interaction in the incoming leads. We find \textit{continuous} bunching and antibunching behaviors for the \textit{entangled} pairs -- triplet and singlet -- as a function of the Rashba rotation angle. In addition, we find that unentangled triplets and the entangled one exhibit distinct shot noise. Shot noise for spin-polarized currents shows sizable oscillations as a function of the Rashba phase. This happens only for electrons injected perpendicular to the Rashba rotation axis; spin-polarized carriers along the Rashba axis are noiseless. We find an additional spin rotation for electrons with energies near the crossing of the bands where s-o induced interband coupling is relevant. This gives rise to an additional modulation of the noise for both electron pairs and spin-polarized currents. Finally, we briefly discuss shot noise for a double dot near the Kondo regime.