Shot noise for entangled and spin-polarized electrons

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 briefly survey some of the available possibilities for spin-polarized sources. We use the scattering approach to calculate current and shot noise for spin-polarized currents and entangled/unentangled electron pairs in a novel beam-splitter geometry with a local Rashba spin-orbit (s-o) interaction in the incoming leads. For single-moded incoming leads, we find continuous bunching and antibunching behaviors for the 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; this should allow their identification via noise measurements. 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. The Rashba coupling constant alpha is directly related to the Fano factor and could be extracted via noise measurements. For incoming leads with s-o induced interband-coupled channels, we find an additional spin rotation for electrons with energies near the crossing of the bands where 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.