Spin noise and Bell inequalities in a realistic superconductor-quantum dot entangler

Abstract

Charge and spin current correlations are analyzed in a source of spin-entangled electrons built from a superconductor and two quantum dots in parallel. In addition to the ideal (crossed Andreev) channel, parasitic channels (direct Andreev and cotunneling) and spin flip processes are fully described in a density matrix framework. The way they reduce both the efficiency and the fidelity of the entangler is quantitatively described by analyzing the zero-frequency noise correlations of charge current as well as spin current in the two output branches. Spin current noise is characterized by a spin Fano factor, equal to 0 (total current noise) and -1 (crossed correlations) for an ideal entangler. The violation of the Bell inequalities, as a test of non-locality (entanglement) of split pairs, is formulated in terms of the correlations of electron charge and spin numbers counted in a specific time window $\tau$. The efficiency of the test is analyzed, comparing $\tau$ to the various time scales in the entangler operation.

8 pages, 5 figures, references added, to appear in Phys. Rev. B

References in corpus (17)

• Single-shot read-out of an individual electron spin in a quantum dot
• Evidence for crossed Andreev reflection in superconductor-ferromagnet hybrid structures
• Two-particle Aharonov-Bohm effect and Entanglement in the electronic Hanbury Brown Twiss setup
• Experimental observation of bias-dependent non-local Andreev reflection
• Orbital entanglement and violation of Bell inequalities in mesoscopic conductors
• Production and detection of entangled electron-hole pairs in a degenerate electron gas
• Spin current shot noise as a probe of interactions in mesoscopic systems
• Andreev scattering and cotunneling between two superconductor-normal metal interfaces : the dirty limit
• Quantum master equations for the superconductor--dot entangler
• Electrical current noise of a beam splitter as a test of spin-entanglement
• Lower bound for electron spin entanglement from beamsplitter current correlations
• Quantum teleportation by particle-hole annihilation in the Fermi sea
• Entanglement in a Noninteracting Mesoscopic Structure
• Full Counting Statistics with Spin-sensitive Detectors reveals Spin-singlets
• Clauser-Horne inequality for electron counting statistics in multiterminal mesoscopic conductors
• Coulomb scattering in a 2D interacting electron gas and production of EPR pairs
• Electron spin teleportation current through a quantum dot array operating in the stationary regime

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