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arXiv:0906.4042 · Physical Review B

Quantum coherence of electrons field-emitted from a superconductor: Correlations and entanglement

Kazuya Yuasa

Published Sep 29, 2009• 4 citations
arXivHTMLPDF

Abstract

The correlations of the electrons field-emitted from a superconductor are fully analyzed, both in space and time. It is proposed that a coincidence experiment would reveal a positive correlation between the electrons emitted in opposite directions. The electrons can be entangled and can even violate Bell's inequality. The crucial role played by Andreev's process is scrutinized, analytical formulas are derived for the correlations, and the physics behind the phenomenon is clarified.

DOI
10.1103/physrevb.80.104516

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The correlations of the electrons field-emitted from a superconductor are fully analyzed, both in space and time. It is proposed that a coincidence experiment would reveal a positive correlation between the electrons emitted in opposite directions. The electrons can be entangled and can even violate Bell's inequality. The crucial role played by Andreev's process is scrutinized, analytical formulas are derived for the correlations, and the physics behind the phenomenon is clarified.
Bell-inequality checks constitute a probe of entanglement---given a source of entangled particles, their violation is a signature of the nonlocal nature of quantum mechanics. Here, we study a solid-state device producing pairs of entangled electrons, a superconductor emitting Cooper pairs properly split into the two arms of a normal-metallic fork with the help of appropriate filters. We formulate Bell-type inequalities in terms of current-current cross correlators, the natural quantities measured in mesoscopic physics; their violation provides evidence that this device indeed is a source of entangled electrons.
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 τ\tauτ. The efficiency of the test is analyzed, comparing τ\tauτ to the various time scales in the entangler operation.
Abstract Correlations are fundamental in describing many body systems - not only in natural sciences. However, in experiments, correlations are notoriously difficult to assess on the microscopic scale, especially for electron spins. Here, we demonstrate a direct measurement of the spin cross-correlations between the currents of a Cooper pair splitter, an electronic device that emits electrons originating from Cooper pairs in a superconductor. While it is firmly established theoretically that these electron pairs form maximally spin-entangled singlet states with opposite spin projections, no spin correlation experiments have been demonstrated so far. We use ferromagnetic sidegates, compatible with superconducting electronic structures, to individually spin polarize the transmissions of two quantum dots fabricated in the two electronic paths, which act as tunable spin filters. The signals are detected in standard transport and in highly sensitive transconductance experiments. We find that the spin-cross correlation is negative, compatible with spin singlet emission, and deviates from the ideal value mostly due to a finite overlap of the Zeeman split quantum dot states. Our results demonstrate a new route to perform spin auto- and cross correlation experiments in nanometer scaled electronic devices, especially suitable for those relying on magnetic field sensitive superconducting elements, like unconventional, triplet or topologically non-trivial superconductors, or to perform Bell tests with massive particles, like electrons.
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 $\ensuremath{-}1$ (crossed correlations) for an ideal entangler. The violation of the Bell inequalities, as a test of nonlocality (entanglement) of split pairs, is formulated in terms of the correlations of electron charge and spin numbers counted in a specific time window $\ensuremath{\tau}$. The efficiency of the test is analyzed, comparing $\ensuremath{\tau}$ to the various time scales in the entangler operation.
In recent decades it was established that the measurements of physical quantities in space-time points divided by large space-like intervals can be correlated.The correlation is created by the measurements while their mutual influence requires the corresponding supraliminal velocities.This situation is commonly known as the violation of the Bell inequality in the Bohm version of Einstein-Podolsky-Rosen paradox.Nearly 40 years the question remains disputable with a variety of contradicting views.The most frequently the violation is explained by the existence of some momentary action at a distance which obliges the quantum mechanics (as well as all nature) to be nonlocal.We find the "common cause in the past" as the origin of the observed quantum correlation which so far was unnoticed either by the partisans of quantum non-locality or their opponents.The novelty of our approach is the accent on the expressions for the observed physical quantities rather than on the "entangled" two-particle wave functions.We show the crucial role of phases in the correlation process that is hard to notice using the traditional approach.