Bell inequalities and entanglement in solid-state devices

Chtchelkatchev, N. M.; Blatter, G.; Lesovik, G. B.; Martin, Thierry

doi:10.1103/physrevb.66.161320

Cited by 237 publications

(241 citation statements)

References 44 publications

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“…3a for temperature T = 10 −2 Δ andhω 0 = 0.4Δ. The behaviour for the different wavectors is qualitatively similar: for eV <hω 1 ,hω 2 the EC processes dominate, whereas CAR becomes more important in the voltage windowhω 1 < eV <hω 2 and finally both contributions cancel for eV >hω 2 .…”

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confidence: 51%

Entangled Andreev pairs and collective excitations in nanoscale superconductors

et al. 2007

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Nanoscale superconductors connected to normal metallic electrodes provide a potential source of entangled electron pairs 1-5 . Such states would arise from the splitting of Cooper pairs in the superconductor into two electrons with opposite spins, which then tunnel into different leads by means of a process known as crossed Andreev reflection (refs 6-8). In an actual system, the detection of these processes is hindered by the elastic transmission of individual electrons between the leads, which yields an opposite contribution to the non-local conductance. Here we demonstrate that low-energy collective excitations, which appear in superconducting structures of reduced dimensionality 9 , can have a significant influence on the transport properties of this type of hybrid nanostructure. When an electron tunnels into the superconductor it can excite such low-energy excitations that alter the balance between the different electronic processes, leading to a dominance of one over the other depending on the spatial symmetry of these excitations. These findings help to clarify some intriguing experimental results and provide future strategies for the detection of entangled electron pairs in solid-state devices for quantum computation.A generic set-up for the study of non-local transport through a superconductor is shown in Fig. 1a. It represents a superconducting region attached to three normal electrodes. Two of the leads (labelled 1 and 2 in Fig. 1a) are used to inject a current while the voltage drop is measured on the third one. The two basic microscopic processes contributing to the non-local conductance are illustrated in Fig. 1c,d. In the case of elastic cotunnelling (EC) processes, the injected electron tunnels elastically into the third lead, whereas in the case of crossed Andreev reflection (CAR) processes, it combines with an electron emerging from the third lead to form a Cooper pair in the superconductors. The probability of these processes decays exponentially on the scale of the superconducting coherence length, ξ, which can range between 10 and 100 nm for typical superconductors used in experiments 10,11 . On the other hand, the two processes yield opposite contributions to the non-local conductance (conventionally the CAR contribution is taken as positive) and, as demonstrated by previous theoretical studies 12-14 , tend to cancel each other in the case of Bardeen-Cooper-Schrieffer (BCS) superconductors weakly coupled to non-magnetic leads. Surprisingly, recent experiments by Russo et al. 11 have shown that even in this case the subgap non-local conductance can be appreciably large, exhibiting an intriguing behaviour in which either process can dominate depending on the energy of the injected electrons. This behaviour cannot be accounted for by the existing non-interacting theories.The importance of interactions in breaking the balance between EC and CAR processes can be understood by considering the case where the superconducting region is sufficiently small and can be characterized by a finite charging ...

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confidence: 51%

Entangled Andreev pairs and collective excitations in nanoscale superconductors

et al. 2007

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“…[2][3][4][5][6] Presently, the realization of the charge or spin entanglement of two electrons remains a major challenge in the solid state physics, even though the polarization entanglement of photons has been implemented in experiment. 7 A superconductor (S) may be a natural source of Einstein Podolasky Rosen pairs of electrons, as a Cooper pair consists of two electrons that are both spin-and momentumentangled.…”

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confidence: 99%

Crossed Andreev reflection in a zigzag graphene nanoribbon-superconductor junction

Wang

Liu

2012

Phys. Rev. B

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We investigate the crossed Andreev reflection (CAR) in a zigzag graphene nanoribbon/superconductor/nanoribbon junction. It is shown that when the zigzag chain number of the ribbon is even and only the zero-energy mode is involved in transport, either the elastic cotunneling or the local Andreev reflection could be entirely suppressed by using a gate voltage whereas a sizeable CAR is achieved. When one of the ribbon leads is magnetized, not only the CAR is exclusive but also the spin state of the CAR transmission is nonlocally controllable. The physical origin is the peculiar valley selection rule in the even zigzag graphene nanoribbon. The ideal Cooper-pair splitting in the proposed device holds for all applied bias in the superconducting energy gap.

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“…For symmetric voltages smaller than |∆ (k)| and at the tunneling limit, due to the cancellation of the EC and the negligible contributions from AR and Q, CAR become the dominant processes giving dS dV e T h ab / (4 / ) 3 as a result an efficiency equal to one. For higher voltages, Q and AR contributions increase causing a decrease in the efficiency and the Fano factor (Fig.…”

Section: S-wave Superconductorsmentioning

confidence: 99%

“…The use of a superconductor to produce entangled electrons has been proposed [2][3][4][5][6][7][8] because its ground state is composed of Cooper pairs. A Cooper pair in the superconductor can be break up into two nonlocal entangled electrons that enter into different normal metal leads via the Cooper pair splitting (CPS) [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Noise cross-correlation and Cooper pair splitting efficiency in multi-teminal superconductor junctions

Gil

Herrera

2017

Solid State Communications

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We analyze the non-local shot noise in a multi-terminal junction formed by two Normal metal leads connected to one superconductor. Using the cross Fano factor and the shot noise, we calculate the efficiency of the Cooper pair splitting. The method is applied to d-wave and iron based superconductors. We determine that the contributions to the noise cross-correlation are due to crossed Andreev reflections (CAR), elastic cotunneling, quasiparticles transmission and local Andreev reflections. In the tunneling limit, the CAR contribute positively to the noise cross-correlation whereas the other processes contribute negatively. Depending on the pair potential symmetry, the CAR are the dominant processes, giving as a result a high efficiency for Cooper pair split. We propose the use of the Fano factor to test the efficiency of a Cooper pair splitter device.

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Bell inequalities and entanglement in solid-state devices

Cited by 237 publications

References 44 publications

Entangled Andreev pairs and collective excitations in nanoscale superconductors

Entangled Andreev pairs and collective excitations in nanoscale superconductors

Crossed Andreev reflection in a zigzag graphene nanoribbon-superconductor junction

Noise cross-correlation and Cooper pair splitting efficiency in multi-teminal superconductor junctions

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