Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0612197 · Europhysics Letters (EPL)

Elementary charge transfer processes in a superconductor-ferromagnet entangler

Jan Petter Morten, Daniel Huertas‐Hernando, Wolfgang Belzig, Arne Brataas

Published Jan 15, 2008• 19 citations
arXivHTMLPDF

Abstract

We study the production of spatially separated entangled electrons in ferromagnetic leads from Cooper pairs in a superconducting lead. We give a complete description of the elementary charge transfer processes, i) transfer of Cooper pairs out of the superconductor by Andreev reflection and ii) distribution of the entangled quasiparticles among the ferromagnetic leads, in terms of their statistics. The probabilities that entangled electrons flow into spatially separated leads are completely determined by experimentally measurable tunnel conductances and polarizations. Finally, we investigate how currents, noise and cross-correlations are affected by transport of entangled electrons.

DOI
10.1209/0295-5075/81/40002

Related papers

Superconductor coupled to two Luttinger liquids as an entangler for electron spins

Patrik Recher, Daniel Loss

We consider an s-wave superconductor (SC) which is tunnel coupled to two spatially separated Luttinger-liquid (LL) leads. We demonstrate that such a setup acts as an entangler, i.e., it creates spin singlets of two electrons which are spatially separated, thereby providing a source of electronic Einstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage, which is smaller than the energy gap in the SC, a stationary current of spin-entangled electrons can flow from the SC to the LL leads due to Andreev tunneling events. We discuss two competing transport channels for Cooper pairs to tunnel from the SC into the LL leads. On the one hand, the coherent tunneling of two electrons into the same LL lead is shown to be suppressed by strong LL correlations compared to single-electron tunneling into a LL. On the other hand, the tunneling of two spin-entangled electrons into different leads is suppressed by the initial spatial separation of the two electrons coming from the same Cooper pair. We show that the latter suppression depends crucially on the effective dimensionality of the SC. We identify a regime of experimental interest in which the separation of two spin-entangled electrons is favored. We determine the decay of the singlet state of two electrons injected into different leads caused by the LL correlations. Although the electron is not a proper quasiparticle of the LL, the spin information can still be transported via the spin-density fluctuations produced by the injected spin-entangled electrons.

arXiv:cond-mat/0112298•Physical review. B, Condensed matter•Apr 10, 2002•143 citations

Creation and Detection of Mobile and Non-Local Spin-Entangled Electrons

Patrik Recher, Daniel S. Saraga, Daniel Loss

We present electron spin entanglers-devices creating mobile spin-entangled electrons that are spatially separated-where the spin-entanglement in a superconductor present in form of Cooper pairs and in a single quantum dot with a spin singlet groundstate is transported to two spatially separated leads by means of a correlated two-particle tunneling event. The unwanted process of both electrons tunneling into the same lead is suppressed by strong Coulomb blockade effects caused by quantum dots, Luttinger liquid effects or by resistive outgoing leads. In this review we give a transparent description of the different setups, including discussions of the feasibility of the subsequent detection of spin-entanglement via charge noise measurements. Finally, we show that quantum dots in the spin filter regime can be used to perform Bell-type measurements that only require the measurement of zero frequency charge noise correlators.

arXiv:cond-mat/0408526•Kluwer Academic Publishers eBooks•Mar 8, 2006•6 citations

Andreev tunneling, Coulomb blockade, and resonant transport of nonlocal spin-entangled electrons

Patrik Recher, Eugene V. Sukhorukov, Daniel Loss

We propose and analyze a spin-entangler for electrons based on an s-wave superconductor coupled to two quantum dots, each of which is coupled to normal Fermi leads. We show that in the presence of a voltage bias and in the Coulomb blockade regime two correlated electrons provided by the Andreev process can coherently tunnel from the superconductor via different dots into different leads. The spin singlet coming from the Cooper pair remains preserved in this process, and the setup provides a source of mobile and nonlocal spin-entangled electrons. The transport current is calculated and shown to be dominated by a two-particle Breit-Wigner resonance that allows the injection of two spin-entangled electrons into different leads at exactly the same orbital energy, which is a crucial requirement for the detection of spin entanglement via noise measurements. The coherent tunneling of both electrons into the same lead is suppressed by the on-site Coulomb repulsion and/or the superconducting gap, while the tunneling into different leads is suppressed through the initial separation of the tunneling electrons. In the regime of interest the particle-hole excitations of the leads are shown to be negligible. The Aharonov-Bohm oscillations in the current are shown to contain single- and two-electron periods with amplitudes that both vanish with increasing Coulomb repulsion albeit differently fast.

arXiv:cond-mat/0009452•Physical review. B, Condensed matter•Apr 4, 2001•499 citations

Full counting statistics of generic spin entangler with quantum dot-ferromagnet detectors

O. Malkoc, C. Bergenfeldt, Peter Samuelsson

Entanglement between spatially separated electrons in nanoscale transport is a fundamental property, yet to be demonstrated experimentally. Here we propose and analyse theoretically the transport statistics of a generic spin entangler coupled to a hybrid quantum dot-ferromagnet detector system. We show that the full distribution of charges arriving at the ferromagnetic terminals provides complete information on the spin state of the particles emitted by the entangler. This provides means for spin entanglement detection via electrical current correlations, with optimal measurement strategies depending on the a priori knowledge of ferromagnet polarization and spin-flip rates in the detector dots. The scheme is exemplified by applying it to Andreev and triple dot entanglers.

arXiv:1312.3982•Europhysics Letters (EPL)•Feb 1, 2014•8 citations

Dynamical current correlations in Cooper pair splitters based on proximized quantum dots

Grzegorz Michałek, Bogdan R. Bułka

Abstract Entanglement of electrons is studied by means of current–current correlations in two Cooper pair splitter devices: with one and two proximized quantum dots (1QD and 2QD), in presence of intra- and inter-dot Coulomb interactions, and weakly coupled with metallic electrodes. The 1QD system, where Cooper pairs can be transmitted to the same or split to different normal electrodes, is contrasted with the 2QD device, where double occupancy of a single quantum dot is forbidden and transport is only through an inter-dot singlet due to non-local crossed Andreev reflection processes deep in the superconducting energy gap. Separating the current correlation function into components for partial currents of electrons and holes through various Andreev bound states, one can see bunching and antibunching of split particles: inter-level components between electron and hole currents flowing to different electrodes are positive, while intra-level electron–electron or hole–hole components are negative, respectively. Spectral decomposition of the frequency-dependent current cross-correlation is performed to get better insight into mechanisms of entanglement and dynamics of split Cooper pairs, and to extract various charge fluctuation processes with different relaxation times, related to electron and hole currents flowing through the Andreev bound states. Only low frequency polarization fluctuations are seen in the current cross-correlations, while various negative and positive high frequency (charge fluctuations) components compensate each other in the symmetric system.

New Journal of Physics•Dec 12, 2020•4 citations

Circuit influence on Cooper-pair current in solid-state entanglers

Vladimir Bubanja, Shuichi Iwabuchi

We study the effects of the circuit impedance on tunneling of Cooper pairs from a superconductor into two normal-metal leads. We derive the expressions for the crossed and direct Andreev current and consider the limits of ballistic and diffusive electron motion in the electrodes. The derived analytic expressions show that voltage cross correlations, induced by the capacitive coupling of normal-metal leads, narrow the region where the crossed Andreev current dominates over the direct Andreev current, thereby reducing the efficiency of the entangler.

Physical Review B•Sep 6, 2011•5 citations
We study the production of spatially separated entangled electrons in ferromagnetic leads from Cooper pairs in a superconducting lead. We give a complete description of the elementary charge transfer processes, i) transfer of Cooper pairs out of the superconductor by Andreev reflection and ii) distribution of the entangled quasiparticles among the ferromagnetic leads, in terms of their statistics. The probabilities that entangled electrons flow into spatially separated leads are completely determined by experimentally measurable tunnel conductances and polarizations. Finally, we investigate how currents, noise and cross-correlations are affected by transport of entangled electrons.
We consider an s-wave superconductor (SC) which is tunnel coupled to two spatially separated Luttinger-liquid (LL) leads. We demonstrate that such a setup acts as an entangler, i.e., it creates spin singlets of two electrons which are spatially separated, thereby providing a source of electronic Einstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage, which is smaller than the energy gap in the SC, a stationary current of spin-entangled electrons can flow from the SC to the LL leads due to Andreev tunneling events. We discuss two competing transport channels for Cooper pairs to tunnel from the SC into the LL leads. On the one hand, the coherent tunneling of two electrons into the same LL lead is shown to be suppressed by strong LL correlations compared to single-electron tunneling into a LL. On the other hand, the tunneling of two spin-entangled electrons into different leads is suppressed by the initial spatial separation of the two electrons coming from the same Cooper pair. We show that the latter suppression depends crucially on the effective dimensionality of the SC. We identify a regime of experimental interest in which the separation of two spin-entangled electrons is favored. We determine the decay of the singlet state of two electrons injected into different leads caused by the LL correlations. Although the electron is not a proper quasiparticle of the LL, the spin information can still be transported via the spin-density fluctuations produced by the injected spin-entangled electrons.
We present electron spin entanglers-devices creating mobile spin-entangled electrons that are spatially separated-where the spin-entanglement in a superconductor present in form of Cooper pairs and in a single quantum dot with a spin singlet groundstate is transported to two spatially separated leads by means of a correlated two-particle tunneling event. The unwanted process of both electrons tunneling into the same lead is suppressed by strong Coulomb blockade effects caused by quantum dots, Luttinger liquid effects or by resistive outgoing leads. In this review we give a transparent description of the different setups, including discussions of the feasibility of the subsequent detection of spin-entanglement via charge noise measurements. Finally, we show that quantum dots in the spin filter regime can be used to perform Bell-type measurements that only require the measurement of zero frequency charge noise correlators.
We propose and analyze a spin-entangler for electrons based on an s-wave superconductor coupled to two quantum dots, each of which is coupled to normal Fermi leads. We show that in the presence of a voltage bias and in the Coulomb blockade regime two correlated electrons provided by the Andreev process can coherently tunnel from the superconductor via different dots into different leads. The spin singlet coming from the Cooper pair remains preserved in this process, and the setup provides a source of mobile and nonlocal spin-entangled electrons. The transport current is calculated and shown to be dominated by a two-particle Breit-Wigner resonance that allows the injection of two spin-entangled electrons into different leads at exactly the same orbital energy, which is a crucial requirement for the detection of spin entanglement via noise measurements. The coherent tunneling of both electrons into the same lead is suppressed by the on-site Coulomb repulsion and/or the superconducting gap, while the tunneling into different leads is suppressed through the initial separation of the tunneling electrons. In the regime of interest the particle-hole excitations of the leads are shown to be negligible. The Aharonov-Bohm oscillations in the current are shown to contain single- and two-electron periods with amplitudes that both vanish with increasing Coulomb repulsion albeit differently fast.
Entanglement between spatially separated electrons in nanoscale transport is a fundamental property, yet to be demonstrated experimentally. Here we propose and analyse theoretically the transport statistics of a generic spin entangler coupled to a hybrid quantum dot-ferromagnet detector system. We show that the full distribution of charges arriving at the ferromagnetic terminals provides complete information on the spin state of the particles emitted by the entangler. This provides means for spin entanglement detection via electrical current correlations, with optimal measurement strategies depending on the a priori knowledge of ferromagnet polarization and spin-flip rates in the detector dots. The scheme is exemplified by applying it to Andreev and triple dot entanglers.
Abstract Entanglement of electrons is studied by means of current–current correlations in two Cooper pair splitter devices: with one and two proximized quantum dots (1QD and 2QD), in presence of intra- and inter-dot Coulomb interactions, and weakly coupled with metallic electrodes. The 1QD system, where Cooper pairs can be transmitted to the same or split to different normal electrodes, is contrasted with the 2QD device, where double occupancy of a single quantum dot is forbidden and transport is only through an inter-dot singlet due to non-local crossed Andreev reflection processes deep in the superconducting energy gap. Separating the current correlation function into components for partial currents of electrons and holes through various Andreev bound states, one can see bunching and antibunching of split particles: inter-level components between electron and hole currents flowing to different electrodes are positive, while intra-level electron–electron or hole–hole components are negative, respectively. Spectral decomposition of the frequency-dependent current cross-correlation is performed to get better insight into mechanisms of entanglement and dynamics of split Cooper pairs, and to extract various charge fluctuation processes with different relaxation times, related to electron and hole currents flowing through the Andreev bound states. Only low frequency polarization fluctuations are seen in the current cross-correlations, while various negative and positive high frequency (charge fluctuations) components compensate each other in the symmetric system.
We study the effects of the circuit impedance on tunneling of Cooper pairs from a superconductor into two normal-metal leads. We derive the expressions for the crossed and direct Andreev current and consider the limits of ballistic and diffusive electron motion in the electrodes. The derived analytic expressions show that voltage cross correlations, induced by the capacitive coupling of normal-metal leads, narrow the region where the crossed Andreev current dominates over the direct Andreev current, thereby reducing the efficiency of the entangler.