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:1609.01902 · physica status solidi (b)

Entanglement‐symmetry control in a quantum‐dot Cooper‐pair splitter

Robert Hussein, Alessandro Braggio, Michele Governale

Published Feb 21, 2017• 9 citations
arXivHTMLPDF

Abstract

Abstract The control of nonlocal entanglement in solid state systems is a crucial ingredient of quantum technologies. We investigate a Cooper‐pair splitter based on a double quantum dot realized in a semiconducting nanowire. In the presence of interdot tunneling the system provides a simple mechanism to develop spatial entanglement even in absence of nonlocal coupling with the superconducting lead. We discuss the possibility to control the symmetry (singlet or triplet) of spatially separated, entangled electron pairs taking advantage of the spin‐orbit coupling of the nanowire. We also demonstrate that the spin‐orbit coupling does not impact over the entanglement purity of the nonlocal state generated in the double quantum dot system. Cooper‐pair splitter realized in a nanowire acting as double quantum dot which is coupled to one superconductor (S) and two normal leads (N). Electron singlets in the superconductor are split nonlocally into the different dots as schematically shown in the figure. The entangled electrons in the two quantum dots are then transferred by tunneling, with rate , to the normal leads.

DOI
10.1002/pssb.201600603

Related papers

Double quantum dot Cooper-pair splitter at finite couplings

Robert Hussein, Lina Jaurigue, Michele Governale +1 more

We consider the subgap physics of a hybrid double-quantum dot Cooper-pair splitter with large single-level spacings, in the presence of tunneling between the dots and finite Coulomb intra- and interdot Coulomb repulsion. In the limit of a large superconducting gap, we treat the coupling of the dots to the superconductor exactly. We employ a generalized master-equation method, which easily yields currents, noise, and cross-correlators. In particular, for finite inter- and intradot Coulomb interaction, we investigate how the transport properties are determined by the interplay between local and nonlocal tunneling processes between the superconductor and the dots. We examine the effect of interdot tunneling on the particle-hole symmetry of the currents with and without spin-orbit interaction. We show that spin-orbit interaction in combination with finite Coulomb energy opens the possibility to control the nonlocal entanglement and its symmetry (singlet/triplet). We demonstrate that the generation of nonlocal entanglement can be achieved even without any direct nonlocal coupling to the superconducting lead.

arXiv:1608.00504•Physical review. B./Physical review. B•Dec 14, 2016•25 citations

Nonlocal quantum state engineering with the Cooper pair splitter beyond the Coulomb blockade regime

Ehud Amitai, Rakesh P. Tiwari, Stefan Walter +2 more

A Cooper pair splitter consists of two quantum dots side-coupled to a conventional superconductor. Usually, the quantum dots are assumed to have a large charging energy compared to the superconducting gap, in order to suppress processes other than the coherent splitting of Cooper pairs. In this work, in contrast, we investigate the limit in which the charging energy is smaller than the superconducting gap. This allows us, in particular, to study the effect of a Zeeman field comparable to the charging energy. We find analytically that in this parameter regime the superconductor mediates an interdot tunneling term with a spin symmetry determined by the Zeeman field. Together with electrostatically tunable quantum dots, we show that this makes it possible to engineer a spin triplet state shared between the quantum dots. Compared to previous works, we thus extend the capabilities of the Cooper pair splitter to create entangled nonlocal electron pairs.

arXiv:1512.02952•Physical review. B./Physical review. B•Feb 11, 2016•11 citations

Spin blockade in Cooper pair splitters

Jami Rönkkö

Entanglement is a valuable resource for quantum computing and information technologies. A promising way to obtain spin-entangled electrons is the splitting of Cooper pairs residing in superconductors. This is realized by a nanodevice called Cooper pair splitter. A Cooper pair splitter is realized by tunnel-coupling a superconductor to two quantum dots, which are each further tunnelcoupled to separate terminal leads. This setup enables the extraction and splitting of Cooper pairs from the superconductor into the terminals via the quantum dots. The quantum dots are commonly fabricated from semiconducting materials like InAs and InSb, that can manifest spin-orbit interaction. This thesis studies the effect of spin-orbit interaction on the spin state of the electron pair in the Cooper pair splitter. Activating the spin-orbit effects in a Cooper pair splitter requires a static magnetic field to be applied to the quantum dots. Together with the gate electrodes controlling the electrostatic energy of the quantum dots, the external magnetic field provides a handle for addressing different two-particle spin states. The spin-orbit interaction can be activated by various combinations of the gate voltage and Zeeman magnetic field, that create resonances between different states of the system. The most interesting coherent evolution, that can be invoked in this way, involves the simultaneous activation of the two spin-polarized triplet states. This gives a rise to an entangled Bell state, (|↑↑>+|↓↓>) / √2, that moreover exhibits spin blockade and thus stabilizes entanglement in the Cooper pair splitter. Secondly, the spin-orbit interaction can be used to bypass suppressed Cooper pair tunneling at a high superconductor-quantum dots detuning. Introducing a large Zeeman magnetic field allows Cooper pairs to tunnel in to the dots given that their spin state flips to the triplet |↓↓>. Although this regime lacks spin-entanglement, it is of interest for creating triplet Cooper pairs and spin-polarized superconducting currents.

Työväentutkimus Vuosikirja•Jan 1, 2020•0 citations

Cooper pair splitter realized in a two-quantum-dot Y-junction

L. Hofstetter, S. Csonka, Jesper Nygård +1 more

Electron entanglement: splitting pairs One of the most counterintuitive aspects of quantum mechanics is non-locality, manifesting as spatially separated objects influencing each other in a direct way. Experimental verifications of such concepts have been conducted successfully using entangled pairs of photons to test so-called Bell inequalities, but similar demonstrations using electrons have remained elusive owing to the inherent difficulty of creating and splitting pairs of entangled electrons. Lukas Hofstetter and colleagues now demonstrate that this is possible in a Y-shaped electron entangler consisting of a superconductor at its stem, coupled via tunnelling barriers to two separate quantum dots along the fork-like branches of the device. The entangled pairs of electrons are naturally formed in the superconductor, which in its ground state consists of Cooper pairs of electrons, and split by Coulomb interactions and careful tuning of the energy levels of the quantum dots. The study paves the way for the study of electronic entanglement and experimental tests of Bell inequalities in the solid state.

•Jan 1, 2009•0 citations

Finite-Bias Cooper Pair Splitting

L. Hofstetter, Szabolcs Csonka, Andreas Baumgartner +4 more

In a device with a superconductor coupled to two parallel quantum dots (QDs) the electrical tunability of the QD levels can be used to exploit nonclassical current correlations due to the splitting of Cooper pairs. We experimentally investigate the effect of a finite potential difference across one quantum dot on the conductance through the other completely grounded QD in a Cooper pair splitter fabricated on an InAs nanowire. We demonstrate that the nonlocal electrical transport through the device can be tuned by electrical means and that the energy dependence of the effective density of states in the QDs is relevant for the rates of Cooper pair splitting (CPS) and elastic cotunneling. Such experimental tools are necessary to understand and develop CPS-based sources of entangled electrons in solid-state devices.

arXiv:1105.2583•Physical Review Letters•Sep 19, 2011•166 citations

Adiabatic Cooper pair splitter

Fredrik Brange, Riya Baruah, Christian Flindt

By adiabatically changing the energy levels of two quantum dots, theoreticians predict that it should be possible to control the splitting of Cooper pairs from a superconductor. Such an adiabatic Cooper pair splitter could serve as an on-demand source of entangled electrons in future solid-state quantum technologies.

arXiv:2307.13997•Physical review. B./Physical review. B•Feb 6, 2024•11 citations
Abstract The control of nonlocal entanglement in solid state systems is a crucial ingredient of quantum technologies. We investigate a Cooper‐pair splitter based on a double quantum dot realized in a semiconducting nanowire. In the presence of interdot tunneling the system provides a simple mechanism to develop spatial entanglement even in absence of nonlocal coupling with the superconducting lead. We discuss the possibility to control the symmetry (singlet or triplet) of spatially separated, entangled electron pairs taking advantage of the spin‐orbit coupling of the nanowire. We also demonstrate that the spin‐orbit coupling does not impact over the entanglement purity of the nonlocal state generated in the double quantum dot system. Cooper‐pair splitter realized in a nanowire acting as double quantum dot which is coupled to one superconductor (S) and two normal leads (N). Electron singlets in the superconductor are split nonlocally into the different dots as schematically shown in the figure. The entangled electrons in the two quantum dots are then transferred by tunneling, with rate , to the normal leads.
We consider the subgap physics of a hybrid double-quantum dot Cooper-pair splitter with large single-level spacings, in the presence of tunneling between the dots and finite Coulomb intra- and interdot Coulomb repulsion. In the limit of a large superconducting gap, we treat the coupling of the dots to the superconductor exactly. We employ a generalized master-equation method, which easily yields currents, noise, and cross-correlators. In particular, for finite inter- and intradot Coulomb interaction, we investigate how the transport properties are determined by the interplay between local and nonlocal tunneling processes between the superconductor and the dots. We examine the effect of interdot tunneling on the particle-hole symmetry of the currents with and without spin-orbit interaction. We show that spin-orbit interaction in combination with finite Coulomb energy opens the possibility to control the nonlocal entanglement and its symmetry (singlet/triplet). We demonstrate that the generation of nonlocal entanglement can be achieved even without any direct nonlocal coupling to the superconducting lead.
A Cooper pair splitter consists of two quantum dots side-coupled to a conventional superconductor. Usually, the quantum dots are assumed to have a large charging energy compared to the superconducting gap, in order to suppress processes other than the coherent splitting of Cooper pairs. In this work, in contrast, we investigate the limit in which the charging energy is smaller than the superconducting gap. This allows us, in particular, to study the effect of a Zeeman field comparable to the charging energy. We find analytically that in this parameter regime the superconductor mediates an interdot tunneling term with a spin symmetry determined by the Zeeman field. Together with electrostatically tunable quantum dots, we show that this makes it possible to engineer a spin triplet state shared between the quantum dots. Compared to previous works, we thus extend the capabilities of the Cooper pair splitter to create entangled nonlocal electron pairs.
Entanglement is a valuable resource for quantum computing and information technologies. A promising way to obtain spin-entangled electrons is the splitting of Cooper pairs residing in superconductors. This is realized by a nanodevice called Cooper pair splitter. A Cooper pair splitter is realized by tunnel-coupling a superconductor to two quantum dots, which are each further tunnelcoupled to separate terminal leads. This setup enables the extraction and splitting of Cooper pairs from the superconductor into the terminals via the quantum dots. The quantum dots are commonly fabricated from semiconducting materials like InAs and InSb, that can manifest spin-orbit interaction. This thesis studies the effect of spin-orbit interaction on the spin state of the electron pair in the Cooper pair splitter. Activating the spin-orbit effects in a Cooper pair splitter requires a static magnetic field to be applied to the quantum dots. Together with the gate electrodes controlling the electrostatic energy of the quantum dots, the external magnetic field provides a handle for addressing different two-particle spin states. The spin-orbit interaction can be activated by various combinations of the gate voltage and Zeeman magnetic field, that create resonances between different states of the system. The most interesting coherent evolution, that can be invoked in this way, involves the simultaneous activation of the two spin-polarized triplet states. This gives a rise to an entangled Bell state, (|↑↑>+|↓↓>) / √2, that moreover exhibits spin blockade and thus stabilizes entanglement in the Cooper pair splitter. Secondly, the spin-orbit interaction can be used to bypass suppressed Cooper pair tunneling at a high superconductor-quantum dots detuning. Introducing a large Zeeman magnetic field allows Cooper pairs to tunnel in to the dots given that their spin state flips to the triplet |↓↓>. Although this regime lacks spin-entanglement, it is of interest for creating triplet Cooper pairs and spin-polarized superconducting currents.
Electron entanglement: splitting pairs One of the most counterintuitive aspects of quantum mechanics is non-locality, manifesting as spatially separated objects influencing each other in a direct way. Experimental verifications of such concepts have been conducted successfully using entangled pairs of photons to test so-called Bell inequalities, but similar demonstrations using electrons have remained elusive owing to the inherent difficulty of creating and splitting pairs of entangled electrons. Lukas Hofstetter and colleagues now demonstrate that this is possible in a Y-shaped electron entangler consisting of a superconductor at its stem, coupled via tunnelling barriers to two separate quantum dots along the fork-like branches of the device. The entangled pairs of electrons are naturally formed in the superconductor, which in its ground state consists of Cooper pairs of electrons, and split by Coulomb interactions and careful tuning of the energy levels of the quantum dots. The study paves the way for the study of electronic entanglement and experimental tests of Bell inequalities in the solid state.
In a device with a superconductor coupled to two parallel quantum dots (QDs) the electrical tunability of the QD levels can be used to exploit nonclassical current correlations due to the splitting of Cooper pairs. We experimentally investigate the effect of a finite potential difference across one quantum dot on the conductance through the other completely grounded QD in a Cooper pair splitter fabricated on an InAs nanowire. We demonstrate that the nonlocal electrical transport through the device can be tuned by electrical means and that the energy dependence of the effective density of states in the QDs is relevant for the rates of Cooper pair splitting (CPS) and elastic cotunneling. Such experimental tools are necessary to understand and develop CPS-based sources of entangled electrons in solid-state devices.