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:1606.07297 · Physical review. B./Physical review. B

Signatures of nonlocal Cooper-pair transport and of a singlet-triplet transition in the critical current of a double-quantum-dot Josephson junction

Benedikt Probst, Fernando Domínguez, Alexander Schroer, A. Levy Yeyati, Patrik Recher

Published Oct 28, 2016• 32 citations
arXivHTMLPDF

Abstract

We study the critical Josephson current flowing through a double quantum dot weakly coupled to two superconducting leads. We use analytical as well as numerical methods to investigate this setup in the limit of small and large bandwidth leads in all possible charging states, where we account for on-site interactions exactly. Our results provide clear signatures of nonlocal spin-entangled pairs, which support interpretations of recent experiments [R. S. Deacon, A. Oiwa, J. Sailer, S. Baba, Y. Kanai, K. Shibata, K. Hirakawa, and S. Tarucha, Nat. Commun. 6, 7446 (2015)]. In addition, we find that the ground state with one electron on each quantum dot can undergo a tunable singlet-triplet phase transition in the regime where the superconducting gap in the leads is not too large, which gives rise to an additional new signature of nonlocal Cooper-pair transport.

DOI
10.1103/physrevb.94.155445

Related papers

Magnetic flux controlled current phase relationship in double quantum dot Josephson junction

Yiyan Wang, Cong Li, Bing Dong

Abstract In this study, we investigate the quantum phase transition in a Josephson junction consisting of parallel-connected quantum dots (QDs) with a magnetic flux φ B threading the central region. Employing the surrogate model approach, we discretize the superconducting (SC) electrode into three discrete energy levels, which enables direct diagonalization of the Hamiltonian to determine the system’s ground state. Our calculations demonstrate that when Coulomb interaction is present in only one QD, the system exhibits a phase transition between singlet and doublet states. The magnetic flux exerts a minor influence on the singlet state while substantially affecting the doublet state. When both QDs possess Coulomb interactions, the system undergoes two successive phase transitions as the SC phase difference increases: the ground state evolves from a doublet to a singlet and subsequently to a triplet state at ϕ = π . Enhancement of the magnetic flux suppresses the doublet and triplet phases, ultimately stabilizing the singlet state. Within this regime, increasing the Coulomb interaction strength U does not trigger a singlet-triplet transition; rather, it induces a transition between upper and lower singlet states, resulting in a pronounced peak in the critical current as U increases. Finally, we explore the scenario where the tunneling self-energy Γ between the QDs and SCs exceeds the SC pairing potential Δ. In this case, doublet states prevail, and the system manifests a phase transition exclusively between doublet and triplet states when ϕ B = 0 . Upon application of a magnetic flux, all three states converge, giving rise to a triple point in the ( φ , φ B ) parameter space.

arXiv:2509.17517•New Journal of Physics•Mar 31, 2026•0 citations

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

Cooper pair splitting in parallel quantum dot Josephson junctions

Russell Deacon, A. Oiwa, J. Sailer +5 more

Devices to generate on-demand non-local spin entangled electron pairs have potential application as solid-state analogues of the entangled photon sources used in quantum optics. Recently, Andreev entanglers that use two quantum dots as filters to adiabatically split and separate the quasi-particles of Cooper pairs have shown efficient splitting through measurements of the transport charge but the spin entanglement has not been directly confirmed. Here we report measurements on parallel quantum dot Josephson junction devices allowing a Josephson current to flow due to the adiabatic splitting and recombination of the Cooper pair between the dots. The evidence for this non-local transport is confirmed through study of the non-dissipative supercurrent while tuning independently the dots with local electrical gates. As the Josephson current arises only from processes that maintain the coherence, we can confirm that a current flows from the spatially separated entangled pair.

Nature Communications•Jul 1, 2015•82 citations

Josephson Junction π−0 Transition Induced by Orbital Hybridization in a Double Quantum Dot

Rousan Debbarma, Athanasios Tsintzis, Markus Aspegren +5 more

In this Letter, we manipulate the phase shift of a Josephson junction using a parallel double quantum dot (QD). By employing a superconducting quantum interference device, we determine how orbital hybridization and detuning affect the current-phase relation in the Coulomb blockade regime. For weak hybridization between the QDs, we find π junction characteristics if at least one QD has an unpaired electron. Notably the critical current is higher when both QDs have an odd electron occupation. By increasing the inter-QD hybridization the critical current is reduced, until eventually a π-0 transition occurs. A similar transition appears when detuning the QD levels at finite hybridization. Based on a zero-bandwidth model, we argue that both cases of phase-shift transitions can be understood considering an increased weight of states with a double occupancy in the ground state and with the Cooper pair transport dominated by local Andreev reflection.

arXiv:2311.11867•Physical Review Letters•Dec 21, 2023•8 citations

Superconducting transport in single and parallel double InAs quantum dot Josephson junctions with Nb-based superconducting electrodes

Shoji Baba, Juergen Sailer, Russell Deacon +4 more

We report conductance and supercurrent measurements for InAs single and parallel double quantum dot Josephson junctions contacted with Nb or NbTiN superconducting electrodes. Large superconducting gap energy, high critical field, and large switching current are observed, all reflecting the features of Nb-based electrodes. For the parallel double dots, we observe an enhanced supercurrent when both dots are on resonance, which may reflect split Cooper pair tunneling.

arXiv:1512.02344•Applied Physics Letters•Nov 30, 2015•14 citations
We study the critical Josephson current flowing through a double quantum dot weakly coupled to two superconducting leads. We use analytical as well as numerical methods to investigate this setup in the limit of small and large bandwidth leads in all possible charging states, where we account for on-site interactions exactly. Our results provide clear signatures of nonlocal spin-entangled pairs, which support interpretations of recent experiments [R. S. Deacon, A. Oiwa, J. Sailer, S. Baba, Y. Kanai, K. Shibata, K. Hirakawa, and S. Tarucha, Nat. Commun. 6, 7446 (2015)]. In addition, we find that the ground state with one electron on each quantum dot can undergo a tunable singlet-triplet phase transition in the regime where the superconducting gap in the leads is not too large, which gives rise to an additional new signature of nonlocal Cooper-pair transport.
Abstract In this study, we investigate the quantum phase transition in a Josephson junction consisting of parallel-connected quantum dots (QDs) with a magnetic flux φ B threading the central region. Employing the surrogate model approach, we discretize the superconducting (SC) electrode into three discrete energy levels, which enables direct diagonalization of the Hamiltonian to determine the system’s ground state. Our calculations demonstrate that when Coulomb interaction is present in only one QD, the system exhibits a phase transition between singlet and doublet states. The magnetic flux exerts a minor influence on the singlet state while substantially affecting the doublet state. When both QDs possess Coulomb interactions, the system undergoes two successive phase transitions as the SC phase difference increases: the ground state evolves from a doublet to a singlet and subsequently to a triplet state at ϕ = π . Enhancement of the magnetic flux suppresses the doublet and triplet phases, ultimately stabilizing the singlet state. Within this regime, increasing the Coulomb interaction strength U does not trigger a singlet-triplet transition; rather, it induces a transition between upper and lower singlet states, resulting in a pronounced peak in the critical current as U increases. Finally, we explore the scenario where the tunneling self-energy Γ between the QDs and SCs exceeds the SC pairing potential Δ. In this case, doublet states prevail, and the system manifests a phase transition exclusively between doublet and triplet states when ϕ B = 0 . Upon application of a magnetic flux, all three states converge, giving rise to a triple point in the ( φ , φ B ) parameter space.
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.
Devices to generate on-demand non-local spin entangled electron pairs have potential application as solid-state analogues of the entangled photon sources used in quantum optics. Recently, Andreev entanglers that use two quantum dots as filters to adiabatically split and separate the quasi-particles of Cooper pairs have shown efficient splitting through measurements of the transport charge but the spin entanglement has not been directly confirmed. Here we report measurements on parallel quantum dot Josephson junction devices allowing a Josephson current to flow due to the adiabatic splitting and recombination of the Cooper pair between the dots. The evidence for this non-local transport is confirmed through study of the non-dissipative supercurrent while tuning independently the dots with local electrical gates. As the Josephson current arises only from processes that maintain the coherence, we can confirm that a current flows from the spatially separated entangled pair.
In this Letter, we manipulate the phase shift of a Josephson junction using a parallel double quantum dot (QD). By employing a superconducting quantum interference device, we determine how orbital hybridization and detuning affect the current-phase relation in the Coulomb blockade regime. For weak hybridization between the QDs, we find π junction characteristics if at least one QD has an unpaired electron. Notably the critical current is higher when both QDs have an odd electron occupation. By increasing the inter-QD hybridization the critical current is reduced, until eventually a π-0 transition occurs. A similar transition appears when detuning the QD levels at finite hybridization. Based on a zero-bandwidth model, we argue that both cases of phase-shift transitions can be understood considering an increased weight of states with a double occupancy in the ground state and with the Cooper pair transport dominated by local Andreev reflection.