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:1205.2252 · Physical Review B

Microwave spectroscopy of a Cooper pair beam splitter

Audrey Cottet

Published Aug 6, 2012• 18 citations
arXivHTMLPDF

Abstract

This article discusses how to demonstrate the entanglement of the split Cooper pairs produced in a double-quantum-dot based Cooper pair beam splitter (CPS), by performing the microwave spectroscopy of the CPS. More precisely, one can study the dc current response of such a CPS to two on-phase microwave gate irradiations applied to the two CPS dots. Some of the current peaks caused by the microwaves show a strongly nonmonotonic variation with the amplitude of the irradiation applied individually to one dot. This effect is directly due to a subradiance property caused by the coherence of the split pairs. Using realistic parameters, one finds that this effect has a measurable amplitude.

DOI
10.1103/physrevb.86.075107

Related papers

Subradiant Split Cooper Pairs

Audrey Cottet, Takis Kontos, A. Levy Yeyati

We suggest a way to characterize the coherence of the split Cooper pairs emitted by a double-quantum-dot based Cooper pair splitter (CPS), by studying the radiative response of such a CPS inside a microwave cavity. The coherence of the split pairs manifests in a strongly nonmonotonic variation of the emitted radiation as a function of the parameters controlling the coupling of the CPS to the cavity. The idea to probe the coherence of the electronic states using the tools of cavity quantum electrodynamics could be generalized to many other nanoscale circuits.

arXiv:1111.7112•Physical Review Letters•Apr 20, 2012•51 citations

Probing coherent Cooper pair splitting with cavity photons

Audrey Cottet

This work discusses theoretically the behavior of a microwave cavity and a Cooper pair beam splitter (CPS) coupled nonresonantly. The cavity frequency pull is modified when the CPS is resonant with a microwave excitation. This provides a direct way to probe the coherence of the Cooper pair splitting process. More precisely, the cavity frequency pull displays an anticrossing whose specificities can be attributed unambiguously to coherent Cooper pair injection. This work illustrates that microwave cavities represent a powerful tool to investigate current transport in complex nanocircuits.

arXiv:1406.4666•Physical Review B•Sep 23, 2014•14 citations

Cooper Pair Splitting by Means of Graphene Quantum Dots

Zhenbing Tan, D. Cox, T. Nieminen +4 more

A split Cooper pair is a natural source for entangled electrons which is a basic ingredient for quantum information in the solid state. We report an experiment on a superconductor-graphene double quantum dot (QD) system, in which we observe Cooper pair splitting (CPS) up to a CPS efficiency of ∼10%. With bias on both QDs, we are able to detect a positive conductance correlation across the two distinctly decoupled QDs. Furthermore, with bias only on one QD, CPS and elastic cotunneling can be distinguished by tuning the energy levels of the QDs to be asymmetric or symmetric with respect to the Fermi level in the superconductor.

arXiv:1412.8451•Physical Review Letters•Mar 4, 2015•129 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

Entangled Photon-Pair Emission in Waveguide Circuit QED from a Cooper Pair Splitter

Michele Governale, Christian Schönenberger, Pasquale Scarlino +1 more

As a waveguide circuit QED architecture, we investigate theoretically the single-photon pair emission of a Cooper pair splitter composed of two double quantum dots, each coupled to a microwave transmission line. We find that this system can generate frequency-entangled photon pairs in the left and right transmission lines, specifically a superposition of two photon wave packets at different frequencies. The frequency entanglement of the two photons arises from the particle-hole coherent superposition (i.e., Andreev bound states) involving the delocalized entangled spin singlet. We also estimate a lower bound for the efficiency of entangled photon-pair generation, accounting for the presence of nonradiative processes such as phonon emissions. Our proposal is realistic and achievable with state-of-the-art techniques in quantum microwave engineering with electostatically defined semiconducting quantum dots.

arXiv:2407.15109•PRX Quantum•May 29, 2025•5 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
This article discusses how to demonstrate the entanglement of the split Cooper pairs produced in a double-quantum-dot based Cooper pair beam splitter (CPS), by performing the microwave spectroscopy of the CPS. More precisely, one can study the dc current response of such a CPS to two on-phase microwave gate irradiations applied to the two CPS dots. Some of the current peaks caused by the microwaves show a strongly nonmonotonic variation with the amplitude of the irradiation applied individually to one dot. This effect is directly due to a subradiance property caused by the coherence of the split pairs. Using realistic parameters, one finds that this effect has a measurable amplitude.
We suggest a way to characterize the coherence of the split Cooper pairs emitted by a double-quantum-dot based Cooper pair splitter (CPS), by studying the radiative response of such a CPS inside a microwave cavity. The coherence of the split pairs manifests in a strongly nonmonotonic variation of the emitted radiation as a function of the parameters controlling the coupling of the CPS to the cavity. The idea to probe the coherence of the electronic states using the tools of cavity quantum electrodynamics could be generalized to many other nanoscale circuits.
This work discusses theoretically the behavior of a microwave cavity and a Cooper pair beam splitter (CPS) coupled nonresonantly. The cavity frequency pull is modified when the CPS is resonant with a microwave excitation. This provides a direct way to probe the coherence of the Cooper pair splitting process. More precisely, the cavity frequency pull displays an anticrossing whose specificities can be attributed unambiguously to coherent Cooper pair injection. This work illustrates that microwave cavities represent a powerful tool to investigate current transport in complex nanocircuits.
A split Cooper pair is a natural source for entangled electrons which is a basic ingredient for quantum information in the solid state. We report an experiment on a superconductor-graphene double quantum dot (QD) system, in which we observe Cooper pair splitting (CPS) up to a CPS efficiency of ∼10%. With bias on both QDs, we are able to detect a positive conductance correlation across the two distinctly decoupled QDs. Furthermore, with bias only on one QD, CPS and elastic cotunneling can be distinguished by tuning the energy levels of the QDs to be asymmetric or symmetric with respect to the Fermi level in the superconductor.
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.
As a waveguide circuit QED architecture, we investigate theoretically the single-photon pair emission of a Cooper pair splitter composed of two double quantum dots, each coupled to a microwave transmission line. We find that this system can generate frequency-entangled photon pairs in the left and right transmission lines, specifically a superposition of two photon wave packets at different frequencies. The frequency entanglement of the two photons arises from the particle-hole coherent superposition (i.e., Andreev bound states) involving the delocalized entangled spin singlet. We also estimate a lower bound for the efficiency of entangled photon-pair generation, accounting for the presence of nonradiative processes such as phonon emissions. Our proposal is realistic and achievable with state-of-the-art techniques in quantum microwave engineering with electostatically defined semiconducting quantum dots.
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.