This projects aims at a single electron pair source which delivers (in principle) on demand pairs of spin-entangled electrons, whereof each electron may leave the device through different arms. While similar photonic EPR sources are widely used in optics in e.g. in teleportation experiments, generating and transporting entanglement in the solid state with electrons is non-trivial due to the strong interaction of the quasiparticles with other particles and excitations. However, in graphene the spin dephasing time now exceeds nanoseconds, yielding a coherent transport distance for spin of impressive 1 mm using the known Fermi velocity of graphene. Hence, entanglement can (in principle) be generated at macroscopic distances beyond millimeters in the solid state.

(a) Principle of Cooper-pair splitting using a double quantum dot. On resonance the Cooper-pair is split due to Coulomb repulsion, resulting in one electron passing through the left dot and the other through the right one. (b) shows an implementation using an InAs semiconducting nanowire with multiple bottom-gates

In the current project we start with a Cooper-pair as a naturally spin entangled electron state (in a conventional BCS superconductor the pair is a spin singlet). The device of interest consists of two quantum dots (QDs) tunnel coupled closely together to a central superconductor (see image). Due to interaction effects, which are enhanced in QDs, the “splitting” of the Cooper-pair may become the dominating transport process. In this non-local process, one of the electron tunnels to the left and the other to the right QD. As long as the spin degree is not measured, the states remains entangled. Splitting efficiencies beyond 90% have been realized. We have realized Cooper-pair splitter (CPS) devices in carbon nanotube and semiconducting nanowire based quantum devices and demonstrated large splitting efficiency and to some extend control down to single electron pairs. The devices can also be used to search for Majorana-like bound states as the topology is very much similar.

Current challenges are: better control of individual tunneling rates (in and out tunneling); detection of the entanglement and its life time; manipulation of the singlet state using the quantum toolbox, e.g. electron spin-resonance, detection of a coherent non-local coupling between the two QDs, non-local Andreev bound states.


Relevant papers (keyword: CPS):


  • Co-existence of classical snake states and Aharanov-Bohm oscillations along graphene p-n junctions
    Peter Makk, Clevin Handschin, Endre Tovari, Kenji Watanabe, Takashi Taniguchi, Klaus Richter, Ming-Hao Liu, and Christian Schönenberger.
    Phys. Rev. X, 2018. arXiv:1804.02590

    Snake states and Aharonov-Bohm interferences are examples of magnetoconductance oscillations that can be observed in a graphene p-n junction. Even though they have already been reported in suspended and encapsulated devices including different geometries, a direct comparison remains challenging as they were observed in separate measurements. Due to the similar experimental signatures of these effects a consistent assignment is difficult, leaving us with an incomplete picture. Here we present measurements on p-n junctions in encapsulated graphene revealing several sets of magnetoconductance oscillations allowing for their direct comparison. We analysed them with respect to their charge carrier density, magnetic field, temperature and bias dependence in order to assign them to either snake states or Aharonov-Bohm oscillations. Furthermore we were able to consistently assign the various Aharonov-Bohm interferences to the corresponding area which the edge states enclose. Surprisingly, we find that snake states and Aharonov-Bohm interferences can co-exist within a limited parameter range

  • Cooper-pair splitting in two parallel InAs nanowires
    Sadashige Matsuo Andreas Baumgartner Yosuke Sato Hiroshi Kamata Kan Li Sören Jeppesen Lars Samuelson Hongqi Xu Christian Schönenberger Seigo Tarucha Shoji Baba Christian Jünger.
    New Journal of Physics, 2018. arXiv:1802.08059

    We report on the fabrication and electrical characterization of an InAs double – nanowire (NW) device consisting of two closely placed parallel NWs coupled to a common superconducting electrode on one side and individual normal metal leads on the other. In this new type of device we detect Cooper-pair splitting (CPS) with a sizeable efficiency of correlated currents in both NWs. In contrast to earlier experiments, where CPS was realized in a single NW, demonstrating an intrawire electron pairing mediated by the superconductor (SC), our experiment demonstrates an inter- wire interaction mediated by the common SC. The latter is the key for the realization of zero-magnetic field Majorana bound states, or Parafermions; in NWs and therefore constitutes a milestone towards topological superconductivity. In addition, we observe transport resonances that occur only in the superconducting state, which we tentatively attribute to Andreev Bound states and/or Yu-Shiba resonances that form in the proximitized section of one NW.


  • Andreev bound states probed in three-terminal quantum dots
    J. Gramich, A. Baumgartner, and C. Schönenberger.
    Phys. Rev. B, 96:195418, nov 2017. [DOI] arXiv:1612.01201

    Andreev bound states (ABSs) are well-de ned many-body quantum states that emerge from the hybridization of individual quantum dot (QD) states with a superconductor and exhibit very rich and fundamental phenomena. We demonstrate several new electron transport phenomena mediated by ABSs that form on three-terminal carbon nanotube (CNT) QDs, with one superconducting (S) contact in the center and two adjacent normal metal (N) contacts. Three-terminal spectroscopy allows us to identify the coupling to the N contacts as the origin of the Andreev resonance (AR) linewidths and to determine the critical coupling strengths to S, for which a ground state (or quantum phase) transition in such S-QD systems can occur. In addition, we ascribe replicas of the lowest-energy ABS resonance to transitions between the ABS and odd-parity excited QD states, a process we call excited state ABS resonances. In the conductance between the two N contacts we find a characteristic pattern of positive and negative differential subgap conductance, which we explain by considering two nonlocal processes, the creation of Cooper pairs in S by electrons from both N terminals, and a novel transport mechanism called resonant ABS tunneling, possible only in multi-terminal QD devices. In the latter process, electrons are transferred via the ABS without effectively creating Cooper pairs in S. The three-terminal geometry also allows spectroscopy experiments with different boundary conditions, for example by leaving S floating. Surprisingly, we find that, depending on the boundary conditions and the device parameters, the experiments either show single-particle Coulomb blockade resonances, ABS characteristics, or both in the same measurements, seemingly contradicting the notion of ABSs replacing the single particle states as eigenstates of the QD. We qualitatively explain these results as originating from the nite time scale required for the coherent oscillations between the superposition states after a single electron tunneling event. These experiments demonstrate that three-terminal experiments on a single complex quantum object can also be useful to investigate charge dynamics otherwise not accessible due to the very high frequencies.


  • Cooper-Paare tunneln durch einen Quantenpunkt
    Andreas Baumgartner, Jörg Gramich, and Christian Schönenberger.
    Physik in unserer Zeit, 47(2):62-63, mar 2016. [DOI]

    Elektronische Bauteile aus Supraleitern und Quantenpunkten zeigen eine Vielzahl von neuen und fundamentalen physikalischen Eigenschaften und stellen neue quantentechnologische Anwendungen in Aussicht. Kuerzlich ist es gelungen, den wohl grundlegendsten Transportprozess in einer solchen Struktur in Experimenten zu identifizieren, naemlich den direkten Transport von Elektronen aus einem Supraleiter durch einen Quantenpunkt, das sogenannte Andreev-Tunneln. Das Verstaendnis dieses Prozesses liefert die Grundlage fuer zukuenftige Anwendungen, die quantenmechanische Phaenomene in elektronischen Bauteilen ausnutzen werden.


  • Magnetic Field Tuning and Quantum Interference in a Cooper Pair Splitter
    G. Fülöp, F. Domínguez, S. d’Hollosy, A. Baumgartner, P. Makk, M. H. Madsen, V. A. Guzenko, J. Nygard, C. Schönenberger, Levy A. Yeyati, Csonka S. -. in cooperation with the Csonka(Budapest), and Levi Yeyati group (Madrid).
    Physical Review Letters, 115(22):227003, nov 2015. [DOI] arXiv:1507.01036

    Cooper pair splitting (CPS) is a process in which the electrons of naturally occurring spin-singlet pairs in a superconductor are spatially separated using two quantum dots. Here we investigate the evolution of the conductance correlations in an InAs CPS device in the presence of an external magnetic field. In our experiments the gate dependence of the signal that depends on both quantum dots continuously evolves from a slightly asymmetric Lorentzian to a strongly asymmetric Fano-type resonance with increasing field. These experiments can be understood in a simple three – site model, which shows that the nonlocal CPS leads to symmetric line shapes, while the local transport processes can exhibit an asymmetric shape due to quantum interference. These findings demonstrate that the electrons from a Cooper pair splitter can propagate coherently after their emission from the superconductor and how a magnetic field can be used to optimize the performance of a CPS device. In addition, the model calculations suggest that the estimate of the CPS efficiency in the experiments is a lower bound for the actual efficiency.

  • Entanglement Detection with Non-Ideal Ferromagnetic Detectors
    P. Rozek, P. Busz, W. Klobus, D. Tomaszewski, A. Grudka, A. Baumgartner, C. Schönenberger, and J. Martinek.
    Acta Physica Polonica A, 127(2):493-495, feb 2015. [DOI]

    Entangled states are essential in basics quantum communication protocols and quantum cryptography. Ferromagnetic contacts can work as a spin detector, giving possibility of converting information about electron spin to the electric charge, and therefore, detection of entangled states with the electric current measurements is possible. Method of conrming entanglement with non-ideal detectors is presented, the impact of decoherence and noise on states and quality of entanglement is discussed. Entanglement witness (EW) operator method is compared with the CHSH inequalities approach. Required spin polarization for the EW is lower than for the CHSH inequalities. System with asymmetric spin polarizations of detectors was analyzed, including the CHSH inequalities and the EW method.


  • Local electrical tuning of the nonlocal signals in a Cooper pair splitter
    G. Fülöp, S. d’Hollosy, A. Baumgartner, P. Makk, V. A. Guzenko, M. H. Madsen, J. Nygård, C. Schönenberger, and S. Csonka.
    Physical Review B, 90:235412, dec 2014. [DOI] arXiv:1409.0818

    A Cooper pair splitter consists of a central superconducting contact, S, from which electrons are injected into two parallel, spatially separated quantum dots (QDs). This geometry and electron interactions can lead to correlated electrical currents due to the spatial separation of spin-singlet Cooper pairs from S. We present experiments on such a device with a series of bottom gates, which allows for spatially resolved tuning of the tunnel couplings between the QDs and the electrical contacts and between the QDs. Our main findings are gate-induced transitions between positive conductance correlation in the QDs due to Cooper pair splitting and negative correlations due to QD dynamics. Using a semi-classical rate equation model we show that the experimental findings are consistent with in-situ electrical tuning of the local and nonlocal quantum transport processes. In particular, we illustrate how the competition between Cooper pair splitting and local processes can be optimized in such hybrid nanostructures.

  • Entanglement witnessing and quantum cryptography with nonideal ferromagnetic detectors
    W. Kobus, A. Grudka, A. Baumgartner, D. Tomaszewski, C. Schönenberger, and Jan Martinek.
    Phys. Rev. B, 89:125404, mar 2014. [DOI] arXiv:1310.5640

    We investigate theoretically the use of non-ideal ferromagnetic contacts as a mean to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of η>1/3–√≈58 required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell’s inequality with η>1/2–√4≈84. In addition, we discuss the impact of decoherence and noise on entanglement detection and apply the presented framework to a simple quantum cryptography protocol. Our results are directly applicable to a large variety of experiments.

  • Nonlocal spectroscopy of Andreev bound states
    J. Schindele, A. Baumgartner, R. Maurand, M. Weiss, and C. Schönenberger.
    Phys. Rev. B, 89:45422, jan 2014. [DOI] arXiv:1311.0659

    We experimentally investigate Andreev bound states (ABSs) in a carbon nanotube quantum dot (QD) connected to a superconducting Nb lead (S). A weakly coupled normal metal contact acts as a tunnel probe that measures the energy dispersion of the ABSs. Moreover, we study the response of the ABS to nonlocal transport processes, namely, Cooper pair splitting and elastic co-tunnelling, which are enabled by a second QD fabricated on the same nanotube on the opposite side of S. We find an appreciable nonlocal conductance with a rich structure, including a sign reversal at the ground-state transition from the ABS singlet to a degenerate magnetic doublet. We describe our device by a simple rate equation model that captures the key features of our observations and demonstrates that the sign of the nonlocal conductance is a measure for the charge distribution of the ABS, given by the respective Bogoliubov-de Gennes amplitudes u and v.


  • Entanglement witnessing in superconducting beamsplitters
    H. Soller, L. Hofstetter, and D. Reeb.
    EPL (Europhysics Letters), 102(5):50009, jun 2013. [DOI] arXiv:1305.7061v1

    We analyse a large class of superconducting beamsplitters for which the Bell parameter (CHSH violation) is a simple function of the spin detector efficiency. For these superconducting beamsplitters all necessary information to compute the Bell parameter can be obtained in Y-junction setups for the beamsplitter. Using the Bell parameter as an entanglement witness, we propose an experiment which allows to verify the presence of entanglement in Cooper pair splitters.


  • Near-Unity Cooper Pair Splitting Efficiency
    J. Schindele, A. Baumgartner, and C. Schönenberger.
    Phys. Rev. Lett., 109(15):157002, oct 2012. [DOI] arXiv:1204.5777

    The two electrons of a Cooper pair in a conventional superconductor form a spin singlet and therefore a maximally entangled state. Recently, it was demonstrated that the two particles can be extracted from the superconductor into two spatially separated contacts via two quantum dots in a process called Cooper pair plitting (CPS). Competing transport processes, however, limit the efficiency of this process. Here we demonstrate efficiencies up to 90 percent, significantly larger than required to demonstrate interactiondominated CPS, and on the right order to test Bell�s inequality with electrons. We compare the CPS currents through both quantum dots, for which large apparent discrepancies are possible. The latter we explain intuitively and in a semiclassical master equation model. Large efficiencies are required to detect electron entanglement and for prospective electronics-based quantum information technologies.

  • Kondo effect and spin-active scattering in ferromagnet-superconductor junctions
    H. Soller, L. Hofstetter, S. Csonka, Levy A. Yeyati, C. Schönenberger, and A. Komnik.
    Phys. Rev. B, 85(17):174512, may 2012. [DOI] arXiv:1204.6581v1

    We study the interplay of superconducting and ferromagnetic correlations on charge transport in different geometries with a focus on both a quantum point contact as well as a quantum dot in the even and the odd state with and without spin-active scattering at the interface. In order to obtain a complete picture of the charge transport we calculate the full counting statistics in all cases and compare the results with experimental data. We show that spin-active scattering is an essential ingredient in the description of quantum point contacts. This holds also for quantum dots in an even charge state whereas it is strongly suppressed in a typical Kondo situation. We explain this feature by the strong asymmetry of the hybridisations with the quantum dot and show how Kondo peak splitting in a magnetic field can be used for spin filtering. For the quantum dot in the even state spin-active scattering allows for an explanation of the experimentally observed mini-gap feature.


  • Finite bias Cooper pair splitting
    L. Hofstetter, S. Csonka, A. Baumgartner, G. Fülöp, S. d’Hollosy, J. Nygård, and C. Schönenberger.
    Phys Rev. Lett., 107(13):136801, sep 2011. [DOI] arXiv:1105.2583

    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.


  • Hybrid superconductor – quantum dot devices
    De S. Franceschi, L. Kouwenhoven, C. Schönenberger, and W. Wernsdorfer.
    Nature Nanotechnology (invited), 5:703-711, sep 2010. [DOI]

    Advances in nanofabrication techniques have made it possible to make devices in which superconducting electrodes are connected to non-superconducting nanostructures such as quantum dots. The properties of these hybrid devices result from a combination of a macroscopic quantum phenomenon involving large numbers of electrons (superconductivity) and the ability to control single electrons, offered by quantum dots. Here we review research into electron transport and other fundamental processes that have been studied in these devices. We also describe potential applications, such as a transistor in which the direction of a supercurrent can be reversed by adding just one electron to a quantum dot.

  • Magnetic field and contact resistance dependence of non-local charge imbalance
    A. Kleine, A. Baumgartner, J. Trbovic, D. S. Golubev, A. D. Zaikin, and C. Schönenberger.
    Nanotechnology, 21:274002, jun 2010. [DOI] arXiv:0911.4427

    Crossed Andreev reflection (CAR) in metallic nanostructures, a possible basis for solid-state electron entangler devices, is usually investigated by detecting non-local voltages in multi-terminal superconductor/normal metal devices. This task is difficult because other subgap processes may mask the effects of CAR. One of these processes is the generation of charge imbalance (CI) and the diffusion of non-equilibrium quasi-particles in the superconductor. Here we demonstrate a characteristic dependence of non-local CI on a magnetic field applied parallel to the superconducting wire, which can be understood by a generalization of the standard description of CI to non-local experiments. These results can be used to distinguish CAR and CI and to extract CI relaxation times in superconducting nanostructures. In addition, we investigate the dependence of non-local CI on the resistance of the injector and detector contacts and demonstrate a quantitative agreement with a recent theory using only material and junction characteristics extracted from separate direct measurements.

  • Eine Trenneinrichtung für Quantenpaare
    C. Schönenberger.
    Physik in unserer Zeit, 41:58-59, mar 2010. [DOI]

    Die Quantenmechanik erlaubt neben der Überlagerung von Zuständen auch deren Verschränkung. Das betrifft Teilchen mit Ruhemasse wie Elektronen ebenso wie masselose Photonen. Zwei Forscherteams ist es jüngst gelungen, verschränkte Elektronen in Form von Cooper-Paaren als Quelle verschränkter Elektronen zu nutzen. Dies eröffnet neue Möglichkeiten für grundlegende Experimente zur Quantenmechanik und könnte den Weg zur Quanteninformation auf einem Chip ebnen.


  • Cooper pair splitter realized in a two-quantum-dot Y-junction
    L. Hofstetter, S. Csonka, J. Nygård, and C. Schönenberger.
    Nature, 461:960-963, aug 2009. [DOI]

    Non-locality is a fundamental property of quantum mechanics that manifests itself as correlations between spatially separated parts of a quantum system. A fundamental route for the exploration of such phenomena is the generation of Einstein–Podolsky–Rosen (EPR) pairs of quantum-entangled objects for the test of so-called Bell inequalities. Whereas such experimental tests of non-locality have been successfully conducted with pairwise entangled photons, it has not yet been possible to realize an electronic analogue of it in the solid state, where spin-1/2 mobile electrons are the natural quantum objects3. The difficulty stems from the fact that electrons are immersed in a macroscopic ground state—the Fermi sea—which prevents the straightforward generation and splitting of entangled pairs of electrons on demand. A superconductor, however, could act as a source of EPR pairs of electrons, because its ground-state is composed of Cooper pairs in a spin-singlet state. These Cooper pairs can be extracted from a superconductor by tunnelling, but, to obtain an efficient EPR source of entangled electrons, the splitting of the Cooper pairs into separate electrons has to be enforced. This can be achieved by having the electrons ‘repel’ each other by Coulomb interaction. Controlled Cooper pair splitting can thereby be realized by coupling of the superconductor to two normal metal drain contacts by means of individually tunable quantum dots. Here we demonstrate the first experimental realization of such a tunable Cooper pair splitter, which shows a surprisingly high efficiency. Our findings open a route towards a first test of the EPR paradox and Bell inequalities in the solid state.

  • Contact resistance dependence of crossed Andreev reflection
    A. Kleine, A. Baumgartner, J. Trbovic, and C. Schönenberger.
    Eur. Phys. Lett., 87:27011, 2009. [DOI] arXiv:0812.3553

    We report experiments in nanometer-scaled superconductor/normal metal hybrid devices which show that in a small window of contact resistances, crossed Andreev reflection (CAR) can dominate the nonlocal transport for all energies below the superconducting gap. Besides crossed Andreev reflection, elastic cotunneling (EC) and nonlocal charge imbalance can be identified as competing subgap transport mechanisms in temperature-dependent four-terminal nonlocal measurements. We demonstrate a systematic change of the nonlocal resistance vs. bias characteristics with increasing contact resistances, which can be varied in the fabrication process. For samples with higher contact resistances, CAR is weakened relative to EC in the midgap regime, possibly due to dynamical Coulomb blockade. Gaining control of crossed Andreev reflection is an important step towards the realization of a solid-state entangler.


  • Shot-noise and conductance measurements of transparent superconductor/two-dimensional electron gas junctions
    B. -R. Choi, A. E. Hansen, T. Kontos, C. Hoffmann, S. Oberholzer, W. Belzig, C. Schönenberger, T. Akazaki, and H. Takayanagi.
    Phys. Rev. B, 72:24501, jul 2005. [DOI] arXiv:0410621

    We have measured the conductance and shot noise of superconductor-normal metal S-N junctions between a niobium Nb film and a two-dimensional electron gas 2DEG, formed in an InAs-based semiconductor heterostructure. Adjacent to the junction, the 2DEG is shaped into a sub-micrometer beam splitter. The current shot noise measured through one arm of the beam splitter is found to be enhanced due to Andreev reflection. Both noise and conductance measurements indicate that the Nb-2DEG interface is of high quality with a transparency approaching 60–70 %. The present device can be seen as a quasi-ballistic S-N beam-splitter junction.