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):

  • Spin Cross-Correlation Experiments in an Electron Entangler
    A. Bordoloi, V. Zannier, L. Sorba, C. Schönenberger, and A. Baumgartner.
    Nature  612, 454-458 (2022)
    [arXiv:2203.07970 ] [ Open Data ] [Abstract ]

    Correlations are fundamental in describing many body systems – not only in natural sciences. However, in experiments, correlations are notoriously difficult to assess on the microscopic scale, especially for electron spins. Here, we demonstrate a direct measurement of the spin cross-correlations between the currents of a Cooper pair splitter, an electronic device that emits electrons originating from Cooper pairs in a superconductor. While it is firmly established theoretically that these electron pairs form maximally spin-entangled singlet states with opposite spin projections, no spin correlation experiments have been demonstrated so far. We use ferromagnetic sidegates, compatible with superconducting electronic structures, to individually spin polarize the transmissions of two quantum dots fabricated in the two electronic paths, which act as tunable spin filters. The signals are detected in standard transport and in highly sensitive transconductance experiments. We find that the spin-cross correlation is negative, compatible with spin singlet emission, and deviates from the ideal value mostly due to a finite overlap of the Zeeman split quantum dot states. Our results demonstrate a new route to perform spin auto- and cross correlation experiments in nanometer scaled electronic devices, especially suitable for those relying on magnetic field sensitive superconducting elements, like unconventional, triplet or topologically non-trivial superconductors, or to perform Bell tests with massive particles, like electrons.

  • From Cooper pair splitting to the nonlocal spectroscopy of a Shiba state
    Z. Scherübl, G. Fülöp, J. Gramich, A. Pályi, C. Schönenberger, J. Nygard, and S. Csonka.
    Phys. Rev. Research  4, 23143 (2022)
    [arXiv:2108.12155 ] [ Open Data ] [Abstract ]

    Cooper pair splitting (CPS) is a way to create spatially separated, entangled electron pairs. To this day, CPS is often identified in experiments as a spatial current correlation. However, such correlations can arise even in the absence of CPS, when a quantum dot is strongly coupled to the superconductor, and a subgap Shiba state is formed. Here, we present a detailed experimental characterization of those spatial current correlations, as the tunnel barrier strength between the quantum dot and the neighboring normal electrode is tuned. The correlation of the non-local signal and the barrier strength reveals a competition between CPS and the non-local probing of the Shiba state. We describe our experiment with a simple transport model, and obtain the tunnel couplings of our device by fitting the model’s prediction to the measured conductance correlation curve. Furthermore, we use our theory to extract the contribution of CPS to the non-local signal.

  • 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. B  98, 35413 (2018)
    [arXiv:1804.02590 ] [Abstract ]

    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
    Shoji Baba, Christian Jünger, Sadashige Matsuo, Andreas Baumgartner, Yosuke Sato, Hiroshi Kamata, Kan Li, Sören Jeppesen, Lars Samuelson, Hongqi Xu, Christian Schönenberger, and Seigo Tarucha.
    New Journal of Physics  20, 63021 (2018)
    [arXiv:1802.08059 ] [Abstract ]

    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 (2017)
    [arXiv:1612.01201 ] [Abstract ]

    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.

  • A success story
    Christel Möller and Christian Schönenberger.
    Nature Nanotechnology  11, 908 (2016)

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

    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, 227003 (2015)
    [arXiv:1507.01036 ] [Abstract ]

    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.

  • 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 (2014)
    [arXiv:1409.0818 ] [Abstract ]

    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 (2014)
    [arXiv:1310.5640 ] [Abstract ]

    We investigate theoretically the use of nonideal ferromagnetic contacts as a means to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of eta > 58\% required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell’s inequality with eta > 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 (2014)
    [arXiv:1311.0659 ] [Abstract ]

    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 non-local transport processes, namely Cooper pair splitting and elastic co-tunnelling, that are enabled by a second QD fabricated on the same nanotube on the opposite side of S. We find an appreciable non-local 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 non-local conductance is a measure for the charge distribution of the ABS, given by the respective Bogoliubov-de Gennes amplitudes u and v.

  • Near-Unity Cooper Pair Splitting Efficiency
    J. Schindele, A. Baumgartner, and C. Schönenberger.
    Phys. Rev. Lett.  109, 157002 (2012)
    [Abstract ]

    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.