Publications by Ferdinand Kuemmeth

  • 2024
    • Real-time two-axis control of a spin qubit - Abstract
      • Optimal control of qubits requires the ability to adapt continuously to their ever-changing environment. We demonstrate a real-time control protocol for a two-electron singlet-triplet qubit with two fluctuating Hamiltonian parameters. Our approach leverages single-shot readout classification and dynamic waveform generation, allowing full Hamiltonian estimation to dynamically stabilize and optimize the qubit performance. Powered by a field-programmable gate array (FPGA), the quantum control electronics estimates the Overhauser field gradient between the two electrons in real time, enabling controlled Overhauser-driven spin rotations and thus bypassing the need for micromagnets or nuclear polarization protocols. It also estimates the exchange interaction between the two electrons and adjusts their detuning, resulting in extended coherence of Hadamard rotations when correcting for fluctuations of both qubit axes. Our study emphasizes the critical role of feedback in enhancing the performance and stability of quantum devices affected by quasistatic noise. Feedback will play an essential role in improving performance in various qubit implementations that go beyond spin qubits, helping realize the full potential of quantum devices for quantum technology applications.
    • Fabrizio Berritta, Torbjørn Rasmussen, Jan A. Krzywda, Joost van der Heijden, Federico Fedele, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Evert van Nieuwenburg, Jeroen Danon, Anasua Chatterjee, Ferdinand Kuemmeth
      Journal reference: Nature Communications 15, 1676 (2024) [pdf]
      DOI: 10.1038/s41467-024-45857-0

  • 2023
    • Gate reflectometry in dense quantum dot arrays - Abstract
      • Silicon quantum devices are maturing from academic single- and two-qubit devices to industrially-fabricated dense quantum-dot (QD) arrays, increasing operational complexity and the need for better pulsed-gate and readout techniques. We perform gate-voltage pulsing and gate-based reflectometry measurements on a dense 2$\times$2 array of silicon quantum dots fabricated in a 300-mm-wafer foundry. Utilizing the strong capacitive couplings within the array, it is sufficient to monitor only one gate electrode via high-frequency reflectometry to establish single-electron occupation in each of the four dots and to detect single-electron movements with high bandwidth. A global top-gate electrode adjusts the overall tunneling times, while linear combinations of side-gate voltages yield detailed charge stability diagrams. To test for spin physics and Pauli spin blockade at finite magnetic fields, we implement symmetric gate-voltage pulses that directly reveal bidirectional interdot charge relaxation as a function of the detuning between two dots. Charge sensing within the array can be established without the involvement of adjacent electron reservoirs, important for scaling such split-gate devices towards longer 2$\times$N arrays. Our techniques may find use in the scaling of few-dot spin-qubit devices to large-scale quantum processors.
    • Fabio Ansaloni, Heorhii Bohuslavskyi, Federico Fedele, Torbjørn Rasmussen, Bertram Brovang, Fabrizio Berritta, Amber Heskes, Jing Li, Louis Hutin, Benjamin Venitucci, Benoit Bertrand, Maud Vinet, Yann-Michel Niquet, Anasua Chatterjee, Ferdinand Kuemmeth
      Journal reference: New J. Phys. 25, 033023 (2023) [pdf]
      DOI: 10.1088/1367-2630/acc126

    • An elongated quantum dot as a distributed charge sensor - Abstract
      • Increasing the separation between semiconductor quantum dots offers scaling advantages by fa- cilitating gate routing and the integration of sensors and charge reservoirs. Elongated quantum dots have been utilized for this purpose in GaAs heterostructures to extend the range of spin-spin interactions. Here, we study a metal-oxide-semiconductor (MOS) device where two quantum dot arrays are separated by an elongated quantum dot (340 nm long, 50 nm wide). We monitor charge transitions of the elongated quantum dot by measuring radiofrequency single-electron currents to a reservoir to which we connect a lumped-element resonator. We operate the dot as a single electron box to achieve charge sensing of remote quantum dots in each array, separated by a distance of 510 nm. Simultaneous charge detection on both ends of the elongated dot demonstrates that the charge is well distributed across its nominal length, supported by the simulated quantum-mechanical electron density. Our results illustrate how single-electron boxes can be realised with versatile foot- prints that may enable novel and compact quantum processor layouts, offering distributed charge sensing in addition to the possibility of mediated coupling.
    • 2301.01650v1 [pdf]
      S. M. Patomäki, J. Williams, F. Berritta, C. Laine, M. A. Fogarty, R. C. C. Leon, J. Jussot, S. Kubicek, A. Chatterjee, B. Govoreanu, F. Kuemmeth, J. J. L. Morton, M. F. Gonzalez-Zalba

    • Probing quantum devices with radio-frequency reflectometry - Abstract
      • Many important phenomena in quantum devices are dynamic, meaning that they cannot be studied using time-averaged measurements alone. Experiments that measure such transient effects are collectively known as fast readout. One of the most useful techniques in fast electrical readout is radio-frequency reflectometry, which can measure changes in impedance (both resistive and reactive) even when their duration is extremely short, down to a microsecond or less. Examples of reflectometry experiments, some of which have been realised and others so far only proposed, include projective measurements of qubits and Majorana devices for quantum computing, real-time measurements of mechanical motion and detection of non-equilibrium temperature fluctuations. However, all of these experiments must overcome the central challenge of fast readout: the large mismatch between the typical impedance of quantum devices (set by the resistance quantum) and of transmission lines (set by the impedance of free space). Here, we review the physical principles of radio-frequency reflectometry and its close cousins, measurements of radio-frequency transmission and emission. We explain how to optimise the speed and sensitivity of a radio-frequency measurement, and how to incorporate new tools such as superconducting circuit elements and quantum-limited amplifiers into advanced radio-frequency experiments. Our aim is three-fold: to introduce the readers to the technique, to review the advances to date and to motivate new experiments in fast quantum device dynamics. Our intended audience includes experimentalists in the field of quantum electronics who want to implement radio-frequency experiments or improve them, together with physicists in related fields who want to understand how the most important radio-frequency measurements work.
    • Florian Vigneau, Federico Fedele, Anasua Chatterjee, David Reilly, Ferdinand Kuemmeth, Fernando Gonzalez-Zalba, Edward Laird, Natalia Ares
      Journal reference: Applied Physics Reviews 10, 021305 (2023) [pdf]
      DOI: 10.1063/5.0088229

    • Electrostatic control of quasiparticle poisoning in a hybrid semiconductor-superconductor island - Abstract
      • The performance of superconducting devices is often degraded by the uncontrolled appearance and disappearance of quasiparticles, a process known as poisoning. We demonstrate electrostatic control of quasiparticle poisoning in the form of single-charge tunneling across a fixed barrier onto a Coulomb island in an InAs/Al hybrid nanowire. High-bandwidth charge sensing was used to monitor charge occupancy of the island across Coulomb blockade peaks, where tunneling rates were maximal, and Coulomb valleys, where tunneling was absent. Electrostatic gates changed on-peak tunneling rates by two orders of magnitude for a barrier with fixed normal-state resistance, which we attribute to gate dependence of the size and softness of the induced superconducting gap on the island, corroborated by separate density-of-states measurements. Temperature and magnetic field dependence of tunneling rates are also investigated.
    • H. Q. Nguyen, D. Sabonis, D. Razmadze, E. T. Mannila, V. F. Maisi, D. M. T. van Zanten, E. C. T. O'Farrell, P. Krogstrup, F. Kuemmeth, J. P. Pekola, C. M. Marcus
      Journal reference: Phys. Rev. B 108, L041302 (2023) [pdf]
      DOI: 10.1103/PhysRevB.108.L041302

  • 2022
    • Autonomous Estimation of High-Dimensional Coulomb Diamonds from Sparse Measurements - Abstract
      • Quantum dot arrays possess ground states governed by Coulomb energies, utilized prominently by singly occupied quantum dots, each implementing a spin qubit. For such quantum processors, the controlled transitions between ground states are of operational significance, as these allow the control of quantum information within the array such as qubit initialization and entangling gates. For few-dot arrays, ground states are traditionally mapped out by performing dense raster-scan measurements in control-voltage space. These become impractical for larger arrays due to the large number of measurements needed to sample the high-dimensional gate-voltage hypercube and the comparatively little information extracted. We develop a hardware-triggered detection method based on reflectometry, to acquire measurements directly corresponding to transitions between ground states. These measurements are distributed sparsely within the high-dimensional voltage space by executing line searches proposed by a learning algorithm. Our autonomous software-hardware algorithm accurately estimates the polytope of Coulomb blockade boundaries, experimentally demonstrated in a 2$\times$2 array of silicon quantum dots.
    • Anasua Chatterjee, Fabio Ansaloni, Torbjørn Rasmussen, Bertram Brovang, Federico Fedele, Heorhii Bohuslavskyi, Oswin Krause, Ferdinand Kuemmeth
      Journal reference: Physical Review Applied 18, 064040 (2022) [pdf]
      DOI: 10.1103/PhysRevApplied.18.064040

    • Microwave sensing of Andreev bound states in a gate-defined superconducting quantum point contact - Abstract
      • We use a superconducting microresonator as a cavity to sense absorption of microwaves by a superconducting quantum point contact defined by surface gates over a proximitized two-dimensional electron gas. Renormalization of the cavity frequency with phase difference across the point contact is consistent with adiabatic coupling to Andreev bound states. Near $\pi$ phase difference, we observe random fluctuations in absorption with gate voltage, related to quantum interference-induced modulations in the electron transmission. We identify features consistent with the presence of single Andreev bound states and describe the Andreev-cavity interaction using a dispersive Jaynes-Cummings model. By fitting the weak Andreev-cavity coupling, we extract ~GHz decoherence consistent with charge noise and the transmission dispersion associated with a localized state.
    • Vivek Chidambaram, Anders Kringhøj, Lucas Casparis, Ferdinand Kuemmeth, Tiantian Wang, Candice Thomas, Sergei Gronin, Geoffrey C. Gardner, Zhengyi Cui, Chenlu Liu, Kristof Moors, Michael J. Manfra, Karl D. Petersson, Malcolm R. Connolly
      Journal reference: Phys. Rev. Research 4, 023170 (2022) [pdf]
      DOI: 10.1103/PhysRevResearch.4.023170

    • Learning Coulomb Diamonds in Large Quantum Dot Arrays - Abstract
      • We introduce an algorithm that is able to find the facets of Coulomb diamonds in quantum dot arrays. We simulate these arrays using the constant-interaction model, and rely only on one-dimensional raster scans (rays) to learn a model of the device using regularized maximum likelihood estimation. This allows us to determine, for a given charge state of the device, which transitions exist and what the compensated gate voltages for these are. For smaller devices the simulator can also be used to compute the exact boundaries of the Coulomb diamonds, which we use to assess that our algorithm correctly finds the vast majority of transitions with high precision.
    • Oswin Krause, Anasua Chatterjee, Ferdinand Kuemmeth, Evert van Nieuwenburg
      Journal reference: SciPost Phys. 13, 084 (2022) [pdf]
      DOI: 10.21468/SciPostPhys.13.4.084

    • Estimation of Convex Polytopes for Automatic Discovery of Charge State Transitions in Quantum Dot Arrays - Abstract
      • In spin based quantum dot arrays, material or fabrication imprecisions affect the behaviour of the device, which must be taken into account when controlling it. This requires measuring the shape of specific convex polytopes. In this work, we present an algorithm that automatically discovers count, shape and size of the facets of a convex polytope from measurements. Results on simulated devices as well as a real 2x2 spin qubit array show that we can reliably find the facets of the convex polytopes, including small facets with sizes on the order of the measurement precision.
    • Oswin Krause, Torbjørn Rasmussen, Bertram Brovang, Anasua Chatterjee, Ferdinand Kuemmeth
      Journal reference: Electronics 11, 2327 (2022) [pdf]
      DOI: 10.3390/electronics11152327

  • 2021
    • Protected solid-state qubits - Abstract
      • The implementation of large-scale fault-tolerant quantum computers calls for the integration of millions of physical qubits, with error rates of physical qubits significantly below 1%. This outstanding engineering challenge may benefit from emerging qubits that are protected from dominating noise sources in the qubits' environment. In addition to different noise reduction techniques, protective approaches typically encode qubits in global or local decoherence-free subspaces, or in dynamical sweet spots of driven systems. We exemplify such protective qubits by reviewing the state-of-art in protected solid-state qubits based on semiconductors, superconductors, and hybrid devices.
    • Jeroen Danon, Anasua Chatterjee, András Gyenis, Ferdinand Kuemmeth
      Journal reference: Appl. Phys. Lett. 119, 260502 (2021) [pdf]
      DOI: 10.1063/5.0073945

    • Simultaneous Operations in a Two-Dimensional Array of Singlet-Triplet Qubits - Abstract
      • In many physical approaches to quantum computation, error-correction schemes assume the ability to form two-dimensional qubit arrays with nearest-neighbor couplings and parallel operations at multiple qubit sites. While semiconductor spin qubits exhibit long coherence times relative to their operation speed and single-qubit fidelities above error correction thresholds, multiqubit operations in two-dimensional arrays have been limited by fabrication, operation, and readout challenges. We present a two-by-two array of four singlet-triplet qubits in gallium arsenide and show simultaneous coherent operations and four-qubit measurements via exchange oscillations and frequency-multiplexed single-shot measurements. A larger multielectron quantum dot is fabricated in the center of the array as a tunable interqubit link, which we utilize to demonstrate coherent spin exchange with selected qubits. Our techniques are extensible to other materials, indicating a path towards quantum processors with gate-controlled spin qubits.
    • Federico Fedele, Anasua Chatterjee, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Ferdinand Kuemmeth
      Journal reference: PRX Quantum 2, 040306 (2021) [pdf]
      DOI: 10.1103/PRXQuantum.2.040306

    • Roadmap on quantum nanotechnologies - Abstract
      • Quantum phenomena are typically observable at length and time scales smaller than those of our everyday experience, often involving individual particles or excitations. The past few decades have seen a revolution in the ability to structure matter at the nanoscale, and experiments at the single particle level have become commonplace. This has opened wide new avenues for exploring and harnessing quantum mechanical effects in condensed matter. These quantum phenomena, in turn, have the potential to revolutionize the way we communicate, compute and probe the nanoscale world. Here, we review developments in key areas of quantum research in light of the nanotechnologies that enable them, with a view to what the future holds. Materials and devices with nanoscale features are used for quantum metrology and sensing, as building blocks for quantum computing, and as sources and detectors for quantum communication. They enable explorations of quantum behaviour and unconventional states in nano- and opto-mechanical systems, low-dimensional systems, molecular devices, nano-plasmonics, quantum electrodynamics, scanning tunnelling microscopy, and more. This rapidly expanding intersection of nanotechnology and quantum science/technology is mutually beneficial to both fields, laying claim to some of the most exciting scientific leaps of the last decade, with more on the horizon.
    • Arne Laucht, Frank Hohls, Niels Ubbelohde, M Fernando Gonzalez-Zalba, David J Reilly, Søren Stobbe, Tim Schröder, Pasquale Scarlino, Jonne V Koski, Andrew Dzurak, Chih-Hwan Yang, Jun Yoneda, Ferdinand Kuemmeth, Hendrik Bluhm, Jarryd Pla, Charles Hill, Joe Salfi, Akira Oiwa, Juha T Muhonen, Ewold Verhagen, Matthew D LaHaye, Hyun Ho Kim, Adam W Tsen, Dimitrie Culcer, Attila Geresdi, Jan A Mol, Varun Mohan, Prashant K Jain, Jonathan Baugh
      Journal reference: Nanotechnology 32, 162003 (2021) [pdf]
      DOI: 10.1088/1361-6528/abb333

    • Roadmap on quantum nanotechnologies - Abstract
      • Gate-defined quantum dots in gallium arsenide (GaAs) have been used extensively for pioneering spin qubit devices due to the relative simplicity of fabrication and favourable electronic properties such as a single conduction band valley, a small effective mass, and stable dopants. GaAs spin qubits are readily produced in many labs and are currently studied for various applications, including entanglement, quantum non-demolition measurements, automatic tuning, multi-dot arrays, coherent exchange coupling, and teleportation. Even while much attention is shifting to other materials, GaAs devices will likely remain a workhorse for proof-of-concept quantum information processing and solid-state experiments.
    • Ferdinand Kuemmeth, Hendrik Bluhm
      Journal reference: Nanotechnology 32, 162003 (2021) [pdf]
      DOI: 10.1088/1361-6528/abb333

    • Semiconductor qubits in practice - Abstract
      • In recent years semiconducting qubits have undergone a remarkable evolution, making great strides in overcoming decoherence as well as in prospects for scalability, and have become one of the leading contenders for the development of large-scale quantum circuits. In this Review we describe the current state of the art in semiconductor charge and spin qubits based on gate-controlled semiconductor quantum dots, shallow dopants, and color centers in wide band gap materials. We frame the relative strengths of the different semiconductor qubit implementations in the context of quantum simulations, computing, sensing and networks. By highlighting the status and future perspectives of the basic types of semiconductor qubits, this Review aims to serve as a technical introduction for non-specialists as well as a forward-looking reference for scientists intending to work in this field.
    • Anasua Chatterjee, Paul Stevenson, Silvano De Franceschi, Andrea Morello, Nathalie de Leon, Ferdinand Kuemmeth
      Journal reference: Nature Reviews Physics (2021) [pdf]
      DOI: 10.1038/s42254-021-00283-9

  • 2020
    • Parity-Protected Superconductor-Semiconductor Qubit - Abstract
      • Coherence of superconducting qubits can be improved by implementing designs that protect the parity of Cooper pairs on superconducting islands. Here, we introduce a parity-protected qubit based on voltage-controlled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energy-phase relation of few-channel junctions. A symmetric interferometer formed by two such junctions, gate-tuned into balance and frustrated by a half-quantum of applied flux, yields a cos(2{\phi}) Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate that relaxation of the qubit can be suppressed tenfold by tuning into the protected regime.
    • T. W. Larsen, M. E. Gershenson, L. Casparis, A. Kringhøj, N. J. Pearson, R. P. G. McNeil, F. Kuemmeth, P. Krogstrup, K. D. Petersson, C. M. Marcus
      Journal reference: Phys. Rev. Lett. 125, 056801 (2020) [pdf]
      DOI: 10.1103/PhysRevLett.125.056801

    • Single-electron operations in a foundry-fabricated array of quantum dots - Abstract
      • Silicon spin qubits have achieved high-fidelity one- and two-qubit gates, above error correction thresholds, promising an industrial route to fault-tolerant quantum computation. A significant next step for the development of scalable multi-qubit processors is the operation of foundry-fabricated, extendable two-dimensional (2D) arrays. In gallium arsenide, 2D quantum-dot arrays recently allowed coherent spin operations and quantum simulations. In silicon, 2D arrays have been limited to transport measurements in the many-electron regime. Here, we operate a foundry-fabricated silicon 2x2 array in the few-electron regime, achieving single-electron occupation in each of the four gate-defined quantum dots, as well as reconfigurable single, double, and triple dots with tunable tunnel couplings. Pulsed-gate and gate-reflectometry techniques permit single-electron manipulation and single-shot charge readout, while the two-dimensionality allows the spatial exchange of electron pairs. The compact form factor of such arrays, whose foundry fabrication can be extended to larger 2xN arrays, along with the recent demonstration of coherent spin control and readout, paves the way for dense qubit arrays for quantum computation and simulation.
    • Fabio Ansaloni, Anasua Chatterjee, Heorhii Bohuslavskyi, Benoit Bertrand, Louis Hutin, Maud Vinet, Ferdinand Kuemmeth
      Journal reference: Nature Communications 11, 6399 (2020) [pdf]
      DOI: 10.1038/s41467-020-20280-3

  • 2019
    • Fast Charge Sensing of Si/SiGe Quantum Dots via a High-Frequency Accumulation Gate - Abstract
      • Quantum dot arrays are a versatile platform for the implementation of spin qubits, as high-bandwidth sensor dots can be integrated with single-, double- and triple-dot qubits yielding fast and high-fidelity qubit readout. However, for undoped silicon devices, reflectometry off sensor ohmics suffers from the finite resistivity of the two-dimensional electron gas (2DEG), and alternative readout methods are limited to measuring qubit capacitance, rather than qubit charge. By coupling a surface-mount resonant circuit to the plunger gate of a high-impedance sensor, we realized a fast charge sensing technique that is compatible with resistive 2DEGs. We demonstrate this by acquiring at high speed charge stability diagrams of double- and triple-dot arrays in Si/SiGe heterostructures as well as pulsed-gate single-shot charge and spin readout with integration times as low as 2.4 $\mu$s.
    • Christian Volk, Anasua Chatterjee, Fabio Ansaloni, Charles M. Marcus, Ferdinand Kuemmeth
      Journal reference: Nano Letters 19, 5628-5633 (2019) [pdf]
      DOI: 10.1021/acs.nanolett.9b02149

    • Radio-Frequency Methods for Majorana-Based Quantum Devices: Fast Charge Sensing and Phase-Diagram Mapping - Abstract
      • Radio-frequency (RF) reflectometry is implemented in hybrid semiconductor-superconductor nanowire systems designed to probe Majorana zero modes. Two approaches are presented. In the first, hybrid nanowire-based devices are part of a resonant circuit, allowing conductance to be measured as a function of several gate voltages ~40 times faster than using conventional low-frequency lock-in methods. In the second, nanowire devices are capacitively coupled to a nearby RF single-electron transistor made from a separate nanowire, allowing RF detection of charge, including charge-only measurement of the crossover from 2e inter-island charge transitions at zero magnetic field to 1e transitions at axial magnetic fields above 0.6 T, where a topological state is expected. Single-electron sensing yields signal-to-noise exceeding 3 and visibility 99.8% for a measurement time of 1 {\mu}s.
    • Davydas Razmadze, Deividas Sabonis, Filip K. Malinowski, Gerbold C. Menard, Sebastian Pauka, Hung Nguyen, David M. T. van Zanten, Eoin C. T. O'Farrell, Judith Suter, Peter Krogstrup, Ferdinand Kuemmeth, Charles M. Marcus
      Journal reference: Phys. Rev. Applied 11, 064011 (2019) [pdf]
      DOI: 10.1103/PhysRevApplied.11.064011

    • Fast spin exchange across a multielectron mediator - Abstract
      • The Heisenberg exchange interaction between neighboring quantum dots allows precise voltage control over spin dynamics, due to the ability to precisely control the overlap of orbital wavefunctions by gate electrodes. This allows the study of fundamental electronic phenomena and finds applications in quantum information processing. Although spin-based quantum circuits based on short-range exchange interactions are possible, the development of scalable, longer-range coupling schemes constitutes a critical challenge within the spin-qubit community. Approaches based on capacitative coupling and cavity-mediated interactions effectively couple spin qubits to the charge degree of freedom, making them susceptible to electrically-induced decoherence. The alternative is to extend the range of the Heisenberg exchange interaction by means of a quantum mediator. Here, we show that a multielectron quantum dot with 50-100 electrons serves as an excellent mediator, preserving speed and coherence of the resulting spin-spin coupling while providing several functionalities that are of practical importance. These include speed (mediated two-qubit rates up to several gigahertz), distance (of order of a micrometer), voltage control, possibility of sweet spot operation (reducing susceptibility to charge noise), and reversal of the interaction sign (useful for dynamical decoupling from noise).
    • Filip K. Malinowski, Frederico Martins, Thomas B. Smith, Stephen D. Bartlett, Andrew C. Doherty, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth
      Journal reference: Nature Communications 10, 1196 (2019) [pdf]
      DOI: 10.1038/s41467-019-09194-x

    • Voltage-controlled superconducting quantum bus - Abstract
      • We demonstrate the ability of an epitaxial semiconductor-superconductor nanowire to serve as a field-effect switch to tune a superconducting cavity. Two superconducting gatemon qubits are coupled to the cavity, which acts as a quantum bus. Using a gate voltage to control the superconducting switch yields up to a factor of 8 change in qubit-qubit coupling between the on and off states without detrimental effect on qubit coherence. High-bandwidth operation of the coupling switch on nanosecond timescales degrades qubit coherence.
    • L. Casparis, N. J. Pearson, A. Kringhøj, T. W. Larsen, F. Kuemmeth, J. Nygård, P. Krogstrup, K. D. Petersson, C. M. Marcus
      Journal reference: Phys. Rev. B 99, 085434 (2019) [pdf]
      DOI: 10.1103/PhysRevB.99.085434

  • 2018
    • Superconducting gatemon qubit based on a proximitized two-dimensional electron gas - Abstract
      • The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies and interqubit coupling strengths, to the gain of parametric amplifiers for quantum-limited readout. The inductance is either set by tailoring the metal-oxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices (SQUIDs) with local current-biased flux lines. JJs based on superconductor-semiconductor hybrids represent a tantalizing all-electric alternative. The gatemon is a recently developed transmon variant which employs locally gated nanowire (NW) superconductor-semiconductor JJs for qubit control. Here, we go beyond proof-of-concept and demonstrate that semiconducting channels etched from a wafer-scale two-dimensional electron gas (2DEG) are a suitable platform for building a scalable gatemon-based quantum computer. We show 2DEG gatemons meet the requirements by performing voltage-controlled single qubit rotations and two-qubit swap operations. We measure qubit coherence times up to ~2 us, limited by dielectric loss in the 2DEG host substrate.
    • Lucas Casparis, Malcolm R. Connolly, Morten Kjaergaard, Natalie J. Pearson, Anders Kringhøj, Thorvald W. Larsen, Ferdinand Kuemmeth, Tiantian Wang, Candice Thomas, Sergei Gronin, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Karl D. Petersson
      Journal reference: Nature Nanotechnology 13, 915 (2018) [pdf]
      DOI: 10.1038/s41565-018-0207-y

    • Spin of a Multielectron Quantum Dot and Its Interaction with a Neighboring Electron - Abstract
      • We investigate the spin of a multielectron GaAs quantum dot in a sequence of nine charge occupancies, by exchange coupling the multielectron dot to a neighboring two-electron double quantum dot. For all nine occupancies, we make use of a leakage spectroscopy technique to reconstruct the spectrum of spin states in the vicinity of the interdot charge transition between a single- and a multielectron quantum dot. In the same regime we also perform time-resolved measurements of coherent exchange oscillations between the single- and multielectron quantum dot. With these measurements, we identify distinct characteristics of the multielectron spin state, depending on whether the dot's occupancy is even or odd. For three out of four even occupancies we do not observe any exchange interaction with the single quantum dot, indicating a spin-0 ground state. For the one remaining even occupancy, we observe an exchange interaction that we associate with a spin-1 multielectron quantum dot ground state. For all five of the odd occupancies, we observe an exchange interaction associated with a spin-1/2 ground state. For three of these odd occupancies, we clearly demonstrate that the exchange interaction changes sign in the vicinity of the charge transition. For one of these, the exchange interaction is negative (i.e. triplet-preferring) beyond the interdot charge transition, consistent with the observed spin-1 for the next (even) occupancy. Our experimental results are interpreted through the use of a Hubbard model involving two orbitals of the multielectron quantum dot. Allowing for the spin correlation energy (i.e. including a term favoring Hund's rules) and different tunnel coupling to different orbitals, we qualitatively reproduce the measured exchange profiles for all occupancies.
    • Filip K. Malinowski, Frederico Martins, Thomas B. Smith, Stephen D. Bartlett, Andrew C. Doherty, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth
      Journal reference: Phys. Rev. X 8, 011045 (2018) [pdf]
      DOI: 10.1103/PhysRevX.8.011045

    • Anharmonicity of a superconducting qubit with a few-mode Josephson junction - Abstract
      • Coherent operation of gate-voltage-controlled hybrid transmon qubits (gatemons) based on semiconductor nanowires was recently demonstrated. Here we experimentally investigate the anharmonicity in epitaxial InAs-Al Josephson junctions, a key parameter for their use as a qubit. Anharmonicity is found to be reduced by roughly a factor of two compared to conventional metallic junctions, and dependent on gate voltage. Experimental results are consistent with a theoretical model, indicating that Josephson coupling is mediated by a small number of highly transmitting modes in the semiconductor junction.
    • A. Kringhøj, L. Casparis, M. Hell, T. W. Larsen, F. Kuemmeth, M. Leijnse, K. Flensberg, P. Krogstrup, J. Nygård, K. D. Petersson, C. M. Marcus
      Journal reference: Phys. Rev. B 97, 060508 (2018) [pdf]
      DOI: 10.1103/PhysRevB.97.060508

  • 2017
    • Negative Spin Exchange in a Multielectron Quantum Dot - Abstract
      • By operating a one-electron quantum dot (fabricated between a multielectron dot and a one-electron reference dot) as a spectroscopic probe, we study the spin properties of a gate-controlled multielectron GaAs quantum dot at the transition between odd and even occupation number. We observe that the multielectron groundstate transitions from spin-1/2-like to singlet-like to triplet-like as we increase the detuning towards the next higher charge state. The sign reversal in the inferred exchange energy persists at zero magnetic field, and the exchange strength is tunable by gate voltages and in-plane magnetic fields. Complementing spin leakage spectroscopy data, the inspection of coherent multielectron spin exchange oscillations provides further evidence for the sign reversal and, inferentially, for the importance of non-trivial multielectron spin exchange correlations.
    • Frederico Martins, Filip K. Malinowski, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth
      Journal reference: Phys. Rev. Lett. 119, 227701 (2017) [pdf]
      DOI: 10.1103/PhysRevLett.119.227701

    • Spectrum of the Nuclear Environment for GaAs Spin Qubits - Abstract
      • Using a singlet-triplet spin qubit as a sensitive spectrometer of the GaAs nuclear spin bath, we demonstrate that the spectrum of Overhauser noise agrees with a classical spin diffusion model over six orders of magnitude in frequency, from 1 mHz to 1 kHz, is flat below 10 mHz, and falls as $1/f^2$ for frequency $f \! \gtrsim \! 1$ Hz. Increasing the applied magnetic field from 0.1 T to 0.75 T suppresses electron-mediated spin diffusion, which decreases spectral content in the $1/f^2$ region and lowers the saturation frequency, each by an order of magnitude, consistent with a numerical model. Spectral content at megahertz frequencies is accessed using dynamical decoupling, which shows a crossover from the few-pulse regime ($\lesssim \! 16$ $\pi$-pulses), where transverse Overhauser fluctuations dominate dephasing, to the many-pulse regime ($\gtrsim \! 32$ $\pi$-pulses), where longitudinal Overhauser fluctuations with a $1/f$ spectrum dominate.
    • Filip K. Malinowski, Frederico Martins, Łukasz Cywiński, Mark S. Rudner, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth
      Journal reference: Phys. Rev. Lett. 118, 177702 (2017) [pdf]
      DOI: 10.1103/PhysRevLett.118.177702

    • Symmetric operation of the resonant exchange qubit - Abstract
      • We operate a resonant exchange qubit in a highly symmetric triple-dot configuration using IQ-modulated RF pulses. At the resulting three-dimensional sweet spot the qubit splitting is an order of magnitude less sensitive to all relevant control voltages, compared to the conventional operating point, but we observe no significant improvement in the quality of Rabi oscillations. For weak driving this is consistent with Overhauser field fluctuations modulating the qubit splitting. For strong driving we infer that effective voltage noise modulates the coupling strength between RF drive and the qubit, thereby quickening Rabi decay. Application of CPMG dynamical decoupling sequences consisting of up to n = 32 {\pi} pulses significantly prolongs qubit coherence, leading to marginally longer dephasing times in the symmetric configuration. This is consistent with dynamical decoupling from low frequency noise, but quantitatively cannot be explained by effective gate voltage noise and Overhauser field fluctuations alone. Our results inform recent strategies for the utilization of partial sweet spots in the operation and long-distance coupling of triple-dot qubits.
    • Filip K. Malinowski, Frederico Martins, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth
      Journal reference: Phys. Rev. B 96, 045443 (2017) [pdf]
      DOI: 10.1103/PhysRevB.96.045443

    • Notch filtering the nuclear environment of a spin qubit - Abstract
      • Electron spins in gate-defined quantum dots provide a promising platform for quantum computation. In particular, spin-based quantum computing in gallium arsenide takes advantage of the high quality of semiconducting materials, reliability in fabricating arrays of quantum dots, and accurate qubit operations. However, the effective magnetic noise arising from the hyperfine interaction with uncontrolled nuclear spins in the host lattice constitutes a major source of decoherence. Low frequency nuclear noise, responsible for fast (10 ns) inhomogeneous dephasing, can be removed by echo techniques. High frequency nuclear noise, recently studied via echo revivals, occurs in narrow frequency bands related to differences in Larmor precession of the three isotopes $\mathbf{^{69}Ga}$, $\mathbf{^{71}Ga}$, and $\mathbf{^{75}As}$. Here we show that both low and high frequency nuclear noise can be filtered by appropriate dynamical decoupling sequences, resulting in a substantial enhancement of spin qubit coherence times. Using nuclear notch filtering, we demonstrate a spin coherence time ($\mathbf{T_{2}}$) of 0.87 ms, five orders of magnitude longer than typical exchange gate times, and exceeding the longest coherence times reported to date in Si/SiGe gate-defined quantum dots.
    • F. K. Malinowski, F. Martins, P. D. Nissen, E. Barnes, Ł. Cywiński, M. S. Rudner, S. Fallahi, G. C. Gardner, M. J. Manfra, C. M. Marcus, F. Kuemmeth
      Journal reference: Nat. Nanotechnol. 12, 16-20 (2017) [pdf]
      DOI: 10.1038/nnano.2016.170

    • Transport Signatures of Quasiparticle Poisoning in a Majorana Island - Abstract
      • We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (~ 1 {\mu}s) and sets a bound for a weakly coupled island (> 10 {\mu}s). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. In energy units, fluctuations are consistent with previous measurements.
    • S. M. Albrecht, E. B. Hansen, A. P. Higginbotham, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, J. Danon, K. Flensberg, C. M. Marcus
      Journal reference: Phys. Rev. Lett. 118, 137701 (2017) [pdf]
      DOI: 10.1103/PhysRevLett.118.137701

  • 2016
    • Filter function formalism beyond pure dephasing and non-Markovian noise in singlet-triplet qubits - Abstract
      • The filter function formalism quantitatively describes the dephasing of a qubit by a bath that causes Gaussian fluctuations in the qubit energies with an arbitrary noise power spectrum. Here, we extend this formalism to account for more general types of noise that couple to the qubit through terms that do not commute with the qubit's bare Hamiltonian. Our approach applies to any power spectrum that generates slow noise fluctuations in the qubit's evolution. We demonstrate our formalism in the case of singlet-triplet qubits subject to both quasistatic nuclear noise and $1/\omega^\alpha$ charge noise and find good agreement with recent experimental findings. This comparison shows the efficacy of our approach in describing real systems and additionally highlights the challenges with distinguishing different types of noise in free induction decay experiments.
    • Edwin Barnes, Mark S. Rudner, Frederico Martins, Filip K. Malinowski, Charles M. Marcus, Ferdinand Kuemmeth
      Journal reference: Phys. Rev. B 93, 121407 (2016) [pdf]
      DOI: 10.1103/PhysRevB.93.121407

    • Exponential protection of zero modes in Majorana islands - Abstract
      • Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers [1]. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, and the pinning is predicted to be exponential as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in proximitized nanowires and atomic chains, with small mode-splitting potentially explained by hybridization of Majoranas. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire segment with epitaxial aluminum, which forms a proximity-induced superconducting Coulomb island (a Majorana island) that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometers, sub-gap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half micrometer of increased wire length. For devices longer than about one micrometer, transport in strong magnetic fields occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. Our results help explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode separation.
    • S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, C. M. Marcus
      Journal reference: Nature 531, 206 (2016) [pdf]
      DOI: 10.1038/nature17162

    • Noise Suppression Using Symmetric Exchange Gates in Spin Qubits - Abstract
      • We demonstrate a substantial improvement in the spin-exchange gate using symmetric control instead of conventional detuning in GaAs spin qubits, up to a factor-of-six increase in the quality factor of the gate. For symmetric operation, nanosecond voltage pulses are applied to the barrier that controls the interdot potential between quantum dots, modulating the exchange interaction while maintaining symmetry between the dots. Excellent agreement is found with a model that separately includes electrical and nuclear noise sources for both detuning and symmetric gating schemes. Unlike exchange control via detuning, the decoherence of symmetric exchange rotations is dominated by rotation-axis fluctuations due to nuclear field noise rather than direct exchange noise.
    • Frederico Martins, Filip K. Malinowski, Peter D. Nissen, Edwin Barnes, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth
      Journal reference: Phys. Rev. Lett. 116, 116801 (2016) [pdf]
      DOI: 10.1103/PhysRevLett.116.116801

    • Gatemon Benchmarking and Two-Qubit Operations - Abstract
      • Recent experiments have demonstrated superconducting transmon qubits with semiconductor nanowire Josephson junctions. These hybrid gatemon qubits utilize field effect tunability characteristic for semiconductors to allow complete qubit control using gate voltages, potentially a technological advantage over conventional flux-controlled transmons. Here, we present experiments with a two-qubit gatemon circuit. We characterize qubit coherence and stability and use randomized benchmarking to demonstrate single-qubit gate errors below 0.7% for all gates, including voltage-controlled $Z$ rotations. We show coherent capacitive coupling between two gatemons and coherent swap operations. Finally, we perform a two-qubit controlled-phase gate with an estimated fidelity of 91%, demonstrating the potential of gatemon qubits for building scalable quantum processors.
    • L. Casparis, T. W. Larsen, M. S. Olsen, F. Kuemmeth, P. Krogstrup, J. Nygård, K. D. Petersson, C. M. Marcus
      Journal reference: Phys. Rev. Lett. 116, 150505 (2016) [pdf]
      DOI: 10.1103/PhysRevLett.116.150505

  • 2015
    • Quantum transport in carbon nanotubes - Abstract
      • Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries, enabled by sophisticated fabrication, have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and from valley freedom. We focus on the interplay between the two. In single quantum dots defined in short lengths of nanotube, the energy levels associated with each degree of freedom, and the spin-orbit coupling between them, are revealed by Coulomb blockade spectroscopy. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits, and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electron-electron interactions in one dimension strongly modifies their transport behaviour. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the well-understood overall picture, we also state clearly open questions for the field. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a very low level.
    • E. A. Laird, F. Kuemmeth, G. Steele, K. Grove-Rasmussen, J. Nygård, K. Flensberg, L. P. Kouwenhoven
      Journal reference: Rev. Mod. Phys. 87, 703 (2015) [pdf]
      DOI: 10.1103/RevModPhys.87.703

    • Semiconductor-Nanowire-Based Superconducting Qubit - Abstract
      • We introduce a hybrid qubit based on a semiconductor nanowire with an epitaxially grown superconductor layer. Josephson energy of the transmon-like device ("gatemon") is controlled by an electrostatic gate that depletes carriers in a semiconducting weak link region. Strong coupling to an on-chip microwave cavity and coherent qubit control via gate voltage pulses is demonstrated, yielding reasonably long relaxation times (0.8 {\mu}s) and dephasing times (1 {\mu}s), exceeding gate operation times by two orders of magnitude, in these first-generation devices. Because qubit control relies on voltages rather than fluxes, dissipation in resistive control lines is reduced, screening reduces crosstalk, and the absence of flux control allows operation in a magnetic field, relevant for topological quantum information.
    • T. W. Larsen, K. D. Petersson, F. Kuemmeth, T. S. Jespersen, P. Krogstrup, J. Nygard, C. M. Marcus
      Journal reference: Phys. Rev. Lett. 115, 127001 (2015) [pdf]
      DOI: 10.1103/PhysRevLett.115.127001

    • Hard gap in epitaxial semiconductor–superconductor nanowires - Abstract
      • Many present and future applications of superconductivity would benefit from electrostatic control of carrier density and tunneling rates, the hallmark of semiconductor devices. One particularly exciting application is the realization of topological superconductivity as a basis for quantum information processing. Proposals in this direction based on proximity effect in semiconductor nanowires are appealing because the key ingredients are currently in hand. However, previous instances of proximitized semiconductors show significant tunneling conductance below the superconducting gap, suggesting a continuum of subgap states---a situation that nullifies topological protection. Here, we report a hard superconducting gap induced by proximity effect in a semiconductor, using epitaxial Al-InAs superconductor-semiconductor nanowires. The hard gap, along with favorable material properties and gate-tunability, makes this new hybrid system attractive for a number of applications, as well as fundamental studies of mesoscopic superconductivity.
    • W. Chang, S. M. Albrecht, T. S. Jespersen, F. Kuemmeth, P. Krogstrup, J. Nygård, C. M. Marcus
      Journal reference: Nature Nanotechnology 10, 232 (2015) [pdf]
      DOI: 10.1038/nnano.2014.306

    • Parity lifetime of bound states in a proximitized semiconductor nanowire - Abstract
      • Quasiparticle excitations can compromise the performance of superconducting devices, causing high frequency dissipation, decoherence in Josephson qubits, and braiding errors in proposed Majorana-based topological quantum computers. Quasiparticle dynamics have been studied in detail in metallic superconductors but remain relatively unexplored in semiconductor-superconductor structures, which are now being intensely pursued in the context of topological superconductivity. To this end, we introduce a new physical system comprised of a gate-confined semiconductor nanowire with an epitaxially grown superconductor layer, yielding an isolated, proximitized nanowire segment. We identify Andreev-like bound states in the semiconductor via bias spectroscopy, determine the characteristic temperatures and magnetic fields for quasiparticle excitations, and extract a parity lifetime (poisoning time) of the bound state in the semiconductor exceeding 10 ms.
    • A. P. Higginbotham, S. M. Albrecht, G. Kirsanskas, W. Chang, F. Kuemmeth, P. Krogstrup, T. S. Jespersen, J. Nygard, K. Flensberg, C. M. Marcus
      Journal reference: Nature Physics 11, 1017 (2015) [pdf]
      DOI: 10.1038/nphys3461

  • 2014
    • Hole Spin Coherence in a Ge/Si Heterostructure Nanowire - Abstract
      • Relaxation and dephasing of hole spins are measured in a gate-defined Ge/Si nanowire double quantum dot using a fast pulsed-gate method and dispersive readout. An inhomogeneous dephasing time $T_2^* \sim 0.18~\mathrm{\mu s}$ exceeds corresponding measurements in III-V semiconductors by more than an order of magnitude, as expected for predominately nuclear-spin-free materials. Dephasing is observed to be exponential in time, indicating the presence of a broadband noise source, rather than Gaussian, previously seen in systems with nuclear-spin-dominated dephasing.
    • A. P. Higginbotham, T. W. Larsen, J. Yao, H. Yan, C. M. Lieber, C. M. Marcus, F. Kuemmeth
      Journal reference: Nano Letters 14, 3582 (2014) [pdf]
      DOI: 10.1021/nl501242b

    • Antilocalization of Coulomb Blockade in a Ge/Si Nanowire - Abstract
      • The distribution of Coulomb blockade peak heights as a function of magnetic field is investigated experimentally in a Ge-Si nanowire quantum dot. Strong spin-orbit coupling in this hole-gas system leads to antilocalization of Coulomb blockade peaks, consistent with theory. In particular, the peak height distribution has its maximum away from zero at zero magnetic field, with an average that decreases with increasing field. Magnetoconductance in the open-wire regime places a bound on the spin-orbit length ($l_{so}$ < 20 nm), consistent with values extracted in the Coulomb blockade regime ($l_{so}$ < 25 nm).
    • A. P. Higginbotham, F. Kuemmeth, T. W. Larsen, M. Fitzpatrick, J. Yao, H. Yan, C. M. Lieber, C. M. Marcus
      Journal reference: Phys. Rev. Lett. 112, 216806 (2014) [pdf]
      DOI: 10.1103/PhysRevLett.112.216806

    • Coherent Operations and Screening in Multielectron Spin Qubits - Abstract
      • The performance of multi-electron spin qubits is examined by comparing exchange oscillations in coupled single-electron and multi-electron quantum dots in the same device. Fast (> 1 GHz) exchange oscillations with a quality factor Q > 15 are found for the multi-electron case, compared to Q ~ 2 for the single-electron case, the latter consistent with previous experiments. A model of dephasing that includes voltage and hyperfine noise is developed that is in good agreement with both single- and multi-electron data, though in both cases additional exchange-independent dephasing is needed to obtain quantitative agreement across a broad parameter range.
    • A. P. Higginbotham, F. Kuemmeth, M. P. Hanson, A. C. Gossard, C. M. Marcus
      Journal reference: Phys. Rev. Lett. 112, 026801 (2014) [pdf]
      DOI: 10.1103/PhysRevLett.112.026801

  • 2013
    • Observation and spectroscopy of a two-electron Wigner molecule in an ultraclean carbon nanotube - Abstract
      • Coulomb interactions can have a decisive effect on the ground state of electronic systems. The simplest system in which interactions can play an interesting role is that of two electrons on a string. In the presence of strong interactions the two electrons are predicted to form a Wigner molecule, separating to the ends of the string due to their mutual repulsion. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet to date a direct measurement of such a spectrum in a controllable one-dimensional setting is still missing. Here we use an ultra-clean suspended carbon nanotube to realize this system in a tunable potential. Using tunneling spectroscopy we measure the excitation spectra of two interacting carriers, electrons or holes, and identify seven low-energy states characterized by their spin and isospin quantum numbers. These states fall into two multiplets according to their exchange symmetries. The formation of a strongly-interacting Wigner molecule is evident from the small energy splitting measured between the two multiplets, that is quenched by an order of magnitude compared to the non-interacting value. Our ability to tune the two-electron state in space and to study it for both electrons and holes provides an unambiguous demonstration of the fundamental Wigner molecule state.
    • S. Pecker, F. Kuemmeth, A. Secchi, M. Rontani, D. C. Ralph, P. L. McEuen, S. Ilani
      Journal reference: Nature Physics 9, 576-581 (2013) [pdf]
      DOI: 10.1038/nphys2692