1
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Ubbelohde N, Freise L, Pavlovska E, Silvestrov PG, Recher P, Kokainis M, Barinovs G, Hohls F, Weimann T, Pierz K, Kashcheyevs V. Two electrons interacting at a mesoscopic beam splitter. NATURE NANOTECHNOLOGY 2023; 18:733-740. [PMID: 37169898 DOI: 10.1038/s41565-023-01370-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Accepted: 03/10/2023] [Indexed: 05/13/2023]
Abstract
The nonlinear response of a beam splitter to the coincident arrival of interacting particles enables numerous applications in quantum engineering and metrology. Yet, it poses considerable challenges to control interactions on the individual particle level. Here, we probe the coincidence correlations at a mesoscopic constriction between individual ballistic electrons in a system with unscreened Coulomb interactions and introduce concepts to quantify the associated parametric nonlinearity. The full counting statistics of joint detection allows us to explore the interaction-mediated energy exchange. We observe an increase from 50% up to 70% in coincidence counts between statistically indistinguishable on-demand sources and a correlation signature consistent with the independent tomography of the electron emission. Analytical modelling and numerical simulations underpin the consistency of the experimental results with Coulomb interactions between two electrons counterpropagating in a quadratic saddle potential. Coulomb repulsion energy and beam splitter dispersion define a figure of merit, which in this experiment is demonstrated to be sufficiently large to enable future applications, such as single-shot in-flight detection and quantum logic gates.
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Affiliation(s)
- Niels Ubbelohde
- Physikalisch-Technische Bundesanstalt, Braunschweig, Germany.
| | - Lars Freise
- Physikalisch-Technische Bundesanstalt, Braunschweig, Germany
| | | | - Peter G Silvestrov
- Institut für Mathematische Physik, Technische Universität Braunschweig, Braunschweig, Germany
| | - Patrik Recher
- Institut für Mathematische Physik, Technische Universität Braunschweig, Braunschweig, Germany
- Laboratory for Emerging Nanometrology Braunschweig, Braunschweig, Germany
| | - Martins Kokainis
- Department of Physics, University of Latvia, Riga, Latvia
- Faculty of Computing, University of Latvia, Riga, Latvia
| | - Girts Barinovs
- Department of Physics, University of Latvia, Riga, Latvia
| | - Frank Hohls
- Physikalisch-Technische Bundesanstalt, Braunschweig, Germany
| | - Thomas Weimann
- Physikalisch-Technische Bundesanstalt, Braunschweig, Germany
| | - Klaus Pierz
- Physikalisch-Technische Bundesanstalt, Braunschweig, Germany
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2
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Fletcher JD, Park W, Ryu S, See P, Griffiths JP, Jones GAC, Farrer I, Ritchie DA, Sim HS, Kataoka M. Time-resolved Coulomb collision of single electrons. NATURE NANOTECHNOLOGY 2023:10.1038/s41565-023-01369-4. [PMID: 37169897 DOI: 10.1038/s41565-023-01369-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Accepted: 03/10/2023] [Indexed: 05/13/2023]
Abstract
A series of recent experiments have shown that collision of ballistic electrons in semiconductors can be used to probe the indistinguishability of single-electron wavepackets. Perhaps surprisingly, their Coulomb interaction has not been seen due to screening. Here we show Coulomb-dominated collision of high-energy single electrons in counter-propagating ballistic edge states, probed by measuring partition statistics while adjusting the collision timing. Although some experimental data suggest antibunching behaviour, we show that this is not due to quantum statistics but to strong repulsive Coulomb interactions. This prevents the wavepacket overlap needed for fermionic exchange statistics but suggests new ways to utilize Coulomb interactions: microscopically isolated and time-resolved interactions between ballistic electrons can enable the use of the Coulomb interaction for high-speed sensing or gate operations on flying electron qubits.
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Affiliation(s)
| | - W Park
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, Korea.
| | - S Ryu
- Instituto de Física Interdisciplinary Sistemas Complejos IFISC (CSIC-UIB), Palma de Mallorca, Spain
| | - P See
- National Physical Laboratory, Teddington, UK
| | - J P Griffiths
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | - G A C Jones
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | - I Farrer
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
- Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield, UK
| | - D A Ritchie
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | - H-S Sim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, Korea.
| | - M Kataoka
- National Physical Laboratory, Teddington, UK.
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3
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Ryu S, Sim HS. Partition of Two Interacting Electrons by a Potential Barrier. PHYSICAL REVIEW LETTERS 2022; 129:166801. [PMID: 36306761 DOI: 10.1103/physrevlett.129.166801] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Revised: 09/01/2022] [Accepted: 09/23/2022] [Indexed: 06/16/2023]
Abstract
Scattering or tunneling of an electron at a potential barrier is a fundamental quantum effect. Electron-electron interactions often affect the scattering, and understanding of the interaction effect is crucial in detection of various phenomena of electron transport and their application to electron quantum optics. We theoretically study the partition and collision of two interacting hot electrons at a potential barrier. We predict their kinetic energy change by their Coulomb interaction during the scattering delay time inside the barrier. The energy change results in characteristic deviation of the partition probabilities from the noninteracting case. The derivation includes nonmonotonic dependence of the probabilities on the barrier height, which qualitatively agrees with recent experiments, and reduction of the fermionic antibunching.
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Affiliation(s)
- Sungguen Ryu
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
- Institute for Cross-Disciplinary Physics and Complex Systems IFISC (UIB-CSIC), E-07122 Palma de Mallorca, Spain
| | - H-S Sim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
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4
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Kotilahti J, Burset P, Moskalets M, Flindt C. Multi-Particle Interference in an Electronic Mach-Zehnder Interferometer. ENTROPY (BASEL, SWITZERLAND) 2021; 23:736. [PMID: 34200952 PMCID: PMC8230567 DOI: 10.3390/e23060736] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/18/2021] [Revised: 06/07/2021] [Accepted: 06/07/2021] [Indexed: 11/24/2022]
Abstract
The development of dynamic single-electron sources has made it possible to observe and manipulate the quantum properties of individual charge carriers in mesoscopic circuits. Here, we investigate multi-particle effects in an electronic Mach-Zehnder interferometer driven by a series of voltage pulses. To this end, we employ a Floquet scattering formalism to evaluate the interference current and the visibility in the outputs of the interferometer. An injected multi-particle state can be described by its first-order correlation function, which we decompose into a sum of elementary correlation functions that each represent a single particle. Each particle in the pulse contributes independently to the interference current, while the visibility (given by the maximal interference current) exhibits a Fraunhofer-like diffraction pattern caused by the multi-particle interference between different particles in the pulse. For a sequence of multi-particle pulses, the visibility resembles the diffraction pattern from a grid, with the role of the grid and the spacing between the slits being played by the pulses and the time delay between them. Our findings may be observed in future experiments by injecting multi-particle pulses into a Mach-Zehnder interferometer.
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Affiliation(s)
- Janne Kotilahti
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland; (J.K.); (C.F.)
| | - Pablo Burset
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland; (J.K.); (C.F.)
- Department of Theoretical Condensed Matter Physics, Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Michael Moskalets
- Department of Metal and Semiconductor Physics, NTU “Kharkiv Polytechnic Institute”, 61002 Kharkiv, Ukraine;
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland; (J.K.); (C.F.)
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5
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Abstract
We revisit the arguments underlying two well-known arrival-time distributions in quantum mechanics, viz., the Aharonov–Bohm–Kijowski (ABK) distribution, applicable for freely moving particles, and the quantum flux (QF) distribution. An inconsistency in the original axiomatic derivation of Kijowski’s result is pointed out, along with an inescapable consequence of the ‘negative arrival times’ inherent to this proposal (and generalizations thereof). The ABK free-particle restriction is lifted in a discussion of an explicit arrival-time set-up featuring a charged particle moving in a constant magnetic field. A natural generalization of the ABK distribution is in this case shown to be critically gauge-dependent. A direct comparison to the QF distribution, which does not exhibit this flaw, is drawn (its acknowledged drawback concerning the quantum backflow effect notwithstanding).
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Affiliation(s)
- Siddhant Das
- Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstrasse 39, 80333 München, Germany
| | - Markus Nöth
- Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstrasse 39, 80333 München, Germany
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6
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Norimoto S, Iwakiri S, Yokoi M, Arakawa T, Niimi Y, Kobayashi K. Etching process of narrow wire and application to tunable-barrier electron pump. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2020; 91:085110. [PMID: 32872958 DOI: 10.1063/5.0011767] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Accepted: 07/16/2020] [Indexed: 06/11/2023]
Abstract
Single electron sources have been studied as a device to establish an electric current standard for 30 years and recently as an on-demand coherent source for fermion quantum optics. In order to construct the single electron source on a GaAs/AlGaAs two-dimensional electron gas (2DEG), it is often necessary to fabricate a sub-micrometer wire by etching. We have established techniques to fabricate the wire made of the fragile 2DEG by combining photolithography and electron beam lithography with one-step photoresist coating, which enables us to etch fine and coarse structures simultaneously. It has been demonstrated that the fabricated single electron source pumps a fixed number of electrons per cycle with radio frequency. The fabrication technique improves the lithography process with lower risk of damage to the 2DEG.
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Affiliation(s)
- Shota Norimoto
- Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Shuichi Iwakiri
- Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Masahiko Yokoi
- Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Tomonori Arakawa
- Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Yasuhiro Niimi
- Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Kensuke Kobayashi
- Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
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7
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Filippone M, Marguerite A, Le Hur K, Fève G, Mora C. Phase-Coherent Dynamics of Quantum Devices with Local Interactions. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E847. [PMID: 33286618 PMCID: PMC7517448 DOI: 10.3390/e22080847] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Revised: 06/21/2020] [Accepted: 07/02/2020] [Indexed: 11/16/2022]
Abstract
This review illustrates how Local Fermi Liquid (LFL) theories describe the strongly correlated and coherent low-energy dynamics of quantum dot devices. This approach consists in an effective elastic scattering theory, accounting exactly for strong correlations. Here, we focus on the mesoscopic capacitor and recent experiments achieving a Coulomb-induced quantum state transfer. Extending to out-of-equilibrium regimes, aimed at triggered single electron emission, we illustrate how inelastic effects become crucial, requiring approaches beyond LFLs, shedding new light on past experimental data by showing clear interaction effects in the dynamics of mesoscopic capacitors.
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Affiliation(s)
- Michele Filippone
- Department of Quantum Matter Physics, University of Geneva 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
| | - Arthur Marguerite
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel;
| | - Karyn Le Hur
- CPHT, CNRS, Institut Polytechnique de Paris, Route de Saclay, 91128 Palaiseau, France;
| | - Gwendal Fève
- Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France;
| | - Christophe Mora
- Laboratoire Matériaux et Phénomènes Quantiques, CNRS, Université de Paris, F-75013 Paris, France;
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8
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Freise L, Gerster T, Reifert D, Weimann T, Pierz K, Hohls F, Ubbelohde N. Trapping and Counting Ballistic Nonequilibrium Electrons. PHYSICAL REVIEW LETTERS 2020; 124:127701. [PMID: 32281866 DOI: 10.1103/physrevlett.124.127701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2019] [Accepted: 02/28/2020] [Indexed: 06/11/2023]
Abstract
We demonstrate the trapping of electrons propagating ballistically at far-above-equilibrium energies in GaAs/AlGaAs heterostructures in high magnetic field. We find low-loss transport along a gate-modified mesa edge in contrast to an effective decay of excess energy for the loop around a neighboring, mesa-confined node, enabling high-fidelity trapping. Measuring the full counting statistics via single-charge detection yields the trapping (and escape) probabilities of electrons scattered (and excited) within the node. Energetic and arrival-time distributions of captured electron wave packets are characterized by modulating tunnel barrier transmission.
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Affiliation(s)
- Lars Freise
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - Thomas Gerster
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - David Reifert
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - Thomas Weimann
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - Klaus Pierz
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - Frank Hohls
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - Niels Ubbelohde
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
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9
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Fletcher JD, Johnson N, Locane E, See P, Griffiths JP, Farrer I, Ritchie DA, Brouwer PW, Kashcheyevs V, Kataoka M. Continuous-variable tomography of solitary electrons. Nat Commun 2019; 10:5298. [PMID: 31757944 PMCID: PMC6874662 DOI: 10.1038/s41467-019-13222-1] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2019] [Accepted: 10/15/2019] [Indexed: 11/17/2022] Open
Abstract
A method for characterising the wave-function of freely-propagating particles would provide a useful tool for developing quantum-information technologies with single electronic excitations. Previous continuous-variable quantum tomography techniques developed to analyse electronic excitations in the energy-time domain have been limited to energies close to the Fermi level. We show that a wide-band tomography of single-particle distributions is possible using energy-time filtering and that the Wigner representation of the mixed-state density matrix can be reconstructed for solitary electrons emitted by an on-demand single-electron source. These are highly localised distributions, isolated from the Fermi sea. While we cannot resolve the pure state Wigner function of our excitations due to classical fluctuations, we can partially resolve the chirp and squeezing of the Wigner function imposed by emission conditions and quantify the quantumness of the source. This tomography scheme, when implemented with sufficient experimental resolution, will enable quantum-limited measurements, providing information on electron coherence and entanglement at the individual particle level. Quantum tomographic techniques enable the complete characterisation of continuous variable quantum states. Here the authors demonstrate a broadband tomography protocol for single electrons that goes beyond the bandwidth restrictions of existing methods.
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Affiliation(s)
- J D Fletcher
- National Physical Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW, UK
| | - N Johnson
- National Physical Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW, UK.,London Centre for Nanotechnology and Department of Electronic and Electrical Engineering, University College London, Torrington Place, London, WC1E 7JE, UK.,NTT Basic Research Laboratories, NTT Corporation, Atsugi, Japan
| | - E Locane
- Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany
| | - P See
- National Physical Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW, UK
| | - J P Griffiths
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge, CB3 0HE, UK
| | - I Farrer
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge, CB3 0HE, UK.,Department of Electronic & Electrical Engineering, The University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK
| | - D A Ritchie
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge, CB3 0HE, UK
| | - P W Brouwer
- Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany
| | - V Kashcheyevs
- Department of Physics, University of Latvia, Jelgavas street 3, Riga, LV 1004, Latvia
| | - M Kataoka
- National Physical Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW, UK.
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10
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Bisognin R, Marguerite A, Roussel B, Kumar M, Cabart C, Chapdelaine C, Mohammad-Djafari A, Berroir JM, Bocquillon E, Plaçais B, Cavanna A, Gennser U, Jin Y, Degiovanni P, Fève G. Quantum tomography of electrical currents. Nat Commun 2019; 10:3379. [PMID: 31358764 PMCID: PMC6662746 DOI: 10.1038/s41467-019-11369-5] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2018] [Accepted: 07/04/2019] [Indexed: 11/08/2022] Open
Abstract
In quantum nanoelectronics, time-dependent electrical currents are built from few elementary excitations emitted with well-defined wavefunctions. However, despite the realization of sources generating quantized numbers of excitations, and despite the development of the theoretical framework of time-dependent quantum electronics, extracting electron and hole wavefunctions from electrical currents has so far remained out of reach, both at the theoretical and experimental levels. In this work, we demonstrate a quantum tomography protocol which extracts the generated electron and hole wavefunctions and their emission probabilities from any electrical current. It combines two-particle interferometry with signal processing. Using our technique, we extract the wavefunctions generated by trains of Lorentzian pulses carrying one or two electrons. By demonstrating the synthesis and complete characterization of electronic wavefunctions in conductors, this work offers perspectives for quantum information processing with electrical currents and for investigating basic quantum physics in many-body systems.
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Affiliation(s)
- R Bisognin
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, 75005, France
| | - A Marguerite
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, 75005, France
| | - B Roussel
- Univ Lyon, Ens de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342, Lyon, France
- European Space Agency-Advanced Concepts Team, ESTEC, Keplerlaan 1, 2201 AZ, Noordwijk, The Netherlands
| | - M Kumar
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, 75005, France
| | - C Cabart
- Univ Lyon, Ens de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342, Lyon, France
| | - C Chapdelaine
- Laboratoire des signaux et systèmes, CNRS, Centrale-Supélec-Université Paris-Saclay, Gif-sur-Yvette, F-91190, France
| | - A Mohammad-Djafari
- Laboratoire des signaux et systèmes, CNRS, Centrale-Supélec-Université Paris-Saclay, Gif-sur-Yvette, F-91190, France
| | - J-M Berroir
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, 75005, France
| | - E Bocquillon
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, 75005, France
| | - B Plaçais
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, 75005, France
| | - A Cavanna
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91120, Palaiseau, France
| | - U Gennser
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91120, Palaiseau, France
| | - Y Jin
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91120, Palaiseau, France
| | - P Degiovanni
- Univ Lyon, Ens de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342, Lyon, France
| | - G Fève
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, 75005, France.
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11
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Mi S, Burset P, Flindt C. Electron waiting times in hybrid junctions with topological superconductors. Sci Rep 2018; 8:16828. [PMID: 30442914 PMCID: PMC6237767 DOI: 10.1038/s41598-018-34776-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2018] [Accepted: 10/22/2018] [Indexed: 11/09/2022] Open
Abstract
We investigate the waiting time distributions (WTDs) of superconducting hybrid junctions, considering both conventional and topologically nontrivial superconductors hosting Majorana bound states at their edges. To this end, we employ a scattering matrix formalism that allows us to evaluate the waiting times between the transmissions and reflections of electrons or holes. Specifically, we analyze normal-metal–superconductor (NIS) junctions and NISIN junctions, where Cooper pairs are spatially split into different leads. The distribution of waiting times is sensitive to the simultaneous reflection of electrons and holes, which is enhanced by the zero-energy state in topological superconductors. For the NISIN junctions, the WTDs of trivial superconductors feature a sharp dependence on the applied voltage, while for topological ones they are mostly independent of it. This particular voltage dependence is again connected to the presence of topological edge states, showing that WTDs are a promising tool for identifying topological superconductivity.
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Affiliation(s)
- Shuo Mi
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland. .,Univ. Grenoble Alpes, CEA, INAC-Pheliqs, 38000, Grenoble, France.
| | - Pablo Burset
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland
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12
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Johnson N, Emary C, Ryu S, Sim HS, See P, Fletcher JD, Griffiths JP, Jones GAC, Farrer I, Ritchie DA, Pepper M, Janssen TJBM, Kataoka M. LO-Phonon Emission Rate of Hot Electrons from an On-Demand Single-Electron Source in a GaAs/AlGaAs Heterostructure. PHYSICAL REVIEW LETTERS 2018; 121:137703. [PMID: 30312059 DOI: 10.1103/physrevlett.121.137703] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2017] [Revised: 05/17/2018] [Indexed: 06/08/2023]
Abstract
Using a recent time-of-flight measurement technique with 1 ps time resolution and electron-energy spectroscopy, we develop a method to measure the longitudinal-optical-phonon emission rate of hot electrons traveling along a depleted edge of a quantum Hall bar. Comparison to a single-particle model implies the scattering mechanism involves a two-step process via an intra-Landau-level transition. We show that this can be suppressed by control of the edge potential profile, and a scattering length >1 mm can be achieved, allowing the use of this system for scalable single-electron device applications.
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Affiliation(s)
- N Johnson
- National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom
- London Centre for Nanotechnology, and Department of Electronic and Electrical Engineering, University College London, Torrington Place, London, WC1E 7JE, United Kingdom
| | - C Emary
- Joint Quantum Centre Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - S Ryu
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea
| | - H-S Sim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea
| | - P See
- National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom
| | - J D Fletcher
- National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom
| | - J P Griffiths
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - G A C Jones
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - I Farrer
- Department of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom
| | - D A Ritchie
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - M Pepper
- London Centre for Nanotechnology, and Department of Electronic and Electrical Engineering, University College London, Torrington Place, London, WC1E 7JE, United Kingdom
| | - T J B M Janssen
- National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom
| | - M Kataoka
- National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom
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13
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Roussely G, Arrighi E, Georgiou G, Takada S, Schalk M, Urdampilleta M, Ludwig A, Wieck AD, Armagnat P, Kloss T, Waintal X, Meunier T, Bäuerle C. Unveiling the bosonic nature of an ultrashort few-electron pulse. Nat Commun 2018; 9:2811. [PMID: 30022067 PMCID: PMC6052057 DOI: 10.1038/s41467-018-05203-7] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2018] [Accepted: 06/12/2018] [Indexed: 11/09/2022] Open
Abstract
Quantum dynamics is very sensitive to dimensionality. While two-dimensional electronic systems form Fermi liquids, one-dimensional systems—Tomonaga–Luttinger liquids—are described by purely bosonic excitations, even though they are initially made of fermions. With the advent of coherent single-electron sources, the quantum dynamics of such a liquid is now accessible at the single-electron level. Here, we report on time-of-flight measurements of ultrashort few-electron charge pulses injected into a quasi one-dimensional quantum conductor. By changing the confinement potential we can tune the system from the one-dimensional Tomonaga–Luttinger liquid limit to the multi-channel Fermi liquid and show that the plasmon velocity can be varied over almost an order of magnitude. These results are in quantitative agreement with a parameter-free theory and demonstrate a powerful probe for directly investigating real-time dynamics of fractionalisation phenomena in low-dimensional conductors. Electronic excitations in low-dimensional quantum nanoelectronic devices are collective waves that are strongly affected by the Coulomb interaction. Here, the authors demonstrate that they are able to prepare these collective excitations down to the single electron level and control their propagation.
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Affiliation(s)
- Gregoire Roussely
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Everton Arrighi
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Giorgos Georgiou
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France.,Univ. Savoie Mont-Blanc, CNRS, IMEP-LAHC, 73370, Le Bourget du Lac, France
| | - Shintaro Takada
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France.,National Institute of Advanced Industrial Science and Technology (AIST), National Metrology Institute of Japan (NMIJ), Tsukuba, Ibaraki, 305-8563, Japan
| | - Martin Schalk
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Matias Urdampilleta
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Arne Ludwig
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780, Bochum, Germany
| | - Andreas D Wieck
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780, Bochum, Germany
| | - Pacome Armagnat
- Univ. Grenoble Alpes, CEA, INAC-Pheliqs, 38000, Grenoble, France
| | - Thomas Kloss
- Univ. Grenoble Alpes, CEA, INAC-Pheliqs, 38000, Grenoble, France
| | - Xavier Waintal
- Univ. Grenoble Alpes, CEA, INAC-Pheliqs, 38000, Grenoble, France
| | - Tristan Meunier
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Christopher Bäuerle
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France.
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Bäuerle C, Christian Glattli D, Meunier T, Portier F, Roche P, Roulleau P, Takada S, Waintal X. Coherent control of single electrons: a review of current progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:056503. [PMID: 29355831 DOI: 10.1088/1361-6633/aaa98a] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches that have been developed over the last few years in order to gain full control over a propagating single-electron in a solid-state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single-electron sources that have been developed over the last years and which are compatible with integrated single-electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments in the new physics that has emerged using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.
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Affiliation(s)
- Christopher Bäuerle
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
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Abstract
Single-electron pumps based on isolated impurity atoms have recently been experimentally demonstrated. In these devices the Coulomb potential of an atom creates a localised electron state with a large charging energy and considerable orbital level spacings, enabling robust charge capturing processes. In contrast to the frequently used gate-defined quantum dot pumps, which experience a strongly time-dependent potential, the confinement potential in these single-atom pumps is hardly affected by the periodic driving of the system. Here we describe the behaviour and performance of an atomic, single parameter, electron pump. This is done by considering the loading, isolating and unloading of one electron at the time, on a phosphorous atom embedded in a silicon double gate transistor. The most important feature of the atom pump is its very isolated ground state, which is populated through the fast loading of much higher lying excited states and a subsequent fast relaxation process. This leads to a substantial increase in pumping accuracy, and is opposed to the adverse role of excited states observed for quantum dot pumps due to non-adiabatic excitations. The pumping performance is investigated as a function of dopant position, revealing a pumping behaviour robust against the expected variability in atomic position.
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Ryu S, Kataoka M, Sim HS. Ultrafast Emission and Detection of a Single-Electron Gaussian Wave Packet: A Theoretical Study. PHYSICAL REVIEW LETTERS 2016; 117:146802. [PMID: 27740812 DOI: 10.1103/physrevlett.117.146802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2016] [Indexed: 06/06/2023]
Abstract
Generating and detecting a prescribed single-electron state is an important step towards solid-state fermion optics. We propose how to generate an electron in a Gaussian state, using a quantum-dot pump with gigahertz operation and realistic parameters. With the help of a strong magnetic field, the electron occupies a coherent state in the pump, insensitive to the details of nonadiabatic evolution. The state changes during the emission from the pump, governed by competition between the Landauer-Buttiker traversal time and the passage time. When the former is much shorter than the latter, the emitted state is a Gaussian wave packet. The Gaussian packet can be identified by using a dynamical potential barrier, with a resolution reaching the Heisenberg minimal uncertainty ℏ/2.
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Affiliation(s)
- Sungguen Ryu
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - M Kataoka
- National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom
| | - H-S Sim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
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