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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Cho SU, Park W, Kim BK, Seo M, Park DT, Choi H, Kim N, Sim HS, Bae MH. One-Lead Single-Electron Source with Charging Energy. NANO LETTERS 2022; 22:9313-9318. [PMID: 36442504 DOI: 10.1021/acs.nanolett.2c02893] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Single-electron sources, formed by a quantum dot (QD), are key elements for realizing electron analogue of quantum optics. We develop a new type of single-electron source with functionalities that are absent in existing sources. This source couples with only one lead. By an AC rf drive, it successively emits holes and electrons cotraveling in the lead, as in the mesoscopic capacitor. Thanks to the considerable charging energy of the QD, however, emitted electrons have energy levels a few tens of millielectronvolts above the Fermi level, so that emitted holes and electrons are split by a potential barrier on demand, resulting in a rectified quantized current. The resulting pump map exhibits quantized triangular islands, in good agreement with our theory. We also demonstrate that the source can be operated with another tunable-barrier single-electron source in a series double QD geometry, showing parallel electron pumping by a common gate driving.
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Affiliation(s)
- Sung Un Cho
- Department of Physics & Center for Quantum Coherence in Condensed Matter, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
| | - Wanki Park
- Department of Physics & Center for Quantum Coherence in Condensed Matter, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
| | - Bum-Kyu Kim
- Korea Research Institute of Standards and Science, Daejeon 34113, Republic of Korea
| | - Minky Seo
- Department of Physics & Center for Quantum Coherence in Condensed Matter, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
| | - Dongsung T Park
- Department of Physics & Center for Quantum Coherence in Condensed Matter, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
| | - Hyungkook Choi
- Department of Physics, Jeonbuk National University, Jeonju 54896, Republic of Korea
| | - Nam Kim
- Korea Research Institute of Standards and Science, Daejeon 34113, Republic of Korea
| | - H-S Sim
- Department of Physics & Center for Quantum Coherence in Condensed Matter, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
| | - Myung-Ho Bae
- Korea Research Institute of Standards and Science, Daejeon 34113, Republic of Korea
- Department of Nano Science, University of Science and Technology, Daejeon 34113, Republic of Korea
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4
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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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5
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Weinbub J, Kosik R. Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:163001. [PMID: 35008077 DOI: 10.1088/1361-648x/ac49c6] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2021] [Accepted: 01/10/2022] [Indexed: 06/14/2023]
Abstract
Quantum electronics has significantly evolved over the last decades. Where initially the clear focus was on light-matter interactions, nowadays approaches based on the electron's wave nature have solidified themselves as additional focus areas. This development is largely driven by continuous advances in electron quantum optics, electron based quantum information processing, electronic materials, and nanoelectronic devices and systems. The pace of research in all of these areas is astonishing and is accompanied by substantial theoretical and experimental advancements. What is particularly exciting is the fact that the computational methods, together with broadly available large-scale computing resources, have matured to such a degree so as to be essential enabling technologies themselves. These methods allow to predict, analyze, and design not only individual physical processes but also entire devices and systems, which would otherwise be very challenging or sometimes even out of reach with conventional experimental capabilities. This review is thus a testament to the increasingly towering importance of computational methods for advancing the expanding field of quantum electronics. To that end, computational aspects of a representative selection of recent research in quantum electronics are highlighted where a major focus is on the electron's wave nature. By categorizing the research into concrete technological applications, researchers and engineers will be able to use this review as a source for inspiration regarding problem-specific computational methods.
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Affiliation(s)
- Josef Weinbub
- Christian Doppler Laboratory for High Performance TCAD, Institute for Microelectronics, TU Wien, Austria
| | - Robert Kosik
- Institute for Microelectronics, TU Wien, Austria
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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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7
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Moskalets M. Auto- versus Cross-Correlation Noise in Periodically Driven Quantum Coherent Conductors. ENTROPY 2021; 23:e23040393. [PMID: 33806199 PMCID: PMC8066600 DOI: 10.3390/e23040393] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Revised: 03/21/2021] [Accepted: 03/23/2021] [Indexed: 11/16/2022]
Abstract
Expressing currents and their fluctuations at the terminals of a multi-probe conductor in terms of the wave functions of carriers injected into the Fermi sea provides new insight into the physics of electric currents. This approach helps us to identify two physically different contributions to shot noise. In the quantum coherent regime, when current is carried by non-overlapping wave packets, the product of current fluctuations in different leads, the cross-correlation noise, is determined solely by the duration of the wave packet. In contrast, the square of the current fluctuations in one lead, the autocorrelation noise, is additionally determined by the coherence of the wave packet, which is associated with the spread of the wave packet in energy. The two contributions can be addressed separately in the weak back-scattering regime, when the autocorrelation noise depends only on the coherence. Analysis of shot noise in terms of these contributions allows us, in particular, to predict that no individual traveling particles with a real wave function, such as Majorana fermions, can be created in the Fermi sea in a clean manner, that is, without accompanying electron-hole pairs.
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Affiliation(s)
- Michael Moskalets
- Department of Metal and Semiconductor Physics, NTU "Kharkiv Polytechnic Institute", 61002 Kharkiv, Ukraine
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8
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Rodriguez RH, Parmentier FD, Ferraro D, Roulleau P, Gennser U, Cavanna A, Sassetti M, Portier F, Mailly D, Roche P. Relaxation and revival of quasiparticles injected in an interacting quantum Hall liquid. Nat Commun 2020; 11:2426. [PMID: 32415091 PMCID: PMC7229030 DOI: 10.1038/s41467-020-16331-4] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2020] [Accepted: 04/28/2020] [Indexed: 11/18/2022] Open
Abstract
The one-dimensional, chiral edge channels of the quantum Hall effect are a promising platform in which to implement electron quantum optics experiments; however, Coulomb interactions between edge channels are a major source of decoherence and energy relaxation. It is therefore of large interest to understand the range and limitations of the simple quantum electron optics picture. Here we confirm experimentally for the first time the predicted relaxation and revival of electrons injected at finite energy into an edge channel. The observed decay of the injected electrons is reproduced theoretically within a Tomonaga-Luttinger liquid framework, including an important dissipation towards external degrees of freedom. This gives us a quantitative empirical understanding of the strength of the interaction and the dissipation.
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Affiliation(s)
- R H Rodriguez
- Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette, 91191, France
| | - F D Parmentier
- Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette, 91191, France.
| | - D Ferraro
- Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy
- SPIN-CNR, Via Dodecaneso 33, 16146, Genova, Italy
| | - P Roulleau
- Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette, 91191, France
| | - U Gennser
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), Palaiseau, 91120, France
| | - A Cavanna
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), Palaiseau, 91120, France
| | - M Sassetti
- Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy
- SPIN-CNR, Via Dodecaneso 33, 16146, Genova, Italy
| | - F Portier
- Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette, 91191, France
| | - D Mailly
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), Palaiseau, 91120, France
| | - P Roche
- Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette, 91191, France
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9
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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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