1
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Iyer K, Ronetti F, Grémaud B, Martin T, Rech J, Jonckheere T. Finite Width of Anyons Changes Their Braiding Signature. PHYSICAL REVIEW LETTERS 2024; 132:216601. [PMID: 38856285 DOI: 10.1103/physrevlett.132.216601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2023] [Revised: 03/12/2024] [Accepted: 04/09/2024] [Indexed: 06/11/2024]
Abstract
Anyons are particles intermediate between fermions and bosons, characterized by a nontrivial exchange phase, yielding remarkable braiding statistics. Recent experiments have shown that anyonic braiding has observable consequences on edge transport in the fractional quantum Hall effect (FQHE). Here, we study transport signatures of anyonic braiding when the anyons have a finite width. We show that the width of the anyons, even when extremely small, can have a tremendous impact on transport properties and braiding signatures. In particular, we find that taking the finite width into account allows us to explain recent experimental results on the FQHE at filling factor 2/5 [M. Ruelle et al., Phys. Rev. X 13, 011031 (2023)PRXHAE2160-330810.1103/PhysRevX.13.011031]. Our work shows that the finite width of anyons crucially influences setups involving anyonic braiding, especially when the exchange phase is larger than π/2.
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Affiliation(s)
- K Iyer
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
| | - F Ronetti
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
| | - B Grémaud
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
| | - T Martin
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
| | - J Rech
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
| | - T Jonckheere
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
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2
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Zhang G, Hong C, Alkalay T, Umansky V, Heiblum M, Gornyi I, Gefen Y. Measuring statistics-induced entanglement entropy with a Hong-Ou-Mandel interferometer. Nat Commun 2024; 15:3428. [PMID: 38654002 PMCID: PMC11039745 DOI: 10.1038/s41467-024-47335-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 03/26/2024] [Indexed: 04/25/2024] Open
Abstract
Despite its ubiquity in quantum computation and quantum information, a universally applicable definition of quantum entanglement remains elusive. The challenge is further accentuated when entanglement is associated with other key themes, e.g., quantum interference and quantum statistics. Here, we introduce two novel motifs that characterize the interplay of entanglement and quantum statistics: an 'entanglement pointer' and a 'statistics-induced entanglement entropy'. The two provide a quantitative description of the statistics-induced entanglement: (i) they are finite only in the presence of quantum entanglement underlined by quantum statistics and (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions, bosons, and anyons). We have experimentally implemented these ideas by employing an electronic Hong-Ou-Mandel interferometer fed by two highly diluted electron beams in an integer quantum Hall platform. Performing measurements of auto-correlation and cross-correlation of current fluctuations of the scattered beams (following 'collisions'), we quantify the statistics-induced entanglement by experimentally accessing the entanglement pointer and the statistics-induced entanglement entropy. Our theoretical and experimental approaches pave the way to study entanglement in various correlated platforms, e.g., those involving anyonic Abelian and non-Abelian states.
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Affiliation(s)
- Gu Zhang
- Beijing Academy of Quantum Information Sciences, Beijing, China
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - Changki Hong
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Tomer Alkalay
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Vladimir Umansky
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Moty Heiblum
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel.
| | - Igor Gornyi
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Karlsruhe, Germany.
| | - Yuval Gefen
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel.
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3
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Thamm M, Rosenow B. Effect of the Soliton Width on Nonequilibrium Exchange Phases of Anyons. PHYSICAL REVIEW LETTERS 2024; 132:156501. [PMID: 38682969 DOI: 10.1103/physrevlett.132.156501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Revised: 02/20/2024] [Accepted: 03/20/2024] [Indexed: 05/01/2024]
Abstract
Unlike bosons and fermions, quasiparticles in two-dimensional quantum systems, known as anyons, exhibit statistical exchange phases that range between 0 and π. In fractional quantum Hall states, these anyons, possessing a fraction of the electron charge, traverse along chiral edge channels. This movement facilitates the creation of anyon colliders, where coupling different edge channels through a quantum point contact enables the observation of two-particle interference effects. Such configurations are instrumental in deducing the anyonic exchange phase via current cross-correlations. Prior theoretical models represented dilute anyon beams as discrete steps in the boson fields. However, our study reveals that incorporating the finite width of the soliton shape is crucial for accurately interpreting recent experiments, especially for collider experiments involving anyons with exchange phases θ>π/2, where prior theories fall short.
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Affiliation(s)
- Matthias Thamm
- Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, 04103 Leipzig, Germany
| | - Bernd Rosenow
- Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, 04103 Leipzig, Germany
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4
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McGinley M, Fava M, Parameswaran SA. Signatures of Fractional Statistics in Nonlinear Pump-Probe Spectroscopy. PHYSICAL REVIEW LETTERS 2024; 132:066702. [PMID: 38394597 DOI: 10.1103/physrevlett.132.066702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Revised: 10/30/2023] [Accepted: 01/04/2024] [Indexed: 02/25/2024]
Abstract
We show that the presence of anyons in the excitation spectrum of a two-dimensional system can be inferred from nonlinear spectroscopic quantities. In particular, we consider pump-probe spectroscopy, where a sample is irradiated by two light pulses with an adjustable time delay between them. The relevant response coefficient exhibits a universal form that originates from the statistical phase acquired when anyons created by the first pulse braid around those created by the second. This behavior is shown to be qualitatively unchanged by nonuniversal physics including nonstatistical interactions and small nonzero temperatures. In magnetic systems, the signal of interest can be measured using currently available terahertz-domain probes, highlighting the potential usefulness of nonlinear spectroscopic techniques in the search for quantum spin liquids.
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Affiliation(s)
- Max McGinley
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- T.C.M. Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Michele Fava
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- Philippe Meyer Institute, Physics Department, École Normale Supérieure (ENS), Université PSL, 24 rue Lhomond, F-75231 Paris, France
| | - S A Parameswaran
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
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5
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Schiller N, Shapira Y, Stern A, Oreg Y. Anyon Statistics through Conductance Measurements of Time-Domain Interferometry. PHYSICAL REVIEW LETTERS 2023; 131:186601. [PMID: 37977648 DOI: 10.1103/physrevlett.131.186601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 10/16/2023] [Indexed: 11/19/2023]
Abstract
We propose a method to extract the mutual exchange statistics of the anyonic excitations of a general Abelian fractional quantum Hall state, by comparing the tunneling characteristics of a quantum point contact in two different experimental conditions. In the first, the tunneling current between two edges at different chemical potentials is measured. In the second, one of these edges is strongly diluted by an earlier point contact. We describe the case of the dilute beam in terms of a time-domain interferometer between the anyons flowing along the edge and quasiparticle-quasihole excitations created at the tunneling quantum point contact. In both cases, temperature is kept large, such that the measured current is given to linear response. Remarkably, our proposal does not require the measurement of current correlations, and allows us to carefully separate effects of the fractional charge and statistics from effects of intra- and interedge interactions.
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Affiliation(s)
- Noam Schiller
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Yotam Shapira
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Yuval Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
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6
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Lee JYM, Hong C, Alkalay T, Schiller N, Umansky V, Heiblum M, Oreg Y, Sim HS. Partitioning of diluted anyons reveals their braiding statistics. Nature 2023; 617:277-281. [PMID: 37100910 DOI: 10.1038/s41586-023-05883-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 02/23/2023] [Indexed: 04/28/2023]
Abstract
Correlations of partitioned particles carry essential information about their quantumness1. Partitioning full beams of charged particles leads to current fluctuations, with their autocorrelation (namely, shot noise) revealing the particles' charge2,3. This is not the case when a highly diluted beam is partitioned. Bosons or fermions will exhibit particle antibunching (owing to their sparsity and discreteness)4-6. However, when diluted anyons, such as quasiparticles in fractional quantum Hall states, are partitioned in a narrow constriction, their autocorrelation reveals an essential aspect of their quantum exchange statistics: their braiding phase7. Here we describe detailed measurements of weakly partitioned, highly diluted, one-dimension-like edge modes of the one-third filling fractional quantum Hall state. The measured autocorrelation agrees with our theory of braiding anyons in the time domain (instead of braiding in space); with a braiding phase of 2θ = 2π/3, without any fitting parameters. Our work offers a relatively straightforward and simple method to observe the braiding statistics of exotic anyonic states, such as non-abelian states8, without resorting to complex interference experiments9.
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Affiliation(s)
- June-Young M Lee
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, South Korea
| | - Changki Hong
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Tomer Alkalay
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Noam Schiller
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Vladimir Umansky
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Moty Heiblum
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel.
| | - Yuval Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - H-S Sim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, South Korea.
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7
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Glidic P, Maillet O, Piquard C, Aassime A, Cavanna A, Jin Y, Gennser U, Anthore A, Pierre F. Quasiparticle Andreev scattering in the ν = 1/3 fractional quantum Hall regime. Nat Commun 2023; 14:514. [PMID: 36720855 PMCID: PMC9889737 DOI: 10.1038/s41467-023-36080-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Accepted: 01/12/2023] [Indexed: 02/02/2023] Open
Abstract
The scattering of exotic quasiparticles may follow different rules than electrons. In the fractional quantum Hall regime, a quantum point contact (QPC) provides a source of quasiparticles with field effect selectable charges and statistics, which can be scattered on an 'analyzer' QPC to investigate these rules. Remarkably, for incident quasiparticles dissimilar to those naturally transmitted across the analyzer, electrical conduction conserves neither the nature nor the number of the quasiparticles. In contrast with standard elastic scattering, theory predicts the emergence of a mechanism akin to the Andreev reflection at a normal-superconductor interface. Here, we observe the predicted Andreev-like reflection of an e/3 quasiparticle into a - 2e/3 hole accompanied by the transmission of an e quasielectron. Combining shot noise and cross-correlation measurements, we independently determine the charge of the different particles and ascertain the coincidence of quasielectron and fractional hole. The present work advances our understanding on the unconventional behavior of fractional quasiparticles, with implications toward the generation of novel quasi-particles/holes and non-local entanglements.
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Affiliation(s)
- P Glidic
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - O Maillet
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - C Piquard
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - A Aassime
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - A Cavanna
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - Y Jin
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - U Gennser
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - A Anthore
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France.
- Université Paris Cité, CNRS, Centre de Nanosciences et de Nanotechnologies, F-91120, Palaiseau, France.
| | - F Pierre
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France.
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8
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Feldman DE, Halperin BI. Fractional charge and fractional statistics in the quantum Hall effects. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2021; 84:076501. [PMID: 34015771 DOI: 10.1088/1361-6633/ac03aa] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 05/20/2021] [Indexed: 06/12/2023]
Abstract
Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.
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Affiliation(s)
- D E Feldman
- Brown Theoretical Physics Center and Department of Physics, Brown University, Providence, RI 02912, United States of America
| | - Bertrand I Halperin
- Department of Physics, Harvard University, Cambridge, MA 02138, United States of America
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9
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Rech J, Jonckheere T, Grémaud B, Martin T. Negative Delta-T Noise in the Fractional Quantum Hall Effect. PHYSICAL REVIEW LETTERS 2020; 125:086801. [PMID: 32909784 DOI: 10.1103/physrevlett.125.086801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 07/28/2020] [Indexed: 06/11/2023]
Abstract
We study the current correlations of fractional quantum Hall edges at the output of a quantum point contact subjected to a temperature gradient. This out-of-equilibrium situation gives rise to a form of temperature-activated shot noise, dubbed delta-T noise. We show that the tunneling of Laughlin quasiparticles leads to a negative delta-T noise, in stark contrast with electron tunneling. Moreover, varying the transmission of the quantum point contact or applying a voltage bias across the Hall bar may flip the sign of this noise contribution, yielding signatures that can be accessed experimentally.
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Affiliation(s)
- J Rech
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
| | - T Jonckheere
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
| | - B Grémaud
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
| | - T Martin
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
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10
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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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11
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Bartolomei H, Kumar M, Bisognin R, Marguerite A, Berroir JM, Bocquillon E, Plaçais B, Cavanna A, Dong Q, Gennser U, Jin Y, Fève G. Fractional statistics in anyon collisions. Science 2020; 368:173-177. [PMID: 32273465 DOI: 10.1126/science.aaz5601] [Citation(s) in RCA: 67] [Impact Index Per Article: 16.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Accepted: 03/12/2020] [Indexed: 11/03/2022]
Abstract
Two-dimensional systems can host exotic particles called anyons whose quantum statistics are neither bosonic nor fermionic. For example, the elementary excitations of the fractional quantum Hall effect at filling factor ν = 1/m (where m is an odd integer) have been predicted to obey Abelian fractional statistics, with a phase ϕ associated with the exchange of two particles equal to π/m However, despite numerous experimental attempts, clear signatures of fractional statistics have remained elusive. We experimentally demonstrate Abelian fractional statistics at filling factor ν = ⅓ by measuring the current correlations resulting from the collision between anyons at a beamsplitter. By analyzing their dependence on the anyon current impinging on the splitter and comparing with recent theoretical models, we extract ϕ = π/3, in agreement with predictions.
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Affiliation(s)
- H Bartolomei
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - M Kumar
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - R Bisognin
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - A Marguerite
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - J-M Berroir
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - E Bocquillon
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - B Plaçais
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - A Cavanna
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Saclay, Palaiseau, France
| | - Q Dong
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Saclay, Palaiseau, France
| | - U Gennser
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Saclay, Palaiseau, France
| | - Y Jin
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Saclay, Palaiseau, France
| | - G Fève
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France.
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12
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Lee B, Han C, Sim HS. Negative Excess Shot Noise by Anyon Braiding. PHYSICAL REVIEW LETTERS 2019; 123:016803. [PMID: 31386400 DOI: 10.1103/physrevlett.123.016803] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2018] [Revised: 03/11/2019] [Indexed: 05/12/2023]
Abstract
Anyonic fractional charges e^{*} have been detected by autocorrelation shot noise at a quantum point contact (QPC) between two fractional quantum Hall edges. We find that the autocorrelation noise can also show a fingerprint of Abelian anyonic fractional statistics. We predict the noise of the electrical tunneling current I at the QPC of the fractional-charge detection setup, when anyons are dilutely injected, from an additional edge biased by a voltage, to the setup in equilibrium. At large voltages, the nonequilibrium noise is reduced below the thermal equilibrium noise by the value 2e^{*}I. This negative excess noise is opposite to the positive excess noise 2e^{*}I of the conventional fractional-charge detection and also to the usual positive autocorrelation noises of electrical currents. This is a signature of Abelian fractional statistics, resulting from the effective braiding of an anyon thermally excited at the QPC around another anyon injected from the additional edge.
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Affiliation(s)
- Byeongmok Lee
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Cheolhee Han
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - H-S Sim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
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13
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Bisognin R, Bartolomei H, Kumar M, Safi I, Berroir JM, Bocquillon E, Plaçais B, Cavanna A, Gennser U, Jin Y, Fève G. Microwave photons emitted by fractionally charged quasiparticles. Nat Commun 2019; 10:1708. [PMID: 30979891 PMCID: PMC6461615 DOI: 10.1038/s41467-019-09758-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2019] [Accepted: 03/27/2019] [Indexed: 11/21/2022] Open
Abstract
Strongly correlated low-dimensional systems can host exotic elementary excitations carrying a fractional charge q and potentially obeying anyonic statistics. In the fractional quantum Hall effect, their fractional charge has been successfully determined owing to low frequency shot noise measurements. However, a universal method for sensing them unambiguously and unraveling their intricate dynamics was still lacking. Here, we demonstrate that this can be achieved by measuring the microwave photons emitted by such excitations when they are transferred through a potential barrier biased with a dc voltage Vdc. We observe that only photons at frequencies f below qVdc/h are emitted. This threshold provides a direct and unambiguous determination of the charge q, and a signature of exclusion statistics. Derived initially within the Luttinger model, this feature is also predicted by universal non-equilibrium fluctuation relations which agree fully with our measurements. Our work paves the way for further exploration of anyonic statistics using microwave measurements.
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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, 75005, Paris, France
| | - H Bartolomei
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 75005, Paris, France
| | - M Kumar
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 75005, Paris, France
| | - I Safi
- Laboratoire de Physique des Solides, Université Paris-Saclay, 91405, Orsay, France
| | - J-M Berroir
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 75005, Paris, France
| | - E Bocquillon
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 75005, Paris, France
| | - B Plaçais
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 75005, Paris, 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
| | - G Fève
- Laboratoire de Physique de l' Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 75005, Paris, France.
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14
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Rosenow B, Levkivskyi IP, Halperin BI. Current Correlations from a Mesoscopic Anyon Collider. PHYSICAL REVIEW LETTERS 2016; 116:156802. [PMID: 27127979 DOI: 10.1103/physrevlett.116.156802] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2016] [Indexed: 05/12/2023]
Abstract
Fermions and bosons are fundamental realizations of exchange statistics, which governs the probability for two particles being close to each other spatially. Anyons in the fractional quantum Hall effect are an example for exchange statistics intermediate between bosons and fermions. We analyze a mesoscopic setup in which two dilute beams of anyons collide with each other, and relate the correlations of current fluctuations to the probability of particles excluding each other spatially. While current correlations for fermions vanish, negative correlations for anyons are a clear signature of a reduced spatial exclusion as compared to fermions.
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Affiliation(s)
- Bernd Rosenow
- Institut für Theoretische Physik, Universität Leipzig, D-04009 Leipzig, Germany
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ivan P Levkivskyi
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
- Institute for Theoretical Physics, ETH Zurich, CH-8093 Zurich, Switzerland
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15
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Han C, Park J, Gefen Y, Sim HS. Topological vacuum bubbles by anyon braiding. Nat Commun 2016; 7:11131. [PMID: 27030442 PMCID: PMC4821888 DOI: 10.1038/ncomms11131] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2015] [Accepted: 02/23/2016] [Indexed: 11/09/2022] Open
Abstract
According to a basic rule of fermionic and bosonic many-body physics, known as the linked cluster theorem, physical observables are not affected by vacuum bubbles, which represent virtual particles created from vacuum and self-annihilating without interacting with real particles. Here we show that this conventional knowledge must be revised for anyons, quasiparticles that obey fractional exchange statistics intermediate between fermions and bosons. We find that a certain class of vacuum bubbles of Abelian anyons does affect physical observables. They represent virtually excited anyons that wind around real anyonic excitations. These topological bubbles result in a temperature-dependent phase shift of Fabry-Perot interference patterns in the fractional quantum Hall regime accessible in current experiments, thus providing a tool for direct and unambiguous observation of elusive fractional statistics.
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Affiliation(s)
- Cheolhee Han
- Department of Physics, Korea Advanced Institute of Science and Technology, 291, Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
| | - Jinhong Park
- Department of Physics, Korea Advanced Institute of Science and Technology, 291, Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
| | - Yuval Gefen
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - H.-S. Sim
- Department of Physics, Korea Advanced Institute of Science and Technology, 291, Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
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16
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Campagnano G, Zilberberg O, Gornyi IV, Feldman DE, Potter AC, Gefen Y. Hanbury Brown-Twiss interference of anyons. PHYSICAL REVIEW LETTERS 2012; 109:106802. [PMID: 23005316 DOI: 10.1103/physrevlett.109.106802] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2012] [Indexed: 06/01/2023]
Abstract
We present a study of a Hanbury Brown-Twiss interferometer realized with anyons. Such a device can directly probe entanglement and fractional statistics of initially uncorrelated particles. We calculate Hanbury Brown-Twiss cross correlations of Abelian Laughlin anyons. The correlations we calculate exhibit partial bunching similar to bosons, indicating a substantial statistical transmutation from the underlying electronic degrees of freedom. We also find qualitative differences between the anyonic signal and the corresponding bosonic or fermionic signals, indicating that anyons cannot be simply thought of as intermediate between bosons and fermions.
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Affiliation(s)
- Gabriele Campagnano
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
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17
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Duhot S, Lefloch F, Houzet M. Cross correlation of incoherent multiple Andreev reflections. PHYSICAL REVIEW LETTERS 2009; 102:086804. [PMID: 19257769 DOI: 10.1103/physrevlett.102.086804] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2008] [Indexed: 05/27/2023]
Abstract
We use a semiclassical theory to calculate the current correlations in a multiterminal structure composed of a normal metallic dot connected to all superconducting leads at arbitrary voltage and temperature. This theory holds when the proximity effect is suppressed in the dot. At low voltage, eV<<Delta (Delta is the superconducting gap in the leads), when charge transport is due to incoherent multiple Andreev reflections, the correlations are strongly enhanced compared to those in the normal state. Moreover, we predict that the cross correlation can be positive or negative depending on the properties of the point contacts between the dot and the leads. We also discuss the effect of inelastic scattering in the dot.
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Affiliation(s)
- Sylvie Duhot
- Institut Néel, CNRS and Université Joseph Fourier, F-38042 Grenoble, France
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18
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Vishveshwara S, Stone M, Sen D. Correlators and fractional statistics in the quantum Hall bulk. PHYSICAL REVIEW LETTERS 2007; 99:190401. [PMID: 18233048 DOI: 10.1103/physrevlett.99.190401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2007] [Indexed: 05/25/2023]
Abstract
We derive one-particle and two-particle correlators of anyons in the lowest Landau level. We show that the two-particle correlator exhibits signatures of fractional statistics which can distinguish anyons from their fermionic and bosonic counterparts. These signatures include the zeros of the two-particle correlator and its exclusion behavior. We find that the one-particle correlator in finite geometries carries valuable information relevant to experiments in which quasiparticles on the edge of a quantum Hall system tunnel through its bulk.
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Affiliation(s)
- Smitha Vishveshwara
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
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19
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Averin DV, Nesteroff JA. Coulomb blockade of anyons in quantum antidots. PHYSICAL REVIEW LETTERS 2007; 99:096801. [PMID: 17931025 DOI: 10.1103/physrevlett.99.096801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2007] [Indexed: 05/25/2023]
Abstract
Coulomb interaction turns anyonic quasiparticles of a primary quantum Hall liquid with filling factor nu=1/(2m+1) into hard-core anyons. We have developed a model of coherent transport of such quasiparticles in systems of multiple antidots by extending the Wigner-Jordan description of 1D Abelian anyons to tunneling problems. We show that the anyonic exchange statistics manifests itself in tunneling conductance even in the absence of quasiparticle exchanges. In particular, it can be seen as a nonvanishing resonant peak associated with quasiparticle tunneling through a line of three antidots.
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Affiliation(s)
- Dmitri V Averin
- Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
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20
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McClure DT, Dicarlo L, Zhang Y, Engel HA, Marcus CM, Hanson MP, Gossard AC. Tunable noise cross correlations in a double quantum dot. PHYSICAL REVIEW LETTERS 2007; 98:056801. [PMID: 17358883 DOI: 10.1103/physrevlett.98.056801] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2006] [Indexed: 05/14/2023]
Abstract
We report measurements of the cross correlation between temporal current fluctuations in two capacitively coupled quantum dots in the Coulomb blockade regime. The sign of the cross-spectral density is found to be tunable by gate voltage and source-drain bias. We find good agreement with the data by including an interdot Coulomb interaction in a sequential-tunneling model.
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Affiliation(s)
- D T McClure
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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21
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Kim EA. Aharanov-Bohm interference and fractional statistics in a quantum Hall interferometer. PHYSICAL REVIEW LETTERS 2006; 97:216404. [PMID: 17155758 DOI: 10.1103/physrevlett.97.216404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2006] [Indexed: 05/12/2023]
Abstract
We compute the temperature, voltage, and magnetic field dependences of the conductance oscillations of a model interferometer designed to measure the fractional statistics of the quasiparticles in the fractional quantum Hall effect. The geometry is the same as that used in recent experiments. With appropriate assumptions concerning the relative areas of the inner and outer rings of the interferometer, we find the theoretical results, including the existence of super periodic Aharonov-Bohm oscillations, to be in remarkably good agreement with experiment. We then make additional experimental predictions with no adjustable parameters which, if verified, would confirm the proposed interpretation of the experiment as a measurement of fractional statistics.
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Affiliation(s)
- Eun-Ah Kim
- Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, California 94305, USA
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22
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Feldman DE, Kitaev A. Detecting non-Abelian statistics with an electronic Mach-Zehnder interferometer. PHYSICAL REVIEW LETTERS 2006; 97:186803. [PMID: 17155568 DOI: 10.1103/physrevlett.97.186803] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2006] [Indexed: 05/12/2023]
Abstract
Fractionally charged quasiparticles in the quantum Hall state with a filling factor nu=5/2 are expected to obey non-Abelian statistics. We demonstrate that their statistics can be probed by transport measurements in an electronic Mach-Zehnder interferometer. The tunneling current through the interferometer exhibits a characteristic dependence on the magnetic flux and a nonanalytic dependence on the tunneling amplitudes which can be controlled by gate voltages.
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Affiliation(s)
- D E Feldman
- Department of Physics, Brown University, Providence, Rhode Island 02912, USA
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23
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Rychkov V, Büttiker M. Mesoscopic versus macroscopic division of current fluctuations. PHYSICAL REVIEW LETTERS 2006; 96:166806. [PMID: 16712259 DOI: 10.1103/physrevlett.96.166806] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2006] [Indexed: 05/09/2023]
Abstract
We investigate the current shot noise at a three terminal node in which one of the branches contains a noise generating source and the correlations are measured between the currents flowing through the other two branches. Interestingly, if the node is macroscopic, the current correlations are positive, whereas for a quantum coherent mesoscopic node antibunching of electrons leads to negative correlations. We present specific predictions which permit the experimental investigation of the crossover from the quantum mechanical noise division to the macroscopic noise division.
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Affiliation(s)
- V Rychkov
- Département de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland.
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24
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Kim EA, Lawler M, Vishveshwara S, Fradkin E. Signatures of fractional statistics in noise experiments in quantum Hall fluids. PHYSICAL REVIEW LETTERS 2005; 95:176402. [PMID: 16383842 DOI: 10.1103/physrevlett.95.176402] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2005] [Indexed: 05/05/2023]
Abstract
The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics. Yet, this fundamental prediction has remained an open experimental challenge. Here we show that the cross-current noise in a three-terminal tunneling experiment of a two dimensional electron gas in the FQH regime can be used to detect directly the statistical angle of the excitations of these topological quantum fluids. We show that the noise also reveals signatures of exclusion statistics and of fractional charge. The vortices of Laughlin states should exhibit a bunching effect, while for higher states in the Jain sequences they should exhibit an "antibunching" effect.
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Affiliation(s)
- Eun-Ah Kim
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
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25
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Course 5 Noise in mesoscopic physics. NANOPHYSICS: COHERENCE AND TRANSPORT, ÉCOLE D'ÉTÉ DE PHYSIQUE DES HOUCHES SESSION LXXXI 2005. [DOI: 10.1016/s0924-8099(05)80047-2] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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26
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Kim EA, Vishveshwara S, Fradkin E. Cooper-pair tunneling in junctions of singlet quantum Hall States and superconductors. PHYSICAL REVIEW LETTERS 2004; 93:266803. [PMID: 15698004 DOI: 10.1103/physrevlett.93.266803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2004] [Indexed: 05/24/2023]
Abstract
We propose tunnel junctions of a Hall bar and a superconducting lead for observing Cooper-pair tunneling into singlet fractional quantum Hall edge states. These tunnel junctions provide a natural means of extracting precise information of the spin polarization and the filling factor of the state. The low energy regime of one of the setups is governed by a novel quantum entangled fixed point.
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Affiliation(s)
- Eun-Ah Kim
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
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27
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Cottet A, Belzig W, Bruder C. Positive cross correlations in a three-terminal quantum dot with ferromagnetic contacts. PHYSICAL REVIEW LETTERS 2004; 92:206801. [PMID: 15169373 DOI: 10.1103/physrevlett.92.206801] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2003] [Indexed: 05/24/2023]
Abstract
We study current fluctuations in an interacting three-terminal quantum dot with ferromagnetic leads. For appropriately polarized contacts, the transport through the dot is governed by dynamical spin blockade, i.e., a spin-dependent bunching of tunneling events not present in the paramagnetic case. This leads, for instance, to positive zero-frequency cross correlations of the currents in the output leads even in the absence of spin accumulation on the dot. We include the influence of spin-flip scattering and identify favorable conditions for the experimental observation of this effect with respect to polarization of the contacts and tunneling rates.
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Affiliation(s)
- A Cottet
- Department of Physics and Astronomy, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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28
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Samuelsson P, Sukhorukov EV, Büttiker M. Two-particle Aharonov-Bohm effect and entanglement in the electronic Hanbury Brown-Twiss setup. PHYSICAL REVIEW LETTERS 2004; 92:026805. [PMID: 14753955 DOI: 10.1103/physrevlett.92.026805] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2003] [Indexed: 05/24/2023]
Abstract
We analyze a Hanbury Brown-Twiss geometry in which particles are injected from two independent sources into a mesoscopic conductor in the quantum Hall regime. All partial waves end in different reservoirs without generating any single-particle interference; in particular, there is no single-particle Aharonov-Bohm effect. However, exchange effects lead to two-particle Aharonov-Bohm oscillations in the zero-frequency current cross correlations. We demonstrate that this is related to two-particle orbital entanglement, detected via violation of a Bell inequality. The transport is along edge states and only adiabatic quantum point contacts and normal reservoirs are employed.
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Affiliation(s)
- P Samuelsson
- Département de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland
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29
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Chamon C, Oshikawa M, Affleck I. Junctions of three quantum wires and the dissipative Hofstadter model. PHYSICAL REVIEW LETTERS 2003; 91:206403. [PMID: 14683383 DOI: 10.1103/physrevlett.91.206403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2003] [Indexed: 05/24/2023]
Abstract
We study a junction of three quantum wires enclosing a magnetic flux. This is the simplest problem of a quantum junction between Tomonaga-Luttinger liquids in which Fermi statistics enter in a nontrivial way. We present a direct connection between this problem and the dissipative Hofstadter problem, or quantum Brownian motion in two dimensions in a periodic potential and an external magnetic field, which in turn is connected to open string theory in a background electromagnetic field. We find nontrivial fixed points corresponding to a chiral conductance tensor leading to an asymmetric flow of the current.
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Affiliation(s)
- Claudio Chamon
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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30
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Vishveshwara S. Revisiting the Hanbury Brown-Twiss setup for fractional statistics. PHYSICAL REVIEW LETTERS 2003; 91:196803. [PMID: 14611600 DOI: 10.1103/physrevlett.91.196803] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2003] [Indexed: 05/24/2023]
Abstract
The Hanbury Brown-Twiss experiment has proved to be an effective means of probing statistics of particles. Here, in a setup involving edge-state quasiparticles in a fractional quantum Hall system, we show that a variant of the experiment composed of two sources and two sinks can be used to unearth fractional statistics. We find a clearcut signature of the statistics in the equal-time current-current correlation function for quasiparticle currents emerging from the two sources and collected at the sinks.
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Affiliation(s)
- Smitha Vishveshwara
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801-3080, USA
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31
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Kane CL. Telegraph noise and fractional statistics in the quantum Hall effect. PHYSICAL REVIEW LETTERS 2003; 90:226802. [PMID: 12857331 DOI: 10.1103/physrevlett.90.226802] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2002] [Indexed: 05/24/2023]
Abstract
We study theoretically nonequilibrium noise in the fractional quantum Hall regime for an Aharonov-Bohm ring with a third contact in the middle of the ring. Because of their fractional statistics the tunneling of Laughlin quasiparticles between the inner and outer edges of the ring changes the effective Aharonov-Bohm flux experienced by quasiparticles going around the ring, leading to a change in the conductance across the ring. A small current in the middle contact, therefore, gives rise to fluctuations in the current flowing across the ring which resemble random telegraph noise. We analyze this noise using the chiral Luttinger liquid model. At low frequencies the telegraph noise varies inversely with the tunneling current and can be much larger than the shot noise. We propose that combining the Aharonov-Bohm effect with a noise measurement provides a direct method for observing fractional statistics.
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Affiliation(s)
- C L Kane
- Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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32
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Chen S, Trauzettel B, Egger R. Landauer-type transport theory for interacting quantum wires: application to carbon nanotube y junctions. PHYSICAL REVIEW LETTERS 2002; 89:226404. [PMID: 12485088 DOI: 10.1103/physrevlett.89.226404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2002] [Indexed: 05/24/2023]
Abstract
We propose a Landauerlike theory for nonlinear transport in networks of one-dimensional interacting quantum wires (Luttinger liquids). A concrete example of current experimental focus is given by carbon nanotube Y junctions. Our theory has three basic ingredients that allow one to explicitly solve this transport problem: (i) radiative boundary conditions to describe the coupling to external leads, (ii) the Kirchhoff node rule describing charge conservation, and (iii) density matching conditions at every node.
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Affiliation(s)
- S Chen
- Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
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