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Barbier M, Gaspard P. Microreversibility and the statistics of currents in quantum transport. Phys Rev E 2020; 102:022141. [PMID: 32942403 DOI: 10.1103/physreve.102.022141] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2020] [Accepted: 08/03/2020] [Indexed: 11/07/2022]
Abstract
For the statistics of currents in quantum transport, microreversibility is shown to provide a way to obtain the statistical cumulants at the order n+1 from the measurement of the cumulants at the order n or lower. This fundamental result is based on relations generalizing the fluctuation-dissipation theorem and the Onsager-Casimir reciprocal relations from linear toward nonlinear transport properties, as a consequence of the time-reversal symmetry of the underlying microscopic Hamiltonian dynamics. The method is demonstrated in detail in the case of multiterminal Aharonov-Bohm rings. Within the independent electron approximation, the cumulant generating function, which fully specifies the statistics of the nonequilibrium currents, is obtained from the scattering matrix of these circuits. The time-reversal symmetry relations are explicitly shown to express the cumulants at equilibrium up to the fourth order in terms of lower-order cumulants and their nonequilibrium responses in the presence of an external magnetic field.
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Affiliation(s)
- M Barbier
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (ULB), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
| | - P Gaspard
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (ULB), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
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2
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Rudge SL, Kosov DS. Counting quantum jumps: A summary and comparison of fixed-time and fluctuating-time statistics in electron transport. J Chem Phys 2019; 151:034107. [DOI: 10.1063/1.5108518] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Samuel L. Rudge
- College of Science and Engineering, James Cook University, Townsville, QLD, 4814, Australia
| | - Daniel S. Kosov
- College of Science and Engineering, James Cook University, Townsville, QLD, 4814, Australia
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3
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Dasenbrook D, Flindt C. Dynamical Scheme for Interferometric Measurements of Full-Counting Statistics. PHYSICAL REVIEW LETTERS 2016; 117:146801. [PMID: 27740844 DOI: 10.1103/physrevlett.117.146801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2016] [Indexed: 06/06/2023]
Abstract
We propose a dynamical scheme for measuring the full-counting statistics in a mesoscopic conductor using an electronic Mach-Zehnder interferometer. The conductor couples capacitively to one arm of the interferometer and causes a phase shift which is proportional to the number of transferred charges. Importantly, the full-counting statistics can be obtained from average current measurements at the outputs of the interferometer. The counting field can be controlled by varying the time delay between two separate voltage signals applied to the conductor and the interferometer, respectively. As a specific application, we consider measuring the entanglement entropy generated by partitioning electrons on a quantum point contact. Our scheme is robust against moderate environmental dephasing and may be realized thanks to recent advances in gigahertz quantum electronics.
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Affiliation(s)
- David Dasenbrook
- Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
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4
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Droste S, Governale M. Finite-time full counting statistics and factorial cumulants for transport through a quantum dot with normal and superconducting leads. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:145302. [PMID: 26963047 DOI: 10.1088/0953-8984/28/14/145302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We study the finite-time full counting statistics for subgap transport through a single-level quantum dot tunnel-coupled to one normal and one superconducting lead. In particular, we determine the factorial and the ordinary cumulants both for finite times and in the long-time limit. We find that the factorial cumulants violate the sign criterion, indicating a non-binomial distribution, even in absence of Coulomb repulsion due to the presence of superconducting correlations. At short times the cumulants exhibit oscillations which are a signature of the coherent transfer of Cooper pairs between the dot and the superconductor.
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Affiliation(s)
- Stephanie Droste
- School of Chemical and Physical Sciences and Mac Diarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand
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5
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Buča B, Prosen T. Exactly solvable counting statistics in open weakly coupled interacting spin systems. PHYSICAL REVIEW LETTERS 2014; 112:067201. [PMID: 24580705 DOI: 10.1103/physrevlett.112.067201] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2013] [Indexed: 06/03/2023]
Abstract
We study the full counting statistics for interacting quantum many-body spin systems weakly coupled to the environment. In the leading order in the system-bath coupling, we derive exact spin current statistics for a large class of parity symmetric spin-1/2 systems driven by a pair of Markovian baths with local coupling operators. Interestingly, in this class of systems the leading-order current statistics are universal and do not depend on details of the Hamiltonian. Furthermore, in the specific case of a symmetrically boundary driven anisotropic Heisenberg (XXZ) spin-1/2 chain, we explicitly derive the third-order nonlinear corrections to the current statistics.
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Affiliation(s)
- Berislav Buča
- Department of Physics, FMF, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Department of Physics, FMF, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
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6
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Maisi VF, Kambly D, Flindt C, Pekola JP. Full counting statistics of Andreev tunneling. PHYSICAL REVIEW LETTERS 2014; 112:036801. [PMID: 24484157 DOI: 10.1103/physrevlett.112.036801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2013] [Indexed: 06/03/2023]
Abstract
We employ a single-charge counting technique to measure the full counting statistics of Andreev events in which Cooper pairs are either produced from electrons that are reflected as holes at a superconductor-normal-metal interface or annihilated in the reverse process. The full counting statistics consists of quiet periods with no Andreev processes, interrupted by the tunneling of a single electron that triggers an avalanche of Andreev events giving rise to strongly super-Poissonian distributions.
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Affiliation(s)
- Ville F Maisi
- Low Temperature Laboratory (OVLL), Aalto University School of Science, P.O. Box 13500, 00076 Aalto, Finland and Centre for Metrology and Accreditation (MIKES), P.O. Box 9, 02151 Espoo, Finland
| | - Dania Kambly
- Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland
| | - Christian Flindt
- Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland
| | - Jukka P Pekola
- Low Temperature Laboratory (OVLL), Aalto University School of Science, P.O. Box 13500, 00076 Aalto, Finland
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7
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Noise intensity-intensity correlations and the fourth cumulant of photo-assisted shot noise. Sci Rep 2013; 3:2869. [PMID: 24100407 PMCID: PMC3792424 DOI: 10.1038/srep02869] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2013] [Accepted: 09/19/2013] [Indexed: 11/24/2022] Open
Abstract
We report the measurement of the fourth cumulant of current fluctuations in a tunnel junction under both dc and ac (microwave) excitation. This probes the non-Gaussian character of photo-assisted shot noise. Our measurement reveals the existence of correlations between noise power measured at two different frequencies, which corresponds to two-mode intensity correlations in optics. We observe positive correlations, i.e. photon bunching, which exist only for certain relations between the excitation frequency and the two detection frequencies, depending on the dc bias of the sample.
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8
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Eisler V, Rácz Z. Full counting statistics in a propagating quantum front and random matrix spectra. PHYSICAL REVIEW LETTERS 2013; 110:060602. [PMID: 23432230 DOI: 10.1103/physrevlett.110.060602] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2012] [Indexed: 06/01/2023]
Abstract
One-dimensional free fermions are studied with emphasis on propagating fronts emerging from a step initial condition. The probability distribution of the number of particles at the edge of the front is determined exactly. It is found that the full counting statistics coincide with the eigenvalue statistics of the edge spectrum of matrices from the Gaussian unitary ensemble. The correspondence established between the random matrix eigenvalues and the particle positions yields the order statistics of the rightmost particles in the front and, furthermore, it implies their subdiffusive spreading.
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Affiliation(s)
- Viktor Eisler
- Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Wien, Austria
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9
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Ubbelohde N, Fricke C, Flindt C, Hohls F, Haug RJ. Measurement of finite-frequency current statistics in a single-electron transistor. Nat Commun 2012; 3:612. [PMID: 22215087 PMCID: PMC3272564 DOI: 10.1038/ncomms1620] [Citation(s) in RCA: 121] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2011] [Accepted: 11/28/2011] [Indexed: 11/09/2022] Open
Abstract
Electron transport in nanoscale structures is strongly influenced by the Coulomb interaction that gives rise to correlations in the stream of charges and leaves clear fingerprints in the fluctuations of the electrical current. A complete understanding of the underlying physical processes requires measurements of the electrical fluctuations on all time and frequency scales, but experiments have so far been restricted to fixed frequency ranges, as broadband detection of current fluctuations is an inherently difficult experimental procedure. Here we demonstrate that the electrical fluctuations in a single-electron transistor can be accurately measured on all relevant frequencies using a nearby quantum point contact for on-chip real-time detection of the current pulses in the single-electron device. We have directly measured the frequency-dependent current statistics and, hereby, fully characterized the fundamental tunnelling processes in the single-electron transistor. Our experiment paves the way for future investigations of interaction and coherence-induced correlation effects in quantum transport.
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Affiliation(s)
- Niels Ubbelohde
- Institut für Festkörperphysik, Leibniz Universität Hannover, Hannover 30167, Germany
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10
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Gutman DB, Gefen Y, Mirlin AD. Full counting statistics of a Luttinger liquid conductor. PHYSICAL REVIEW LETTERS 2010; 105:256802. [PMID: 21231608 DOI: 10.1103/physrevlett.105.256802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2010] [Indexed: 05/30/2023]
Abstract
Nonequilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the time resolved full counting statistics of the transmitted charge is derived. It is given by the Fredholm determinant of the counting operator with a time-dependent scattering phase. The result has a form of counting statistics of noninteracting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the noninteracting leads.
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Affiliation(s)
- D B Gutman
- Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel
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11
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Bednorz A, Belzig W. Quasiprobabilistic interpretation of weak measurements in mesoscopic junctions. PHYSICAL REVIEW LETTERS 2010; 105:106803. [PMID: 20867538 DOI: 10.1103/physrevlett.105.106803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2010] [Indexed: 05/29/2023]
Abstract
The impossibility of measuring noncommuting quantum mechanical observables is one of the most fascinating consequences of the quantum mechanical postulates. Hence, to date the investigation of quantum measurement and projection is a fundamentally interesting topic. We propose to test the concept of weak measurement of noncommuting observables in mesoscopic transport experiments, using a quasiprobabilistic description. We derive an inequality for current correlators, which is satisfied by every classical probability but violated by high-frequency fourth-order cumulants in the quantum regime for experimentally feasible parameters.
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Affiliation(s)
- Adam Bednorz
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany.
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12
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Zakka-Bajjani E, Dufouleur J, Coulombel N, Roche P, Glattli DC, Portier F. Experimental determination of the statistics of photons emitted by a tunnel junction. PHYSICAL REVIEW LETTERS 2010; 104:206802. [PMID: 20867050 DOI: 10.1103/physrevlett.104.206802] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2009] [Indexed: 05/29/2023]
Abstract
We report on an Hanbury Brown-Twiss experiment probing the statistics of microwave photons emitted by a tunnel junction in the shot-noise regime at low temperature. By measuring the cross correlation of the fluctuations of the occupation numbers of the photon modes of both detection branches, we show that while the statistics of electrons is Poissonian, the photons obey chaotic statistics. This is observed even for low photon occupation number when the voltage across the junction is close to hν/e.
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Affiliation(s)
- Eva Zakka-Bajjani
- Service de Physique de l'Etat Condensé/IRAMIS/DSM (CNRS URA 2464), CEA Saclay, F-91191 Gif-sur-Yvette, France
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Klich I, Levitov L. Quantum noise as an entanglement meter. PHYSICAL REVIEW LETTERS 2009; 102:100502. [PMID: 19392096 DOI: 10.1103/physrevlett.102.100502] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2008] [Indexed: 05/27/2023]
Abstract
Transport in a quantum point contact (QPC) can be used to generate many-body entanglement of Fermi seas in the leads. A universal relation is found between the generated entanglement entropy and the fluctuations of electric current, which is valid for any protocol of driving the QPC. This relation offers a basis for direct electric measurement of entanglement entropy. In particular, by utilizing space-time duality of 1D systems, we relate electric noise generated by opening and closing the QPC periodically in time with the seminal S=1/3logL prediction of conformal field theory.
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Affiliation(s)
- Israel Klich
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
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14
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Sukhorukov EV, Jordan AN. Achieving the threshold regime with an overscreened Josephson junction. PHYSICAL REVIEW LETTERS 2009; 102:086806. [PMID: 19257771 DOI: 10.1103/physrevlett.102.086806] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2008] [Indexed: 05/27/2023]
Abstract
We demonstrate that by utilizing an overscreened Josephson junction as a noise detector it is possible to achieve the threshold regime, whereby the tails of the fluctuating current distribution are measured. This situation is realized by placing the Josephson junction and mesoscopic conductor in an external circuit with very low impedance. In the underdamped limit, overscreening the junction inhibits the energy diffusion in the junction, effectively creating a tunable activation barrier to the dissipative state. As a result, the activation rate is qualitatively different from the Arrhenius form.
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Affiliation(s)
- Eugene V Sukhorukov
- Départment de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland
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15
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Le Masne Q, Pothier H, Birge NO, Urbina C, Esteve D. Asymmetric noise probed with a josephson junction. PHYSICAL REVIEW LETTERS 2009; 102:067002. [PMID: 19257625 DOI: 10.1103/physrevlett.102.067002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2008] [Indexed: 05/27/2023]
Abstract
Fluctuations of the current through a tunnel junction are measured using a Josephson junction. The current noise adds to the bias current of the Josephson junction and affects its switching out of the supercurrent branch. The experiment is carried out in a regime where switching is determined by thermal activation. The variance of the noise results in an elevated effective temperature, whereas the third cumulant, related to its asymmetric character, leads to a difference in the switching rates observed for opposite signs of the current through the tunnel junction. Measurements are compared quantitatively with recent theoretical predictions.
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Affiliation(s)
- Q Le Masne
- Quantronics group, Service de Physique de l'Etat Condensé (CNRS URA 2464), CEA-Saclay, 91191 Gif-sur-Yvette, France
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16
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Bednorz A, Belzig W. Formulation of time-resolved counting statistics based on a positive-operator-valued measure. PHYSICAL REVIEW LETTERS 2008; 101:206803. [PMID: 19113367 DOI: 10.1103/physrevlett.101.206803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2008] [Indexed: 05/27/2023]
Abstract
We propose a derivation of the full counting statistics of electronic current based on a positive-operator-valued measure. Our approach justifies the Levitov-Lesovik formula in the long-time limit, but can be generalized to the detection of finite-frequency noise correlations. The combined action of the projection postulate and the quantum formula for current noise at high frequencies imply an additional white noise. Estimates for this additional noise are in accordance with known experiments. We propose an experimental test of our conjecture by a simultaneous measurement of high- and low-frequency noise.
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Affiliation(s)
- Adam Bednorz
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany and University of Warsaw, Hoza 69, PL-00681 Warsaw, Poland.
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