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Hurtado-Gutiérrez R, Hurtado PI, Pérez-Espigares C. Spectral signatures of symmetry-breaking dynamical phase transitions. Phys Rev E 2023; 108:014107. [PMID: 37583207 DOI: 10.1103/physreve.108.014107] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 06/12/2023] [Indexed: 08/17/2023]
Abstract
Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. Some of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While macroscopic fluctuation theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging. In this work we shed light on the general spectral mechanism giving rise to continuous DPTs not only for driven diffusive systems, but for any jump process in which a discrete Z_{n} symmetry is broken. By means of a symmetry-aided spectral analysis of the Doob-transformed dynamics, we provide the conditions whereby symmetry-breaking DPTs might emerge and how the different dynamical phases arise from the specific structure of the degenerate eigenvectors. In particular, we show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate subspace. Moreover, by partitioning configuration space into equivalence classes according to a proper order parameter, we achieve a substantial dimensional reduction which allows for the quantitative characterization of the spectral fingerprints of DPTs. We illustrate our predictions in several paradigmatic many-body systems, including (1) the one-dimensional boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (2) the three- and four-state Potts model for spin dynamics, which displays discrete rotational symmetry-breaking DPTs for energy fluctuations, and (3) the closed WASEP which presents a continuous symmetry-breaking DPT into a time-crystal phase characterized by a rotating condensate.
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Affiliation(s)
- R Hurtado-Gutiérrez
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
| | - P I Hurtado
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
| | - C Pérez-Espigares
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
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2
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Kleinherbers E, Stegmann P, Kurzmann A, Geller M, Lorke A, König J. Pushing the Limits in Real-Time Measurements of Quantum Dynamics. PHYSICAL REVIEW LETTERS 2022; 128:087701. [PMID: 35275653 DOI: 10.1103/physrevlett.128.087701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 01/05/2022] [Indexed: 06/14/2023]
Abstract
Time-resolved studies of quantum systems are the key to understanding quantum dynamics at its core. The real-time measurement of individual quantum numbers as they switch between certain discrete values, well known as a "random telegraph signal," is expected to yield maximal physical insight. However, the signal suffers from both systematic errors, such as a limited time resolution and noise from the measurement apparatus, as well as statistical errors due to a limited amount of data. Here we demonstrate that an evaluation scheme based on factorial cumulants can reduce the influence of such errors by orders of magnitude. The error resilience is supported by a general theory for the detection errors as well as experimental data of single-electron tunneling through a self-assembled quantum dot. Thus, factorial cumulants push the limits in the analysis of random telegraph data, which represent a wide class of experiments in physics, chemistry, engineering, and life sciences.
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Affiliation(s)
- E Kleinherbers
- Faculty of Physics and CENIDE, University of Duisburg-Essen, 47057 Duisburg, Germany
| | - P Stegmann
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - A Kurzmann
- 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany
| | - M Geller
- Faculty of Physics and CENIDE, University of Duisburg-Essen, 47057 Duisburg, Germany
| | - A Lorke
- Faculty of Physics and CENIDE, University of Duisburg-Essen, 47057 Duisburg, Germany
| | - J König
- Faculty of Physics and CENIDE, University of Duisburg-Essen, 47057 Duisburg, Germany
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3
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Nakajima S, Utsumi Y. Asymptotic expansion of the solution of the master equation and its application to the speed limit. Phys Rev E 2021; 104:054139. [PMID: 34942842 DOI: 10.1103/physreve.104.054139] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2021] [Accepted: 11/05/2021] [Indexed: 11/07/2022]
Abstract
We investigate an asymptotic expansion of the solution of the master equation under the modulation of control parameters. In this case, the nondecaying part of the solution becomes the dynamical steady state expressed as an infinite series using the pseudoinverse of the Liouvillian, whose convergence is not granted in general. We demonstrate that for the relaxation time approximation model, the Borel summation of the infinite series is compatible with the exact solution. By exploiting the series expansion, we obtain the analytic expression of the heat and the activity. In the two-level system coupled to a single bath, under the linear modulation of the energy as a function of time, we demonstrate that the infinite series expression is the asymptotic expansion of the exact solution. The equality of a trade-off relation between the speed of the state transformation and the entropy production [Shiraishi, Funo, and Saito, Phys. Rev. Lett. 121, 070601 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.070601] holds in the lowest order of the frequency of the energy modulation in the two-level system. To obtain this result, the heat emission and absorption at edges (the initial and end times) or the differences of the Shannon entropy between the instantaneous steady state and the dynamical steady state at edges are essential: If we ignore these effects, the trade-off relation can be violated.
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Affiliation(s)
- Satoshi Nakajima
- Department of Physics Engineering, Faculty of Engineering, Mie University, Tsu, Mie 514-8507, Japan
| | - Yasuhiro Utsumi
- Department of Physics Engineering, Faculty of Engineering, Mie University, Tsu, Mie 514-8507, Japan
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4
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Fiore CE, Harunari PE, Noa CEF, Landi GT. Current fluctuations in nonequilibrium discontinuous phase transitions. Phys Rev E 2021; 104:064123. [PMID: 35030860 DOI: 10.1103/physreve.104.064123] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2021] [Accepted: 11/29/2021] [Indexed: 11/07/2022]
Abstract
Discontinuous phase transitions out of equilibrium can be characterized by the behavior of macroscopic stochastic currents. But while much is known about the average current, the situation is much less understood for higher statistics. In this paper, we address the consequences of the diverging metastability lifetime-a hallmark of discontinuous transitions-in the fluctuations of arbitrary thermodynamic currents, including the entropy production. In particular, we center our discussion on the conditional statistics, given which phase the system is in. We highlight the interplay between integration window and metastability lifetime, which is not manifested in the average current, but strongly influences the fluctuations. We introduce conditional currents and find, among other predictions, their connection to average and scaled variance through a finite-time version of large deviation theory and a minimal model. Our results are then further verified in two paradigmatic models of discontinuous transitions: Schlögl's model of chemical reactions, and a 12-state Potts model subject to two baths at different temperatures.
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Affiliation(s)
- C E Fiore
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
| | - Pedro E Harunari
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil.,Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg L-1511, G.D. Luxembourg
| | - C E Fernández Noa
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
| | - Gabriel T Landi
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
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5
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Aurell E, Donvil B, Mallick K. Large deviations and fluctuation theorem for the quantum heat current in the spin-boson model. Phys Rev E 2020; 101:052116. [PMID: 32575222 DOI: 10.1103/physreve.101.052116] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Accepted: 03/16/2020] [Indexed: 11/07/2022]
Abstract
We study the heat current flowing between two baths consisting of harmonic oscillators interacting with a qubit through a spin-boson coupling. An explicit expression for the generating function of the total heat flowing between the right and left baths is derived by evaluating the corresponding Feynman-Vernon path integral by performing the noninteracting blip approximation (NIBA). We recover the known expression, obtained by using the polaron transform. This generating function satisfies the Gallavotti-Cohen fluctuation theorem, both before and after performing the NIBA. We also verify that the heat conductance is proportional to the variance of the heat current, retrieving the well-known fluctuation dissipation relation. Finally, we present numerical results for the heat current.
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Affiliation(s)
- Erik Aurell
- KTH Royal Institute of Technology, AlbaNova University Center, SE-106 91 Stockholm, Sweden and Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kraków, Poland
| | - Brecht Donvil
- Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland
| | - Kirone Mallick
- Institut de Physique Théorique, Université Paris-Saclay, CEA and CNRS, 91191 Gif-sur-Yvette, France
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6
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Lochner P, Kurzmann A, Kerski J, Stegmann P, König J, Wieck AD, Ludwig A, Lorke A, Geller M. Real-Time Detection of Single Auger Recombination Events in a Self-Assembled Quantum Dot. NANO LETTERS 2020; 20:1631-1636. [PMID: 32023065 DOI: 10.1021/acs.nanolett.9b04650] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Auger recombination is a nonradiative process, where the recombination energy of an electron-hole pair is transferred to a third charge carrier. It is a common effect in colloidal quantum dots that quenches the radiative emission with an Auger recombination time below nanoseconds. In self-assembled QDs, the Auger recombination has been observed with a much longer recombination time on the order of microseconds. Here, we use two-color laser excitation on the exciton and trion transition in resonance fluorescence on a single self-assembled quantum dot to monitor in real-time single quantum events of the Auger process. Full counting statistics on the random telegraph signal give access to the cumulants and demonstrate the tunability of the Fano factor from a Poissonian to a sub-Poissonian distribution by Auger-mediated electron emission from the dot. Therefore, the Auger process can be used to tune optically the charge carrier occupation of the dot by the incident laser intensity, independently from the electron tunneling from the reservoir by the gate voltage. Our findings are not only highly relevant for the understanding of the Auger process but also demonstrate the perspective of the Auger effect for controlling precisely the charge state in a quantum system by optical means.
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Affiliation(s)
- Pia Lochner
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, Germany
| | - Annika Kurzmann
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, Germany
- Solid State Physics Laboratory, ETH Zurich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - Jens Kerski
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, Germany
| | - Philipp Stegmann
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, Germany
| | - Jürgen König
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, Germany
| | - Andreas D Wieck
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstraβe 150, 44780 Bochum, Germany
| | - Arne Ludwig
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstraβe 150, 44780 Bochum, Germany
| | - Axel Lorke
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, Germany
| | - Martin Geller
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, Germany
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7
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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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8
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Kurzmann A, Stegmann P, Kerski J, Schott R, Ludwig A, Wieck AD, König J, Lorke A, Geller M. Optical Detection of Single-Electron Tunneling into a Semiconductor Quantum Dot. PHYSICAL REVIEW LETTERS 2019; 122:247403. [PMID: 31322370 DOI: 10.1103/physrevlett.122.247403] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2019] [Indexed: 06/10/2023]
Abstract
The maximum information of a dynamic quantum system is given by real-time detection of every quantum event, where the ultimate challenge is a stable, sensitive detector with high bandwidth. All physical information can then be drawn from a statistical analysis of the time traces. We demonstrate here an optical detection scheme based on the time-resolved resonance fluorescence on a single quantum dot. Single-electron resolution with high signal-to-noise ratio (4σ confidence) and high bandwidth of 10 kHz make it possible to record the individual quantum events of the transport dynamics. Full counting statistics with factorial cumulants gives access to the nonequilibrium dynamics of spin relaxation of a singly charged dot (γ_{↑↓}=3 ms^{-1}), even in an equilibrium transport measurement.
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Affiliation(s)
- A Kurzmann
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstrasse 1, 47057 Duisburg, Germany
- Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
| | - P Stegmann
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstrasse 1, 47057 Duisburg, Germany
| | - J Kerski
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstrasse 1, 47057 Duisburg, Germany
| | - R Schott
- Chair for Applied Solid State Physics, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
| | - A Ludwig
- Chair for Applied Solid State Physics, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
| | - A D Wieck
- Chair for Applied Solid State Physics, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
| | - J König
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstrasse 1, 47057 Duisburg, Germany
| | - A Lorke
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstrasse 1, 47057 Duisburg, Germany
| | - M Geller
- Faculty of Physics and CENIDE, University of Duisburg-Essen, Lotharstrasse 1, 47057 Duisburg, Germany
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9
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Singh S, Menczel P, Golubev DS, Khaymovich IM, Peltonen JT, Flindt C, Saito K, Roldán É, Pekola JP. Universal First-Passage-Time Distribution of Non-Gaussian Currents. PHYSICAL REVIEW LETTERS 2019; 122:230602. [PMID: 31298917 DOI: 10.1103/physrevlett.122.230602] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2018] [Indexed: 06/10/2023]
Abstract
We investigate the fluctuations of the time elapsed until the electric charge transferred through a conductor reaches a given threshold value. For this purpose, we measure the distribution of the first-passage times for the net number of electrons transferred between two metallic islands in the Coulomb blockade regime. Our experimental results are in excellent agreement with numerical calculations based on a recent theory describing the exact first-passage-time distributions for any nonequilibrium stationary Markov process. We also derive a simple analytical approximation for the first-passage-time distribution, which takes into account the non-Gaussian statistics of the electron transport, and show that it describes the experimental distributions with high accuracy. This universal approximation describes a wide class of stochastic processes, and can be used beyond the context of mesoscopic charge transport. In addition, we verify experimentally a fluctuation relation between the first-passage-time distributions for positive and negative thresholds.
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Affiliation(s)
- Shilpi Singh
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Paul Menczel
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Dmitry S Golubev
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Ivan M Khaymovich
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia
| | - Joonas T Peltonen
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Christian Flindt
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Keiji Saito
- Department of Physics, Keio University-Yokohama 2238522, Japan
| | - Édgar Roldán
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste, Italy
| | - Jukka P Pekola
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
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10
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Giri SK, Goswami HP. Nonequilibrium fluctuations of a driven quantum heat engine via machine learning. Phys Rev E 2019; 99:022104. [PMID: 30934252 DOI: 10.1103/physreve.99.022104] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2018] [Indexed: 11/07/2022]
Abstract
We propose a machine-learning approach based on artificial neural network to efficiently obtain new insights on the role of geometric contributions to the nonequilibrium fluctuations of an adiabatically temperature-driven quantum heat engine coupled to a cavity. Using the artificial neural network we have explored the interplay between bunched and antibunched photon exchange statistics for different engine parameters. We report that beyond a pivotal cavity temperature, the Fano factor oscillates between giant and low values as a function of phase difference between the driving protocols. We further observe that the standard thermodynamic uncertainty relation is not valid when there are finite geometric contributions to the fluctuations but holds true for zero phase difference even in the presence of coherences.
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Affiliation(s)
- Sajal Kumar Giri
- Finite Systems Division, Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
| | - Himangshu Prabal Goswami
- Finite Systems Division, Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany.,Department of Chemical Sciences, Tezpur University, Napaam, Tezpur 784028, Assam, India
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11
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Pinsolle E, Houle S, Lupien C, Reulet B. Non-Gaussian Current Fluctuations in a Short Diffusive Conductor. PHYSICAL REVIEW LETTERS 2018; 121:027702. [PMID: 30085754 DOI: 10.1103/physrevlett.121.027702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2018] [Indexed: 06/08/2023]
Abstract
We report the measurement of the third moment of current fluctuations in a short metallic wire at low temperature. The data are deduced from the statistics of voltage fluctuations across the conductor using a careful determination of environmental contributions. Our results at low bias agree very well with theoretical predictions for coherent transport with no fitting parameter. By increasing the bias voltage we explore the crossover from elastic to inelastic transport.
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Affiliation(s)
- Edouard Pinsolle
- Institut Quantique, Département de Physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - Samuel Houle
- Institut Quantique, Département de Physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - Christian Lupien
- Institut Quantique, Département de Physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - Bertrand Reulet
- Institut Quantique, Département de Physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
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12
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Deger A, Brandner K, Flindt C. Lee-Yang zeros and large-deviation statistics of a molecular zipper. Phys Rev E 2018; 97:012115. [PMID: 29448488 DOI: 10.1103/physreve.97.012115] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2017] [Indexed: 11/07/2022]
Abstract
The complex zeros of partition functions were originally investigated by Lee and Yang to explain the behavior of condensing gases. Since then, Lee-Yang zeros have become a powerful tool to describe phase transitions in interacting systems. Today, Lee-Yang zeros are no longer just a theoretical concept; they have been determined in recent experiments. In one approach, the Lee-Yang zeros are extracted from the high cumulants of thermodynamic observables at finite size. Here we employ this method to investigate a phase transition in a molecular zipper. From the energy fluctuations in small zippers, we can predict the temperature at which a phase transition occurs in the thermodynamic limit. Even when the system does not undergo a sharp transition, the Lee-Yang zeros carry important information about the large-deviation statistics and its symmetry properties. Our work suggests an interesting duality between fluctuations in small systems and their phase behavior in the thermodynamic limit. These predictions may be tested in future experiments.
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Affiliation(s)
- Aydin Deger
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Kay Brandner
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
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13
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Xue HB, Liu XP, Chen B. Probing the internal energy structure of a serially coupled double quantum dot system with Rashba spin-orbit coupling through finite-frequency shot noise. AIP ADVANCES 2018; 8. [DOI: 10.1063/1.5004223] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
The finite-frequency shot noise of electron transport through a serially coupled double quantum dot system with Rashba spin-orbit coupling is studied based on an effective particle-number-resolved quantum master equation. We demonstrate that the finite-frequency shot noise displays an obvious dip, and the dip position, which is independent of the spin polarizations of the source and drain electrodes, is determined by the energy difference between the coherent singly-occupied eigenstates of the quantum dot system. These results suggest that the dip position of the finite-frequency shot noise can be used to quantitatively extract the information about the energy difference between the coherent singly-occupied eigenstates and the magnitude of Rashba spin-orbit coupling. The predicted properties of the finite-frequency shot noise are of particular interest for understanding of the internal dynamics of the coupled quantum dot systems.
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Affiliation(s)
- Hai-Bin Xue
- College of Physics and Optoelectronics, Taiyuan University of Technology , Taiyuan 030024, China
| | - Xu-Ping Liu
- College of Physics and Optoelectronics, Taiyuan University of Technology , Taiyuan 030024, China
| | - Bin Chen
- College of Physics and Optoelectronics, Taiyuan University of Technology , Taiyuan 030024, China
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14
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15
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Contreras-Pulido LD, Bruderer M. Coherent and incoherent charge transport in linear triple quantum dots. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:185301. [PMID: 28294106 DOI: 10.1088/1361-648x/aa66d0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
One of the fundamental questions in quantum transport is how charge transfer through complex nanostructures is influenced by quantum coherence. We address this issue for linear triple quantum dots by comparing a Lindblad density matrix description with a Pauli rate equation approach and analyze the corresponding zero-frequency counting statistics of charge transfer. The impact of decaying coherences of the density matrix due to dephasing is also studied. Our findings reveal that the sensitivity to coherence shown by shot noise and skewness, in particular in the limit of large coupling to the drain reservoir, can be used to unambiguously evidence coherent processes involved in charge transport across triple quantum dots. Our analytical results are obtained by using the characteristic polynomial approach to full counting statistics.
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Affiliation(s)
- L D Contreras-Pulido
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 México D. F., Mexico
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16
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Brandner K, Maisi VF, Pekola JP, Garrahan JP, Flindt C. Experimental Determination of Dynamical Lee-Yang Zeros. PHYSICAL REVIEW LETTERS 2017; 118:180601. [PMID: 28524675 DOI: 10.1103/physrevlett.118.180601] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2016] [Indexed: 06/07/2023]
Abstract
Statistical physics provides the concepts and methods to explain the phase behavior of interacting many-body systems. Investigations of Lee-Yang zeros-complex singularities of the free energy in systems of finite size-have led to a unified understanding of equilibrium phase transitions. The ideas of Lee and Yang, however, are not restricted to equilibrium phenomena. Recently, Lee-Yang zeros have been used to characterize nonequilibrium processes such as dynamical phase transitions in quantum systems after a quench or dynamic order-disorder transitions in glasses. Here, we experimentally realize a scheme for determining Lee-Yang zeros in such nonequilibrium settings. We extract the dynamical Lee-Yang zeros of a stochastic process involving Andreev tunneling between a normal-state island and two superconducting leads from measurements of the dynamical activity along a trajectory. From the short-time behavior of the Lee-Yang zeros, we predict the large-deviation statistics of the activity which is typically difficult to measure. Our method paves the way for further experiments on the statistical mechanics of many-body systems out of equilibrium.
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Affiliation(s)
- Kay Brandner
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Ville F Maisi
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark
| | - Jukka P Pekola
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Christian Flindt
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
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17
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Wagner T, Strasberg P, Bayer JC, Rugeramigabo EP, Brandes T, Haug RJ. Strong suppression of shot noise in a feedback-controlled single-electron transistor. NATURE NANOTECHNOLOGY 2017; 12:218-222. [PMID: 27819692 DOI: 10.1038/nnano.2016.225] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2016] [Accepted: 09/19/2016] [Indexed: 06/06/2023]
Abstract
Feedback control of quantum mechanical systems is rapidly attracting attention not only due to fundamental questions about quantum measurements, but also because of its novel applications in many fields in physics. Quantum control has been studied intensively in quantum optics but progress has recently been made in the control of solid-state qubits as well. In quantum transport only a few active and passive feedback experiments have been realized on the level of single electrons, although theoretical proposals exist. Here we demonstrate the suppression of shot noise in a single-electron transistor using an exclusively electronic closed-loop feedback to monitor and adjust the counting statistics. With increasing feedback response we observe a stronger suppression and faster freezing of charge current fluctuations. Our technique is analogous to the generation of squeezed light with in-loop photodetection as used in quantum optics. Sub-Poisson single-electron sources will pave the way for high-precision measurements in quantum transport similar to optical or optomechanical equivalents.
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Affiliation(s)
- Timo Wagner
- Institut für Festkörperphysik, Leibniz Universität Hannover, D-30167 Hannover, Germany
| | - Philipp Strasberg
- Institut für Theoretische Physik, Hardenbergstr. 36, TU Berlin, D-10623 Berlin, Germany
| | - Johannes C Bayer
- Institut für Festkörperphysik, Leibniz Universität Hannover, D-30167 Hannover, Germany
| | - Eddy P Rugeramigabo
- Institut für Festkörperphysik, Leibniz Universität Hannover, D-30167 Hannover, Germany
| | - Tobias Brandes
- Institut für Theoretische Physik, Hardenbergstr. 36, TU Berlin, D-10623 Berlin, Germany
| | - Rolf J Haug
- Institut für Festkörperphysik, Leibniz Universität Hannover, D-30167 Hannover, Germany
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18
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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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19
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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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20
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Novotný T, Belzig W. Large-voltage behavior of charge transport characteristics in nanosystems with weak electron-vibration coupling. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2015; 6:1853-9. [PMID: 26425436 PMCID: PMC4578416 DOI: 10.3762/bjnano.6.188] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2015] [Accepted: 08/21/2015] [Indexed: 05/30/2023]
Abstract
We study analytically the Full Counting Statistics of the charge transport through a nanosystem consisting of a few electronic levels weakly coupled to a discrete vibrational mode. In the limit of large transport voltage bias the cumulant generating function can be evaluated explicitly based solely on the intuitive physical arguments and classical master equation description of the vibration mode. We find that for the undamped vibrational modes mutual dynamical interplay between electronic and vibronic degrees of freedom leads to strongly nonlinear (in voltage) transport characteristics of the nanosystem. In particular, we find that for large voltages the k-th cumulant of the current grows as V (2k) to be contrasted with the linear dependence in case of more strongly externally damped and thus thermalized vibrational modes.
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Affiliation(s)
- Tomáš Novotný
- Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, CZ-12116 Praha 2, Czech Republic
| | - Wolfgang Belzig
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
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21
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Quantum Phase Coherence in Mesoscopic Transport Devices with Two-Particle Interaction. Sci Rep 2015; 5:12873. [PMID: 26255858 PMCID: PMC4530461 DOI: 10.1038/srep12873] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2014] [Accepted: 07/10/2015] [Indexed: 12/02/2022] Open
Abstract
In this paper we demonstrate a new type of quantum phase coherence (QPC), which is generated by the two-body interaction. This conclusion is based on quantum master equation analysis for the full counting statistics of electron transport through two parallel quantum-dots with antiparallel magnetic fluxes in order to eliminate the Aharonov-Bohm interference of either single-particle or non-interacting two-particle wave functions. The interacting two-particle QPC is realized by the flux-dependent oscillation of the zero-frequency cumulants including the shot noise and skewness with a characteristic period. The accurately quantized peaks of cumulant spectrum may have technical applications to probe the two-body Coulomb interaction.
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22
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Li ZZ, Lam CH, You JQ. Probing Majorana bound states via counting statistics of a single electron transistor. Sci Rep 2015; 5:11416. [PMID: 26098973 PMCID: PMC4476256 DOI: 10.1038/srep11416] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2015] [Accepted: 05/22/2015] [Indexed: 11/09/2022] Open
Abstract
We propose an approach for probing Majorana bound states (MBSs) in a nanowire via counting statistics of a nearby charge detector in the form of a single-electron transistor (SET). We consider the impacts on the counting statistics by both the local coupling between the detector and an adjacent MBS at one end of a nanowire and the nonlocal coupling to the MBS at the other end. We show that the Fano factor and the skewness of the SET current are minimized for a symmetric SET configuration in the absence of the MBSs or when coupled to a fermionic state. However, the minimum points of operation are shifted appreciably in the presence of the MBSs to asymmetric SET configurations with a higher tunnel rate at the drain than at the source. This feature persists even when varying the nonlocal coupling and the pairing energy between the two MBSs. We expect that these MBS-induced shifts can be measured experimentally with available technologies and can serve as important signatures of the MBSs.
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Affiliation(s)
- Zeng-Zhao Li
- Laboratory for Quantum Optics and Quantum Information, Beijing Computational Science Research Center, Beijing 100094, China.,Department of Applied Physics, Hong Kong Polytechnic University, Hung Hom, Hong Kong, China
| | - Chi-Hang Lam
- Department of Applied Physics, Hong Kong Polytechnic University, Hung Hom, Hong Kong, China
| | - J Q You
- Laboratory for Quantum Optics and Quantum Information, Beijing Computational Science Research Center, Beijing 100094, China
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23
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Brange F, Malkoc O, Samuelsson P. Subdecoherence time generation and detection of orbital entanglement in quantum dots. PHYSICAL REVIEW LETTERS 2015; 114:176803. [PMID: 25978249 DOI: 10.1103/physrevlett.114.176803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2015] [Indexed: 06/04/2023]
Abstract
Recent experiments have demonstrated subdecoherence time control of individual single-electron orbital qubits. Here we propose a quantum-dot-based scheme for generation and detection of pairs of orbitally entangled electrons on a time scale much shorter than the decoherence time. The electrons are entangled, via two-particle interference, and transferred to the detectors during a single cotunneling event, making the scheme insensitive to charge noise. For sufficiently long detector dot lifetimes, cross-correlation detection of the dot charges can be performed with real-time counting techniques, providing for an unambiguous short-time Bell inequality test of orbital entanglement.
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Affiliation(s)
- F Brange
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
| | - O Malkoc
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
| | - P Samuelsson
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
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24
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Xue HB, Jiao HJ, Liang JQ, Liu WM. Non-Markovian full counting statistics in quantum dot molecules. Sci Rep 2015; 5:8978. [PMID: 25752245 PMCID: PMC4354005 DOI: 10.1038/srep08978] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2014] [Accepted: 02/12/2015] [Indexed: 11/19/2022] Open
Abstract
Full counting statistics of electron transport is a powerful diagnostic tool for probing the nature of quantum transport beyond what is obtainable from the average current or conductance measurement alone. In particular, the non-Markovian dynamics of quantum dot molecule plays an important role in the nonequilibrium electron tunneling processes. It is thus necessary to understand the non-Markovian full counting statistics in a quantum dot molecule. Here we study the non-Markovian full counting statistics in two typical quantum dot molecules, namely, serially coupled and side-coupled double quantum dots with high quantum coherence in a certain parameter regime. We demonstrate that the non-Markovian effect manifests itself through the quantum coherence of the quantum dot molecule system, and has a significant impact on the full counting statistics in the high quantum-coherent quantum dot molecule system, which depends on the coupling of the quantum dot molecule system with the source and drain electrodes. The results indicated that the influence of the non-Markovian effect on the full counting statistics of electron transport, which should be considered in a high quantum-coherent quantum dot molecule system, can provide a better understanding of electron transport through quantum dot molecules.
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Affiliation(s)
- Hai-Bin Xue
- College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China
| | - Hu-Jun Jiao
- Department of Physics, Shanxi University, Taiyuan 030006, China
| | - Jiu-Qing Liang
- Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China
| | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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25
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Xue HB, Liang JQ, Liu WM. Negative differential conductance and super-Poissonian shot noise in single-molecule magnet junctions. Sci Rep 2015; 5:8730. [PMID: 25736094 PMCID: PMC4348643 DOI: 10.1038/srep08730] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2014] [Accepted: 01/30/2015] [Indexed: 11/25/2022] Open
Abstract
Molecular spintroinic device based on a single-molecule magnet is one of the ultimate goals of semiconductor nanofabrication technologies. It is thus necessary to understand the electron transport properties of a single-molecule magnet junction. Here we study the negative differential conductance and super-Poissonian shot noise properties of electron transport through a single-molecule magnet weakly coupled to two electrodes with either one or both of them being ferromagnetic. We predict that the negative differential conductance and super-Poissonian shot noise, which can be tuned by a gate voltage, depend sensitively on the spin polarization of the source and drain electrodes. In particular, the shot noise in the negative differential conductance region can be enhanced or decreased originating from the different formation mechanisms of negative differential conductance. The effective competition between fast and slow transport channels is responsible for the observed negative differential conductance and super-Poissonian shot noise. In addition, we further discuss the skewness and kurtosis properties of transport current in the super-Poissonian shot noise regions. Our findings suggest a tunable negative differential conductance molecular device, and the predicted properties of high-order current cumulants are very interesting for a better understanding of electron transport through single-molecule magnet junctions.
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Affiliation(s)
- Hai-Bin Xue
- College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China
| | - Jiu-Qing Liang
- Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China
| | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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26
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Sothmann B, Sánchez R, Jordan AN. Thermoelectric energy harvesting with quantum dots. NANOTECHNOLOGY 2015; 26:032001. [PMID: 25549281 DOI: 10.1088/0957-4484/26/3/032001] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We review recent theoretical work on thermoelectric energy harvesting in multi-terminal quantum-dot setups. We first discuss several examples of nanoscale heat engines based on Coulomb-coupled conductors. In particular, we focus on quantum dots in the Coulomb-blockade regime, chaotic cavities and resonant tunneling through quantum dots and wells. We then turn toward quantum-dot heat engines that are driven by bosonic degrees of freedom such as phonons, magnons and microwave photons. These systems provide interesting connections to spin caloritronics and circuit quantum electrodynamics.
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Affiliation(s)
- Björn Sothmann
- Département de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland
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27
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Hickey JM, Flindt C, Garrahan JP. Intermittency and dynamical Lee-Yang zeros of open quantum systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062128. [PMID: 25615065 DOI: 10.1103/physreve.90.062128] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2014] [Indexed: 06/04/2023]
Abstract
We use high-order cumulants to investigate the Lee-Yang zeros of generating functions of dynamical observables in open quantum systems. At long times the generating functions take on a large-deviation form with singularities of the associated cumulant generating functions-or dynamical free energies-signifying phase transitions in the ensemble of dynamical trajectories. We consider a driven three-level system as well as the dissipative Ising model. Both systems exhibit dynamical intermittency in the statistics of quantum jumps. From the short-time behavior of the dynamical Lee-Yang zeros, we identify critical values of the counting field which we attribute to the observed intermittency and dynamical phase coexistence. Furthermore, for the dissipative Ising model we construct a trajectory phase diagram and estimate the value of the transverse field where the stationary state changes from being ferromagnetic (inactive) to paramagnetic (active).
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Affiliation(s)
- James M Hickey
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Christian Flindt
- Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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28
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Gernert R, Emary C, Klapp SHL. Waiting time distribution for continuous stochastic systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062115. [PMID: 25615052 DOI: 10.1103/physreve.90.062115] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2014] [Indexed: 06/04/2023]
Abstract
The waiting time distribution (WTD) is a common tool for analyzing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete, or where it is favourable to discuss the dynamics on a discretized and a continuous level in parallel. An example is the hindered motion of particles through potential landscapes with barriers. In the present paper we propose a consistent generalization of the WTD from the discrete case to situations where the particles perform continuous barrier crossing characterized by a finite duration. To this end, we introduce a recipe to calculate the WTD from the Fokker-Planck (Smoluchowski) equation. In contrast to the closely related first passage time distribution (FPTD), which is frequently used to describe continuous processes, the WTD contains information about the direction of motion. As an application, we consider the paradigmatic example of an overdamped particle diffusing through a washboard potential. To verify the approach and to elucidate its numerical implications, we compare the WTD defined via the Smoluchowski equation with data from direct simulation of the underlying Langevin equation and find full consistency provided that the jumps in the Langevin approach are defined properly. Moreover, for sufficiently large energy barriers, the WTD defined via the Smoluchowski equation becomes consistent with that resulting from the analytical solution of a (two-state) master equation model for the short-time dynamics developed previously by us [Phys. Rev. E 86, 061135 (2012)]. Thus, our approach "interpolates" between these two types of stochastic motion. We illustrate our approach for both symmetric systems and systems under constant force.
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Affiliation(s)
- Robert Gernert
- Institut für Theoretische Physik, Sekr. EW 7-1, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
| | - Clive Emary
- Department of Physics and Mathematics, University of Hull, Kingston-upon-Hull, HU6 7RX, United Kingdom
| | - Sabine H L Klapp
- Institut für Theoretische Physik, Sekr. EW 7-1, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
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29
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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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30
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Xue HB. Full counting statistics as a probe of quantum coherence in a side-coupled double quantum dot system. ANNALS OF PHYSICS 2013; 339:208-217. [DOI: 10.1016/j.aop.2013.09.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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31
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Mordovina U, Emary C. Full-counting statistics of random transition-rate matrices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062148. [PMID: 24483426 DOI: 10.1103/physreve.88.062148] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2013] [Indexed: 06/03/2023]
Abstract
We study the full-counting statistics of current of large open systems through the application of random-matrix theory to transition-rate matrices. We develop a method for calculating the ensemble-averaged current-cumulant generating functions based on an expansion in terms of the inverse system size. We investigate how different symmetry properties and different counting schemes affect the results.
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Affiliation(s)
- Uliana Mordovina
- Institut für Theoretische Physik, Hardenbergstrasse 36, TU Berlin, D-10623 Berlin, Germany
| | - Clive Emary
- Department of Physics and Mathematics, University of Hull, Kingston-upon-Hull, HU6 7RX, United Kingdom
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32
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Li ZZ, Lam CH, Yu T, You JQ. Detector-induced backaction on the counting statistics of a double quantum dot. Sci Rep 2013; 3:3026. [PMID: 24149587 PMCID: PMC3805975 DOI: 10.1038/srep03026] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2013] [Accepted: 10/04/2013] [Indexed: 12/02/2022] Open
Abstract
Full counting statistics of electron transport is of fundamental importance for a deeper understanding of the underlying physical processes in quantum transport in nanoscale devices. The backaction effect from a detector on the nanoscale devices is also essential due to its inevitable presence in experiments. Here we investigate the backaction of a charge detector in the form of a quantum point contact (QPC) on the counting statistics of a biased double quantum dot (DQD). We show that this inevitable QPC-induced backaction can have profound effects on the counting statistics under certain conditions, e.g., changing the shot noise from being sub-Poissonian to super-Poissonian, and changing the skewness from being positive to negative. Also, we show that both Fano factor and skewness can be either enhanced or suppressed by increasing the energy difference between two single-dot levels of the DQD under the detector-induced backaction.
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Affiliation(s)
- Zeng-Zhao Li
- Beijing Computational Science Research Center, Beijing 100084, China
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33
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Herz M, Bouvron S, Ćavar E, Fonin M, Belzig W, Scheer E. Fundamental quantum noise mapping with tunnelling microscopes tested at surface structures of subatomic lateral size. NANOSCALE 2013; 5:9978-9983. [PMID: 23989889 DOI: 10.1039/c3nr02216a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We present a measurement scheme that enables quantitative detection of the shot noise in a scanning tunnelling microscope while scanning the sample. As test objects we study defect structures produced on an iridium single crystal at low temperatures. The defect structures appear in the constant current images as protrusions with curvature radii well below the atomic diameter. The measured power spectral density of the noise is very near to the quantum limit with Fano factor F = 1. While the constant current images show detailed structures expected for tunnelling involving d-atomic orbitals of Ir, we find the current noise to be without pronounced spatial variation as expected for shot noise arising from statistically independent events.
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Affiliation(s)
- Markus Herz
- Department of Physics, University of Konstanz, 78457 Konstanz, Germany.
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34
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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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35
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House MG, Xiao M, Guo G, Li H, Cao G, Rosenthal MM, Jiang H. Detection and measurement of spin-dependent dynamics in random telegraph signals. PHYSICAL REVIEW LETTERS 2013; 111:126803. [PMID: 24093289 DOI: 10.1103/physrevlett.111.126803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2013] [Indexed: 06/02/2023]
Abstract
A quantum point contact was used to observe single-electron fluctuations of a quantum dot in a GaAs heterostructure. The resulting random telegraph signals (RTS) contain statistical information about the electron spin state if the tunneling dynamics are spin dependent. We develop a statistical method to extract information about spin-dependent dynamics from RTS and use it to demonstrate that these dynamics can be studied in the thermal energy regime. The tunneling rates of each spin state are independently measured in a finite external magnetic field. We confirm previous findings of a decrease in overall tunneling rates for the spin excited state compared to the ground state as an external magnetic field is increased.
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Affiliation(s)
- M G House
- Department of Physics and Astronomy, University of California, Los Angeles, Los Angeles, California 90095, USA
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36
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Rajabi L, Pöltl C, Governale M. Waiting time distributions for the transport through a quantum-dot tunnel coupled to one normal and one superconducting lead. PHYSICAL REVIEW LETTERS 2013; 111:067002. [PMID: 23971603 DOI: 10.1103/physrevlett.111.067002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2013] [Indexed: 06/02/2023]
Abstract
We have studied the waiting time distributions (WTDs) for subgap transport through a single-level quantum-dot tunnel coupled to one normal and one superconducting lead. The WTDs reveal the internal dynamics of the system, in particular, the coherent transfer of Cooper pairs between the dot and the superconductor. The WTDs exhibit oscillations that can be directly associated to the coherent oscillation between the empty and doubly occupied dot. The oscillation frequency is equal to the energy splitting between the Andreev bound states. These effects are more pronounced when the empty state and double-occupied state are in resonance.
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Affiliation(s)
- Leila Rajabi
- School of Chemical and Physical Sciences and MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand
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37
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Hickey JM, Flindt C, Garrahan JP. Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:012119. [PMID: 23944426 DOI: 10.1103/physreve.88.012119] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2013] [Indexed: 06/02/2023]
Abstract
We examine the generating function of the time-integrated energy for the one-dimensional Glauber-Ising model. At long times, the generating function takes on a large-deviation form and the associated cumulant generating function has singularities corresponding to continuous trajectory (or "space-time") phase transitions between paramagnetic trajectories and ferromagnetically or antiferromagnetically ordered trajectories. In the thermodynamic limit, the singularities make up a whole curve of critical points in the complex plane of the counting field. We evaluate analytically the generating function by mapping the generator of the biased dynamics to a non-Hermitian Hamiltonian of an associated quantum spin chain. We relate the trajectory phase transitions to the high-order cumulants of the time-integrated energy which we use to extract the dynamical Lee-Yang zeros of the generating function. This approach offers the possibility to detect continuous trajectory phase transitions from the finite-time behavior of measurable quantities.
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Affiliation(s)
- James M Hickey
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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38
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Ren J, Sinitsyn NA. Braid group and topological phase transitions in nonequilibrium stochastic dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:050101. [PMID: 23767466 DOI: 10.1103/physreve.87.050101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2012] [Indexed: 06/02/2023]
Abstract
We show that distinct topological phases of the band structure of a non-Hermitian Hamiltonian can be classified with elements of the braid group. As the proof of principle, we consider the non-Hermitian evolution of the statistics of nonequilibrium stochastic currents. We show that topologically nontrivial phases have detectable properties, including the emergence of decaying oscillations of parity and state probabilities, and discontinuities in the steady state statistics of currents.
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Affiliation(s)
- Jie Ren
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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Battista F, Moskalets M, Albert M, Samuelsson P. Quantum heat fluctuations of single-particle sources. PHYSICAL REVIEW LETTERS 2013; 110:126602. [PMID: 25166830 DOI: 10.1103/physrevlett.110.126602] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2012] [Indexed: 06/03/2023]
Abstract
Optimal single electron sources emit regular streams of particles, displaying no low-frequency charge current noise. Because of the wave packet nature of the emitted particles, the energy is, however, fluctuating, giving rise to heat current noise. We investigate theoretically this quantum source of heat noise for an emitter coupled to an electronic probe in the hot-electron regime. The distribution of temperature and potential fluctuations induced in the probe is shown to provide direct information on the single-particle wave function properties and display strong nonclassical features.
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Affiliation(s)
- F Battista
- Division of Mathematical Physics, Lund University, Box 118, S-221 00 Lund, Sweden
| | - M Moskalets
- Department of Metal and Semiconductor Physics, NTU Kharkiv Polytechnic Institute, 61002 Kharkiv, Ukraine
| | - M Albert
- Laboratoire de Physique des Solides, Université Paris Sud, 91405 Orsay, France
| | - P Samuelsson
- Division of Mathematical Physics, Lund University, Box 118, S-221 00 Lund, Sweden
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40
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Flindt C, Garrahan JP. Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics. PHYSICAL REVIEW LETTERS 2013; 110:050601. [PMID: 23414009 DOI: 10.1103/physrevlett.110.050601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2012] [Indexed: 06/01/2023]
Abstract
We investigate Lee-Yang zeros of generating functions of dynamical observables and establish a general relation between phase transitions in ensembles of trajectories of stochastic many-body systems and the time evolution of high-order cumulants of such observables. This connects dynamical free energies for full counting statistics in the long-time limit, which can be obtained via large-deviation methods and whose singularities indicate dynamical phase transitions, to observables that are directly accessible in simulation and experiment. As an illustration, we consider facilitated spin models of glasses and show that from the short-time behavior of high-order cumulants, it is possible to infer the existence and location of dynamical or "space-time" transitions in these systems.
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Affiliation(s)
- Christian Flindt
- Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland
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Genway S, Garrahan JP, Lesanovsky I, Armour AD. Phase transitions in trajectories of a superconducting single-electron transistor coupled to a resonator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051122. [PMID: 23004718 DOI: 10.1103/physreve.85.051122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2012] [Indexed: 06/01/2023]
Abstract
Recent progress in the study of dynamical phase transitions has been made with a large-deviation approach to study trajectories of stochastic jumps using a thermodynamic formalism. We study this method applied to an open quantum system consisting of a superconducting single-electron transistor, near the Josephson quasiparticle resonance, coupled to a resonator. We find that the dynamical behavior shown in rare trajectories can be rich even when the mean dynamical activity is small, and thus the formalism gives insights into the form of fluctuations. The structure of the dynamical phase diagram found from the quantum-jump trajectories of the resonator is studied, and we see that sharp transitions in the dynamical activity may be related to the appearance and disappearance of bistabilities in the state of the resonator as system parameters are changed. We also demonstrate that for a fast resonator, the trajectories of quasiparticles are similar to the resonator trajectories.
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Affiliation(s)
- Sam Genway
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
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42
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Agarwalla BK, Li B, Wang JS. Full-counting statistics of heat transport in harmonic junctions: transient, steady states, and fluctuation theorems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051142. [PMID: 23004738 DOI: 10.1103/physreve.85.051142] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2011] [Indexed: 06/01/2023]
Abstract
We study the statistics of heat transferred in a given time interval t_{M}, through a finite harmonic chain, called the center, which is connected to two heat baths, the left (L) and the right (R), that are maintained at two temperatures. The center atoms are driven by external time-dependent forces. We calculate the cumulant generating function (CGF) for the heat transferred out of the left lead, Q_{L}, based on the two-time quantum measurement concept and using the nonequilibrium Green's function method. The CGF can be concisely expressed in terms of Green's functions of the center and an argument-shifted self-energy of the lead. The expression of the CGF is valid in both transient and steady-state regimes. We consider three initial conditions for the density operator and show numerically, for a one-atom junction, how their transient behaviors differ from each other but, finally, approach the same steady state, independent of the initial distributions. We also derive the CGF for the joint probability distribution P(Q_{L},Q_{R}), and discuss the correlations between Q_{L} and Q_{R}. We calculate the CGF for total entropy production in the reservoirs. In the steady state we explicitly show that the CGFs obey steady-state fluctuation theorems. We obtain classical results by taking ℏ→0. We also apply our method to the counting of the electron number and electron energy, for which the associated self-energy is obtained from the usual lead self-energy by multiplying a phase and shifting the contour time, respectively.
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Affiliation(s)
- Bijay Kumar Agarwalla
- Department of Physics and Center for Computational Science and Engineering, National University of Singapore, Singapore 117542, Republic of Singapore.
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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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Albert M, Flindt C, Büttiker M. Distributions of waiting times of dynamic single-electron emitters. PHYSICAL REVIEW LETTERS 2011; 107:086805. [PMID: 21929192 DOI: 10.1103/physrevlett.107.086805] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2011] [Indexed: 05/31/2023]
Abstract
The distribution of waiting times between elementary tunneling events is of fundamental importance for understanding the stochastic charge transfer processes in nanoscale conductors. Here we investigate the waiting time distributions (WTDs) of periodically driven single-electron emitters and evaluate them for the specific example of a mesoscopic capacitor. We show that the WTDs provide a particularly informative characterization of periodically driven devices and we demonstrate how the WTDs allow us to reconstruct the full counting statistics (FCS) of charges that have been transferred after a large number of periods. We find that the WTDs are capable of describing short-time physics and correlations which are not accessible via the FCS alone.
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Affiliation(s)
- Mathias Albert
- Département de Physique Théorique, Université de Genève, CH-1211 Genève, Switzerland
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Emary C. Self-consistent electron counting statistics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:025304. [PMID: 21406841 DOI: 10.1088/0953-8984/23/2/025304] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We develop a self-consistent version of perturbation theory in Liouville space which seeks to combine the advantages of master equation approaches in quantum transport with the nonperturbative features that a self-consistent treatment brings. We describe how counting fields may be included in a self-consistent manner in this formalism such that the full counting statistics can be calculated. Non-Markovian effects are also incorporated. Several different self-consistent approximations are introduced and we discuss their relative strengths with a simple example.
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Affiliation(s)
- Clive Emary
- Institut für Theoretische Physik, Hardenbergstraße 36, TU Berlin, D-10623 Berlin, Germany
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46
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Lambert N, Emary C, Chen YN, Nori F. Distinguishing quantum and classical transport through nanostructures. PHYSICAL REVIEW LETTERS 2010; 105:176801. [PMID: 21231065 DOI: 10.1103/physrevlett.105.176801] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2010] [Indexed: 05/30/2023]
Abstract
We consider the question of how to distinguish quantum from classical transport through nanostructures. To address this issue we have derived two inequalities for temporal correlations in nonequilibrium transport in nanostructures weakly coupled to leads. The first inequality concerns local charge measurements and is of general validity; the second concerns the current flow through the device and is relevant for double quantum dots. Violation of either of these inequalities indicates that physics beyond that of a classical Markovian model is occurring in the nanostructure.
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Affiliation(s)
- Neill Lambert
- The Institute of Physical and Chemical Research, RIKEN, Saitama, Japan
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Brandes T. Feedback control of quantum transport. PHYSICAL REVIEW LETTERS 2010; 105:060602. [PMID: 20867968 DOI: 10.1103/physrevlett.105.060602] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2010] [Revised: 06/18/2010] [Indexed: 05/29/2023]
Abstract
The current through nanostructures like quantum dots can be stabilized by a classical feedback loop that continuously adjusts system parameters as a function of the number of tunnelled particles n. At large times, the feedback loop freezes the fluctuations of n, which leads to highly accurate, continuous single particle transfers. For the simplest case of feedback acting simultaneously on all system parameters, we show how to reconstruct the original full counting statistics from the frozen distribution.
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Affiliation(s)
- Tobias Brandes
- Institut für Theoretische Physik, Hardenbergstraße 36, TU Berlin, D-10623 Berlin, Germany
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