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Diba O, Miller HJD, Iles-Smith J, Nazir A. Quantum Work Statistics at Strong Reservoir Coupling. PHYSICAL REVIEW LETTERS 2024; 132:190401. [PMID: 38804950 DOI: 10.1103/physrevlett.132.190401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2023] [Accepted: 03/25/2024] [Indexed: 05/29/2024]
Abstract
Determining the statistics of work done on a quantum system while strongly coupled to a reservoir is a formidable task, requiring the calculation of the full eigenspectrum of the combined system and reservoir. Here, we show that this issue can be circumvented by using a polaron transformation that maps the system into a new frame where weak-coupling theory can be applied. Crucially, this polaron approach reproduces the Jarzynski fluctuation theorem, thus ensuring consistency with the laws of stochastic thermodynamics. We apply our formalism to a system driven across the Landau-Zener transition, where we identify clear signatures in the work distribution arising from a non-negligible coupling to the environment. Our results provide a new method for studying the stochastic thermodynamics of driven quantum systems beyond Markovian, weak-coupling regimes.
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Affiliation(s)
- Owen Diba
- Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Harry J D Miller
- Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Jake Iles-Smith
- Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Ahsan Nazir
- Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
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2
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Arrachea L. Energy dynamics, heat production and heat-work conversion with qubits: toward the development of quantum machines. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:036501. [PMID: 36603220 DOI: 10.1088/1361-6633/acb06b] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2022] [Accepted: 01/05/2023] [Indexed: 06/17/2023]
Abstract
We present an overview of recent advances in the study of energy dynamics and mechanisms for energy conversion in qubit systems with special focus on realizations in superconducting quantum circuits. We briefly introduce the relevant theoretical framework to analyze heat generation, energy transport and energy conversion in these systems with and without time-dependent driving considering the effect of equilibrium and non-equilibrium environments. We analyze specific problems and mechanisms under current investigation in the context of qubit systems. These include the problem of energy dissipation and possible routes for its control, energy pumping between driving sources and heat pumping between reservoirs, implementation of thermal machines and mechanisms for energy storage. We highlight the underlying fundamental phenomena related to geometrical and topological properties, as well as many-body correlations. We also present an overview of recent experimental activity in this field.
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Affiliation(s)
- Liliana Arrachea
- Escuela de Ciencia y Tecnología and ICIFI, Universidad de San Martín, Av. 25 de Mayo y Francia, 1650 Buenos Aires, Argentina
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3
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Chakraborty S, Das A, Chruściński D. Strongly coupled quantum Otto cycle with single qubit bath. Phys Rev E 2022; 106:064133. [PMID: 36671160 DOI: 10.1103/physreve.106.064133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2022] [Accepted: 11/15/2022] [Indexed: 12/27/2022]
Abstract
We discuss a model of a closed quantum evolution of two qubits where the joint Hamiltonian is so chosen such that one of the qubits acts as a bath and thermalizes the other qubit which is acting as the system. The corresponding exact master equation for the system is derived. Interestingly, for a specific choice of parameters the master equation takes the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form, with constant coefficients representing pumping and damping of a single qubit system. Based on this model we construct an Otto cycle connected to a single qubit bath and study its thermodynamic properties. Our analysis goes beyond the conventional weak coupling scenario and illustrates the effects of finite baths, including non-Markovianity. We find closed form expressions for efficiency (coefficient of performance), power (cooling power) for the heat engine regime (refrigerator regime), and for different modifications of the joint Hamiltonian.
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Affiliation(s)
- Sagnik Chakraborty
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziądzka 5/7, 87-100 Toruń, Poland
| | - Arpan Das
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziądzka 5/7, 87-100 Toruń, Poland
| | - Dariusz Chruściński
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziądzka 5/7, 87-100 Toruń, Poland
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4
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Malavazi AHA, Brito F. A Schmidt Decomposition Approach to Quantum Thermodynamics. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1645. [PMID: 36421500 PMCID: PMC9689058 DOI: 10.3390/e24111645] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Revised: 10/29/2022] [Accepted: 11/10/2022] [Indexed: 06/16/2023]
Abstract
The development of a self-consistent thermodynamic theory of quantum systems is of fundamental importance for modern physics. Still, despite its essential role in quantum science and technology, there is no unifying formalism for characterizing the thermodynamics within general autonomous quantum systems, and many fundamental open questions remain unanswered. Along these lines, most current efforts and approaches restrict the analysis to particular scenarios of approximative descriptions and semi-classical regimes. Here, we propose a novel approach to describe the thermodynamics of arbitrary bipartite autonomous quantum systems based on the well-known Schmidt decomposition. This formalism provides a simple, exact, and symmetrical framework for expressing the energetics between interacting systems, including scenarios beyond the standard description regimes, such as strong coupling. We show that this procedure allows straightforward identification of local effective operators suitable for characterizing the physical local internal energies. We also demonstrate that these quantities naturally satisfy the usual thermodynamic notion of energy additivity.
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Affiliation(s)
| | - Frederico Brito
- Instituto de Física de São Carlos, Universidade de São Paulo, C.P. 369, São Carlos 13560-970, SP, Brazil
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Barra F. Efficiency Fluctuations in a Quantum Battery Charged by a Repeated Interaction Process. ENTROPY (BASEL, SWITZERLAND) 2022; 24:820. [PMID: 35741541 PMCID: PMC9223045 DOI: 10.3390/e24060820] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/18/2022] [Revised: 06/05/2022] [Accepted: 06/07/2022] [Indexed: 11/16/2022]
Abstract
A repeated interaction process assisted by auxiliary thermal systems charges a quantum battery. The charging energy is supplied by switching on and off the interaction between the battery and the thermal systems. The charged state is an equilibrium state for the repeated interaction process, and the ergotropy characterizes its charge. The working cycle consists in extracting the ergotropy and charging the battery again. We discuss the fluctuating efficiency of the process, among other fluctuating properties. These fluctuations are dominated by the equilibrium distribution and depend weakly on other process properties.
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Affiliation(s)
- Felipe Barra
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago 8370415, Chile
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6
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Multipartite Correlations in Quantum Collision Models. ENTROPY 2022; 24:e24040508. [PMID: 35455171 PMCID: PMC9032730 DOI: 10.3390/e24040508] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Revised: 04/01/2022] [Accepted: 04/03/2022] [Indexed: 12/10/2022]
Abstract
Quantum collision models have proved to be useful for a clear and concise description of many physical phenomena in the field of open quantum systems: thermalization, decoherence, homogenization, nonequilibrium steady state, entanglement generation, simulation of many-body dynamics, and quantum thermometry. A challenge in the standard collision model, where the system and many ancillas are all initially uncorrelated, is how to describe quantum correlations among ancillas induced by successive system-ancilla interactions. Another challenge is how to deal with initially correlated ancillas. Here we develop a tensor network formalism to address both challenges. We show that the induced correlations in the standard collision model are well captured by a matrix product state (a matrix product density operator) if the colliding particles are in pure (mixed) states. In the case of the initially correlated ancillas, we construct a general tensor diagram for the system dynamics and derive a memory-kernel master equation. Analyzing the perturbation series for the memory kernel, we go beyond the recent results concerning the leading role of two-point correlations and consider multipoint correlations (Waldenfelds cumulants) that become relevant in the higher-order stroboscopic limits. These results open an avenue for the further analysis of memory effects in collisional quantum dynamics.
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Cresser JD, Anders J. Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. PHYSICAL REVIEW LETTERS 2021; 127:250601. [PMID: 35029453 DOI: 10.1103/physrevlett.127.250601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 10/11/2021] [Indexed: 06/14/2023]
Abstract
The Gibbs state is widely taken to be the equilibrium state of a system in contact with an environment at temperature T. However, non-negligible interactions between system and environment can give rise to an altered state. Here, we derive general expressions for this mean force Gibbs state, valid for any system that interacts with a bosonic reservoir. First, we derive the state in the weak coupling limit and find that, in general, it maintains coherences with respect to the bare system Hamiltonian. Second, we develop a new expansion method suited to investigate the ultrastrong coupling regime. This allows us to derive the explicit form for the mean force Gibbs state, and we find that it becomes diagonal in the basis set by the system-reservoir interaction instead of the system Hamiltonian. Several examples are discussed including a single qubit, a three-level V-system, and two coupled qubits all interacting with bosonic reservoirs. The results shed light on the presence of coherences in the strong coupling regime, and provide key tools for nanoscale thermodynamics investigations.
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Affiliation(s)
- J D Cresser
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom
- School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
- Department of Physics and Astronomy, Macquarie University, 2109 New South Wales, Australia
| | - J Anders
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom
- Institut für Physik und Astronomie, University of Potsdam, 14476 Potsdam, Germany
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Seah S, Perarnau-Llobet M, Haack G, Brunner N, Nimmrichter S. Quantum Speed-Up in Collisional Battery Charging. PHYSICAL REVIEW LETTERS 2021; 127:100601. [PMID: 34533344 DOI: 10.1103/physrevlett.127.100601] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Revised: 07/01/2021] [Accepted: 08/06/2021] [Indexed: 06/13/2023]
Abstract
We present a collision model for the charging of a quantum battery by identical nonequilibrium qubit units. When the units are prepared in a mixture of energy eigenstates, the energy gain in the battery can be described by a classical random walk, where both average energy and variance grow linearly with time. Conversely, when the qubits contain quantum coherence, interference effects buildup in the battery and lead to a faster spreading of the energy distribution, reminiscent of a quantum random walk. This can be exploited for faster and more efficient charging of a battery initialized in the ground state. Specifically, we show that coherent protocols can yield higher charging power than any possible incoherent strategy, demonstrating a quantum speed-up at the level of a single battery. Finally, we characterize the amount of extractable work from the battery through the notion of ergotropy.
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Affiliation(s)
- Stella Seah
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | | | - Géraldine Haack
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | - Nicolas Brunner
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | - Stefan Nimmrichter
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Siegen 57068, Germany
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9
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Cattaneo M, De Chiara G, Maniscalco S, Zambrini R, Giorgi GL. Collision Models Can Efficiently Simulate Any Multipartite Markovian Quantum Dynamics. PHYSICAL REVIEW LETTERS 2021; 126:130403. [PMID: 33861108 DOI: 10.1103/physrevlett.126.130403] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2020] [Accepted: 03/02/2021] [Indexed: 06/12/2023]
Abstract
We introduce the multipartite collision model, defined in terms of elementary interactions between subsystems and ancillas, and show that it can simulate the Markovian dynamics of any multipartite open quantum system. We develop a method to estimate an analytical error bound for any repeated interactions model, and we use it to prove that the error of our scheme displays an optimal scaling. Finally, we provide a simple decomposition of the multipartite collision model into elementary quantum gates, and show that it is efficiently simulable on a quantum computer according to the dissipative quantum Church-Turing theorem, i.e., it requires a polynomial number of resources.
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Affiliation(s)
- Marco Cattaneo
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
- QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto, Finland
- QTF Centre of Excellence, Department of Physics, University of Helsinki, P.O. Box 43, FI-00014 Helsinki, Finland
| | - Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Sabrina Maniscalco
- QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto, Finland
- QTF Centre of Excellence, Department of Physics, University of Helsinki, P.O. Box 43, FI-00014 Helsinki, Finland
- QTF Centre of Excellence, Department of Applied Physics, School of Science, Aalto University, FI-00076 Aalto, Finland
| | - Roberta Zambrini
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Gian Luca Giorgi
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
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10
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Strasberg P, Esposito M. Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force. Phys Rev E 2020; 101:050101. [PMID: 32575212 DOI: 10.1103/physreve.101.050101] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2020] [Accepted: 04/22/2020] [Indexed: 11/07/2022]
Abstract
The nonequilibrium thermodynamics of an open (classical or quantum) system in strong contact with a single heat bath can be conveniently described in terms of the Hamiltonian of mean force. However, the conventional formulation is limited by the necessity to measure differences in equilibrium properties of the system-bath composite. We make use of the freedom involved in defining thermodynamic quantities, which leaves the thermodynamics unchanged, to show that the Hamiltonian of mean force can be inferred from measurements on the system alone, up to that irrelevant freedom. In doing so, we refute a key criticism expressed in the works by P. Talkner and P. Hänggi [Phys. Rev. E 94, 022143 (2016)10.1103/PhysRevE.94.022143 and arXiv:1911.11660]. We also discuss the remaining part of the criticism.
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Affiliation(s)
- Philipp Strasberg
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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11
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Rivas Á. Strong Coupling Thermodynamics of Open Quantum Systems. PHYSICAL REVIEW LETTERS 2020; 124:160601. [PMID: 32383934 DOI: 10.1103/physrevlett.124.160601] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2019] [Accepted: 03/17/2020] [Indexed: 06/11/2023]
Abstract
A general thermodynamic framework is presented for open quantum systems in fixed contact with a thermal reservoir. The first and second law are obtained for arbitrary system-reservoir coupling strengths, and including both factorized and correlated initial conditions. The thermodynamic properties are adapted to the generally strong coupling regime, approaching the ones defined for equilibrium, and their standard weak-coupling counterparts as appropriate limits. Moreover, they can be inferred from measurements involving only system observables. Finally, a thermodynamic signature of non-Markovianity is formulated in the form of a negative entropy production rate.
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Affiliation(s)
- Ángel Rivas
- Departamento de Física Teórica, Facultad de Ciencias Físicas, Universidad Complutense, 28040 Madrid, Spain and CCS-Center for Computational Simulation, Campus de Montegancedo UPM, 28660 Boadilla del Monte, Madrid, Spain
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12
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Hewgill A, González JO, Palao JP, Alonso D, Ferraro A, De Chiara G. Three-qubit refrigerator with two-body interactions. Phys Rev E 2020; 101:012109. [PMID: 32069534 DOI: 10.1103/physreve.101.012109] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2019] [Indexed: 06/10/2023]
Abstract
We propose a three-qubit setup for the implementation of a variety of quantum thermal machines where all heat fluxes and work production can be controlled. An important configuration that can be designed is that of an absorption refrigerator, extracting heat from the coldest reservoir without the need of external work supply. Remarkably, we achieve this regime by using only two-body interactions instead of the widely employed three-body interactions. This configuration could be more easily realized in current experimental setups. We model the open-system dynamics with both a global and a local master equation thermodynamic-consistent approach. Finally, we show how this model can be employed as a heat valve, in which by varying the local field of one of the two qubits allows one to control and amplify the heat current between the other qubits.
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Affiliation(s)
- Adam Hewgill
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - J Onam González
- Dpto. de Física and IUdEA: Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, 38203 Spain
| | - José P Palao
- Dpto. de Física and IUdEA: Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, 38203 Spain
| | - Daniel Alonso
- Dpto. de Física and IUdEA: Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, 38203 Spain
| | - Alessandro Ferraro
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, F-34095 Montpellier, France
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