1
|
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.
Collapse
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
| |
Collapse
|
2
|
Boettcher V, Hartmann R, Beyer K, Strunz WT. Dynamics of a strongly coupled quantum heat engine-Computing bath observables from the hierarchy of pure states. J Chem Phys 2024; 160:094108. [PMID: 38436445 DOI: 10.1063/5.0192075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Accepted: 02/07/2024] [Indexed: 03/05/2024] Open
Abstract
We present a fully quantum dynamical treatment of a quantum heat engine and its baths based on the Hierarchy of Pure States (HOPS), an exact and general method for open quantum system dynamics. We show how the change of the bath energy and the interaction energy can be determined within HOPS for arbitrary coupling strength and smooth time dependence of the modulation protocol. The dynamics of all energetic contributions during the operation can be carefully examined both in its initial transient phase and, also later, in its periodic steady state. A quantum Otto engine with a qubit as an inherently nonlinear work medium is studied in a regime where the energy associated with the interaction Hamiltonian plays an important role for the global energy balance and, thus, must not be neglected when calculating its power and efficiency. We confirm that the work required to drive the coupling with the baths sensitively depends on the speed of the modulation protocol. Remarkably, departing from the conventional scheme of well-separated phases by allowing for temporal overlap, we discover that one can even gain energy from the modulation of bath interactions. We visualize these various work contributions using the analog of state change diagrams of thermodynamic cycles. We offer a concise, full presentation of HOPS with its extension to bath observables, as it serves as a universal tool for the numerically exact description of general quantum dynamical (thermodynamic) scenarios far from the weak-coupling limit.
Collapse
Affiliation(s)
- Valentin Boettcher
- Institute of Theoretical Physics, TUD Dresden University of Technology, 01062 Dresden, Germany
- Department of Physics, McGill University, Montréal, Québec H3A 2T8, Canada
| | - Richard Hartmann
- Institute of Theoretical Physics, TUD Dresden University of Technology, 01062 Dresden, Germany
| | - Konstantin Beyer
- Institute of Theoretical Physics, TUD Dresden University of Technology, 01062 Dresden, Germany
- Department of Physics, Stevens Institute of Technology, Hoboken, New Jersey 07030, USA
| | - Walter T Strunz
- Institute of Theoretical Physics, TUD Dresden University of Technology, 01062 Dresden, Germany
| |
Collapse
|
3
|
de Assis RJ, Diniz CM, de Almeida NG, Villas-Bôas CJ. Thermodynamics of the Ramsey Zone. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1430. [PMID: 37895551 PMCID: PMC10605998 DOI: 10.3390/e25101430] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2023] [Revised: 09/28/2023] [Accepted: 10/06/2023] [Indexed: 10/29/2023]
Abstract
We studied the thermodynamic properties such as the entropy, heat (JQ), and work (JW) rates involved when an atom passes through a Ramsey zone, which consists of a mode field inside a low-quality factor cavity that behaves classically, promoting rotations on the atomic state. Focusing on the atom, we show that JW predominates when the atomic rotations are successful, maintaining its maximum purity as computed by the von Neumann entropy. Conversely, JQ stands out when the atomic state ceases to be pure due to its entanglement with the cavity mode. With this, we interpret the quantum-to-classical transition in light of the heat and work rates. Besides, we show that, for the cavity mode to work as a Ramsey zone (classical field), several photons (of the order of 106) need to cross the cavity, which explains its classical behavior, even when the inside average number of photons is of the order of unity.
Collapse
Affiliation(s)
- Rogério Jorge de Assis
- Instituto de Física, Universidade Federal de Goiás, Goiânia 74690-900, GO, Brazil;
- Departamento de Física, Universidade Federal de São Carlos, São Carlos 13565-905, SP, Brazil; (C.M.D.); (C.J.V.-B.)
| | - Ciro Micheletti Diniz
- Departamento de Física, Universidade Federal de São Carlos, São Carlos 13565-905, SP, Brazil; (C.M.D.); (C.J.V.-B.)
| | | | - Celso Jorge Villas-Bôas
- Departamento de Física, Universidade Federal de São Carlos, São Carlos 13565-905, SP, Brazil; (C.M.D.); (C.J.V.-B.)
| |
Collapse
|
4
|
Rossini M, Maile D, Ankerhold J, Donvil BIC. Single-Qubit Error Mitigation by Simulating Non-Markovian Dynamics. PHYSICAL REVIEW LETTERS 2023; 131:110603. [PMID: 37774275 DOI: 10.1103/physrevlett.131.110603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Revised: 06/09/2023] [Accepted: 08/16/2023] [Indexed: 10/01/2023]
Abstract
Quantum simulation is a powerful tool to study the properties of quantum systems. The dynamics of open quantum systems are often described by completely positive (CP) maps, for which several quantum simulation schemes exist. Such maps, however, represent only a subset of a larger class of maps: the general dynamical maps which are linear, Hermitian preserving, and trace preserving but not necessarily positivity preserving. Here we present a simulation scheme for these general dynamical maps, which occur when the underlying system-reservoir model undergoes entangling (and thus non-Markovian) dynamics. Such maps also arise as the inverse of CP maps, which are commonly used in error mitigation. We illustrate our simulation scheme on an IBM quantum processor, demonstrating its ability to recover the initial state of a Lindblad evolution. This paves the way for a novel form of quantum error mitigation. Our scheme only requires one ancilla qubit as an overhead and a small number of one and two qubit gates. Consequently, we expect it to be of practical use in near-term quantum devices.
Collapse
Affiliation(s)
- Mirko Rossini
- Institute for Complex Quantum Systems and IQST, Ulm University-Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| | - Dominik Maile
- Institute for Complex Quantum Systems and IQST, Ulm University-Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| | - Joachim Ankerhold
- Institute for Complex Quantum Systems and IQST, Ulm University-Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| | - Brecht I C Donvil
- Institute for Complex Quantum Systems and IQST, Ulm University-Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| |
Collapse
|
5
|
Zhang ZZ, Tan QS, Wu W. Heat distribution in quantum Brownian motion. Phys Rev E 2023; 108:014138. [PMID: 37583192 DOI: 10.1103/physreve.108.014138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2023] [Accepted: 07/11/2023] [Indexed: 08/17/2023]
Abstract
We investigate the heat statistics in a relaxation process of quantum Brownian motion described by the Caldeira-Leggett model. By employing the normal mode transformation and the phase-space formulation approach, we can analyze the quantum heat distribution within an exactly dynamical framework beyond the traditional paradigm of Born-Markovian and weak-coupling approximations. It is revealed that the exchange fluctuation theorem for quantum heat generally breaks down in the strongly non-Markovian regime. Our results may improve the understanding about the nonequilibrium thermodynamics of open quantum systems when the usual Markovian treatment is no longer appropriate.
Collapse
Affiliation(s)
- Ze-Zhou Zhang
- Key Laboratory of Quantum Theory and Applications of Ministry of Education, Lanzhou University, Lanzhou 730000, China
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
| | - Qing-Shou Tan
- Key Laboratory of Hunan Province on Information Photonics and Freespace Optical Communication, College of Physics and Electronics, Hunan Institute of Science and Technology, Yueyang 414000, China
| | - Wei Wu
- Key Laboratory of Quantum Theory and Applications of Ministry of Education, Lanzhou University, Lanzhou 730000, China
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
| |
Collapse
|
6
|
Ptaszyński K, Esposito M. Ensemble dependence of information-theoretic contributions to the entropy production. Phys Rev E 2023; 107:L052102. [PMID: 37329035 DOI: 10.1103/physreve.107.l052102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Accepted: 05/07/2023] [Indexed: 06/18/2023]
Abstract
The entropy production of an open system coupled to a reservoir initialized in a canonical state can be expressed as a sum of two microscopic information-theoretic contributions: the system-bath mutual information and the relative entropy measuring the displacement of the environment from equilibrium. We investigate whether this result can be generalized to situations where the reservoir is initialized in a microcanonical or in a certain pure state (e.g., an eigenstate of a nonintegrable system), such that the reduced dynamics and thermodynamics of the system are the same as for the thermal bath. We show that while in such a case the entropy production can still be expressed as a sum of the mutual information between the system and the bath and a properly redefined displacement term, the relative weight of those contributions depends on the initial state of the reservoir. In other words, different statistical ensembles for the environment predicting the same reduced dynamics for the system give rise to the same total entropy production but to different information-theoretic contributions to the entropy production.
Collapse
Affiliation(s)
- Krzysztof Ptaszyński
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
- Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| |
Collapse
|
7
|
Kaneyasu M, Hasegawa Y. Quantum Otto cycle under strong coupling. Phys Rev E 2023; 107:044127. [PMID: 37198760 DOI: 10.1103/physreve.107.044127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Accepted: 04/03/2023] [Indexed: 05/19/2023]
Abstract
Quantum heat engines are often discussed under the weak-coupling assumption that the interaction between the system and the reservoirs is negligible. Although this setup is easier to analyze, this assumption cannot be justified on the quantum scale. In this study, a quantum Otto cycle model that can be generally applied without the weak-coupling assumption is proposed. We replace the thermalization process in the weak-coupling model with a process comprising thermalization and decoupling. The efficiency of the proposed model is analytically calculated and indicates that, when the contribution of the interaction terms is neglected in the weak-interaction limit, it reduces to that of the earlier model. The sufficient condition for the efficiency of the proposed model not to surpass that of the weak-coupling model is that the decoupling processes of our model have a positive cost. Moreover, the relation between the interaction strength and the efficiency of the proposed model is numerically examined by using a simple two-level system. Furthermore, we show that our model's efficiency can surpass that of the weak-coupling model under particular cases. From analyzing the majorization relation, we also find a design method of the optimal interaction Hamiltonians, which are expected to provide the maximum efficiency of the proposed model. Under these interaction Hamiltonians, the numerical experiment shows that the proposed model achieves higher efficiency than that of its weak-coupling counterpart.
Collapse
Affiliation(s)
- Mao Kaneyasu
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| |
Collapse
|
8
|
Chen J, Wang Y, Chen J, Su S. Optimal figure of merit of low-dissipation quantum refrigerators. Phys Rev E 2023; 107:044118. [PMID: 37198854 DOI: 10.1103/physreve.107.044118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2022] [Accepted: 03/21/2023] [Indexed: 05/19/2023]
Abstract
The Drazin inverse of the Liouvillian superoperator provides a solution to determine the dynamics of a time-dependent system governed by the Markovian master equation. Under the condition of slow driving, the perturbation expansion of the density operator of the system in powers of time can be derived. As an application, a finite-time cycle model of the quantum refrigerator driven by a time-dependent external field is established. The method of the Lagrange multiplier is adopted as a strategy to find the optimal cooling performance. The figure of merit given by the product of the coefficient of performance and the cooling rate is taken as a new objective function, and, consequently, the optimally operating state of the refrigerator is revealed. The effects of the frequency exponent determining dissipation characteristics on the optimal performance of the refrigerator are discussed systemically. The results obtained show that the adjacent areas of the state of the maximum figure of merit are the best operation region of low-dissipative quantum refrigerators.
Collapse
Affiliation(s)
- Jingyi Chen
- Department of Physics, Xiamen University, Xiamen 361005, People's Republic of China
| | - Youlin Wang
- Department of Physics, Xiamen University, Xiamen 361005, People's Republic of China
| | - Jincan Chen
- Department of Physics, Xiamen University, Xiamen 361005, People's Republic of China
| | - Shanhe Su
- Department of Physics, Xiamen University, Xiamen 361005, People's Republic of China
| |
Collapse
|
9
|
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.
Collapse
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
| |
Collapse
|
10
|
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.
Collapse
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
| |
Collapse
|
11
|
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] [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.
Collapse
|
12
|
Teretenkov AE. Effective Gibbs State for Averaged Observables. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1144. [PMID: 36010808 PMCID: PMC9407324 DOI: 10.3390/e24081144] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Revised: 08/10/2022] [Accepted: 08/15/2022] [Indexed: 06/15/2023]
Abstract
We introduce the effective Gibbs state for the observables averaged with respect to fast free dynamics. We prove that the information loss due to the restriction of our measurement capabilities to such averaged observables is non-negative and discuss a thermodynamic role of it. We show that there are a lot of similarities between this effective Hamiltonian and the mean force Hamiltonian, which suggests a generalization of quantum thermodynamics including both cases. We also perturbatively calculate the effective Hamiltonian and correspondent corrections to the thermodynamic quantities and illustrate it with several examples.
Collapse
Affiliation(s)
- Alexander Evgen'evich Teretenkov
- Department of Mathematical Methods for Quantum Technologies, Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow 119991, Russia
| |
Collapse
|
13
|
Liu J, Jung KA. Optimal linear cyclic quantum heat engines cannot benefit from strong coupling. Phys Rev E 2022; 106:L022105. [PMID: 36109930 DOI: 10.1103/physreve.106.l022105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 08/15/2022] [Indexed: 06/15/2023]
Abstract
Uncovering whether strong system-bath coupling can be an advantageous operation resource for energy conversion can facilitate the development of efficient quantum heat engines (QHEs). Yet, a consensus on this ongoing debate is still lacking owing to challenges arising from treating strong couplings. Here, we conclude the debate for optimal linear cyclic QHEs operated under a small temperature difference by revealing the detrimental role of strong system-bath coupling in their optimal operations. We analytically demonstrate that both the efficiency at maximum power and maximum efficiency of strong-coupling linear cyclic QHEs are upper bounded by their weak-coupling counterparts with the same degree of time-reversal symmetry breaking. Under strong time-reversal symmetry breaking, we further reveal a quadratic suppression of the optimal efficiencies relative to the Carnot limit when away from the weak-coupling regime, along with a quadratic enhancement of the mean entropy production rate.
Collapse
Affiliation(s)
- Junjie Liu
- Department of Physics, International Center of Quantum and Molecular Structures, Shanghai University, Shanghai 200444, China
| | - Kenneth A Jung
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| |
Collapse
|
14
|
Koyanagi S, Tanimura Y. Numerically "exact" simulations of a quantum Carnot cycle: Analysis using thermodynamic work diagrams. J Chem Phys 2022; 157:084110. [DOI: 10.1063/5.0107305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the efficiency of a quantum Carnot engine based on open quantum dynamics theory. The model includes time-dependent external fields for the subsystems controlling the isothermal and isentropic processes and for the system--bath (SB) interactions controlling the transition between these processes. Numerical simulations are conducted in a nonperturbative and non-Markovian SB coupling regime using the hierarchical equations of motion under these fields at different cycle frequencies. The work applied to the total system and the heat exchanged with the baths are rigorously evaluated. In addition, by regarding quasi-static work as free energy, we compute the quantum thermodynamic variables and analyze the simulation results using thermodynamic work diagrams for the first time. Analysis of these diagrams indicates that, in the strong SB coupling region, the fields for the SB interactions are major sources of work, while in other regions, the field for the subsystem is a source of work. We find that the maximum efficiency is achieved in the quasi-static case and is determined solely by the bath temperatures, regardless of the SB coupling strength, which is a numerical manifestation of Carnot's theorem.
Collapse
|
15
|
Entropy Production in Non-Markovian Collision Models: Information Backflow vs. System-Environment Correlations. ENTROPY 2022; 24:e24060824. [PMID: 35741544 PMCID: PMC9222943 DOI: 10.3390/e24060824] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Revised: 06/10/2022] [Accepted: 06/12/2022] [Indexed: 12/04/2022]
Abstract
We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model in both Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the relationship between non-Markovian dynamics and negative entropy production rates. We employ two different types of collision models that do or do not keep the correlations established between the system and the incoming environmental particle, while both of them pertain to their non-Markovian nature through information backflow from the environment to the system. We observe that as the former model, where the correlations between the system and environment are preserved, gives rise to negative entropy production rates in the transient dynamics, the latter one always maintains positive rates, even though the convergence to the steady-state value is slower as compared to the corresponding Markovian dynamics. Our results suggest that the mechanism underpinning the negative entropy production rates is not solely non-Markovianity through information backflow, but rather the contribution to it through established system-environment correlations.
Collapse
|
16
|
Mitchison MT, Rivas Á, Martin-Delgado MA. Robust Nonequilibrium Edge Currents with and without Band Topology. PHYSICAL REVIEW LETTERS 2022; 128:120403. [PMID: 35394306 DOI: 10.1103/physrevlett.128.120403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2021] [Accepted: 03/03/2022] [Indexed: 06/14/2023]
Abstract
We study two-dimensional bosonic and fermionic lattice systems under nonequilibrium conditions corresponding to a sharp gradient of temperature imposed by two thermal baths. In particular, we consider a lattice model with broken time-reversal symmetry that exhibits both topologically trivial and nontrivial phases. Using a nonperturbative Green function approach, we characterize the nonequilibrium current distribution in different parameter regimes. For both bosonic and fermionic systems, we find chiral edge currents that are robust against coupling to reservoirs and to the presence of defects on the boundary or in the bulk. This robustness not only originates from topological effects at zero temperature but, remarkably, also persists as a result of dissipative symmetries in regimes where band topology plays no role. Chirality of the edge currents implies that energy locally flows against the temperature gradient without any external work input. In the fermionic case, there is also a regime with topologically protected boundary currents, which nonetheless do not circulate around all system edges.
Collapse
Affiliation(s)
- Mark T Mitchison
- School of Physics, Trinity College Dublin, College Green, Dublin 2, D02 K8N4, Ireland
| | - Ángel Rivas
- Departamento de Física Teórica, Facultad de Ciencias Físicas, Universidad Complutense, 28040 Madrid, Spain
- CCS-Center for Computational Simulation, Campus de Montegancedo UPM, 28660 Boadilla del Monte, Madrid, Spain
| | - Miguel A Martin-Delgado
- Departamento de Física Teórica, Facultad de Ciencias Físicas, Universidad Complutense, 28040 Madrid, Spain
- CCS-Center for Computational Simulation, Campus de Montegancedo UPM, 28660 Boadilla del Monte, Madrid, Spain
| |
Collapse
|
17
|
Van Vu T, Saito K. Finite-Time Quantum Landauer Principle and Quantum Coherence. PHYSICAL REVIEW LETTERS 2022; 128:010602. [PMID: 35061471 DOI: 10.1103/physrevlett.128.010602] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 11/29/2021] [Indexed: 06/14/2023]
Abstract
The Landauer principle states that any logically irreversible information processing must be accompanied by dissipation into the environment. In this Letter, we investigate the heat dissipation associated with finite-time information erasure and the effect of quantum coherence in such processes. By considering a scenario wherein information is encoded in an open quantum system whose dynamics are described by the Markovian Lindblad equation, we show that the dissipated heat is lower bounded by the conventional Landauer cost, as well as a correction term inversely proportional to the operational time. To clarify the relation between quantum coherence and dissipation, we derive a lower bound for heat dissipation in terms of quantum coherence. This bound quantitatively implies that the creation of quantum coherence in the energy eigenbasis during the erasure process inevitably leads to additional heat costs. The obtained bounds hold for arbitrary operational time and control protocol. By following an optimal control theory, we numerically present an optimal protocol and illustrate our findings by using a single-qubit system.
Collapse
Affiliation(s)
- Tan Van Vu
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
| | - Keiji Saito
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
| |
Collapse
|
18
|
Zakavati S, Tabesh FT, Salimi S. Bounds on charging power of open quantum batteries. Phys Rev E 2021; 104:054117. [PMID: 34942849 DOI: 10.1103/physreve.104.054117] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2020] [Accepted: 10/19/2021] [Indexed: 11/07/2022]
Abstract
In general, quantum systems most likely undergo open-system dynamics due to their smallness and sensitivity. Energy storage devices, so-called quantum batteries, are not excluded from this phenomenon. Here, we study fundamental bounds on the power of open quantum batteries from the geometric point of view. By defining an activity operator, a tight upper bound on the charging power is derived for the open quantum batteries in terms of the fluctuations of the activity operator and the quantum Fisher information. The variance of the activity operator may be interpreted as a generalized thermodynamic force, while the quantum Fisher information describes the speed of evolution in the state space of the battery. The thermodynamic interpretation of the upper bound is discussed in detail. As an example, a model for the battery, taking into account the environmental effects, is proposed, and the effect of dissipation and decoherence during the charging process on both the stored work and the charging power is investigated. Our results show that the upper bound is saturated in some time intervals. Also, the maximum value of both the stored work and the corresponding power is achieved in the non-Markovian underdamped regime.
Collapse
Affiliation(s)
- Shadab Zakavati
- Department of Physics, University of Kurdistan, P.O. Box 66177-15175, Sanandaj, Iran
| | - Fatemeh T Tabesh
- Department of Physics, University of Kurdistan, P.O. Box 66177-15175, Sanandaj, Iran
| | - Shahriar Salimi
- Department of Physics, University of Kurdistan, P.O. Box 66177-15175, Sanandaj, Iran
| |
Collapse
|
19
|
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.
Collapse
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
| |
Collapse
|
20
|
Bernardo BDL. Relating heat and entanglement in strong-coupling thermodynamics. Phys Rev E 2021; 104:044111. [PMID: 34781427 DOI: 10.1103/physreve.104.044111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2021] [Accepted: 09/27/2021] [Indexed: 11/07/2022]
Abstract
Explaining the influence of strong coupling in the dynamics of open quantum systems is one of the most challenging issues in the rapidly growing field of quantum thermodynamics. By using a particular definition of heat, we develop an approach to study the thermodynamics in the strong-coupling regime, which takes into account quantum resources such as coherence and entanglement. We apply the method to calculate the time-dependent thermodynamic properties of a system and an environment interacting via the generalized amplitude-damping channel. The results indicate that the transient imbalance between heat dissipated and heat absorbed that occurs in the process is responsible for the generation of system-environment entanglement.
Collapse
Affiliation(s)
- Bertúlio de Lima Bernardo
- Departamento de Física, Universidade Federal da Paraíba, 58051-900 João Pessoa, PB, Brazil and Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, 58109-970 Campina Grande, PB, Brazil
| |
Collapse
|
21
|
Johal RS, Mehta V. Quantum Heat Engines with Complex Working Media, Complete Otto Cycles and Heuristics. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1149. [PMID: 34573774 PMCID: PMC8468726 DOI: 10.3390/e23091149] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/20/2021] [Revised: 08/26/2021] [Accepted: 08/29/2021] [Indexed: 11/17/2022]
Abstract
Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.
Collapse
Affiliation(s)
- Ramandeep S. Johal
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, S.A.S. Nagar, Manauli PO 140306, Punjab, India;
| | | |
Collapse
|
22
|
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.
Collapse
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
| |
Collapse
|