1
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Das A, Mahunta S, Agarwalla BK, Mukherjee V. Precision bound and optimal control in periodically modulated continuous quantum thermal machines. Phys Rev E 2023; 108:014137. [PMID: 37583225 DOI: 10.1103/physreve.108.014137] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 07/07/2023] [Indexed: 08/17/2023]
Abstract
We use Floquet formalism to study fluctuations in periodically modulated continuous quantum thermal machines. We present a generic theory for such machines, followed by specific examples of sinusoidal, optimal, and circular modulations, respectively. The thermodynamic uncertainty relations (TUR) hold for all modulations considered. Interestingly, in the case of sinusoidal modulation, the TUR ratio assumes a minimum at the heat engine to refrigerator transition point, while the chopped random basis optimization protocol allows us to keep the ratio small for a wide range of modulation frequencies. Furthermore, our numerical analysis suggests that TUR can show signatures of heat engine to refrigerator transition, for more generic modulation schemes. We also study bounds in fluctuations in the efficiencies of such machines; our results indicate that fluctuations in efficiencies are bounded from above for a refrigerator and from below for an engine. Overall, this study emphasizes the crucial role played by different modulation schemes in designing practical quantum thermal machines.
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Affiliation(s)
- Arpan Das
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziądzka 5/7, 87-100 Toruń, Poland
| | - Shishira Mahunta
- Department of Physical Sciences, Indian Institute of Science Education and Research Berhampur, Berhampur 760010, India
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research Pune, Pune 411008, India
| | - Victor Mukherjee
- Department of Physical Sciences, Indian Institute of Science Education and Research Berhampur, Berhampur 760010, India
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2
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Wang SY, Yang Q, Zhang FL. Thermodynamically consistent master equation based on subsystem eigenstates. Phys Rev E 2023; 107:014108. [PMID: 36797865 DOI: 10.1103/physreve.107.014108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2022] [Accepted: 12/20/2022] [Indexed: 06/18/2023]
Abstract
Master equations under appropriate assumptions are efficient tools for the study of open quantum systems. For many-body systems, subsystems of which locally couple to thermal baths and weakly interact with each other, the local approach provides a more convenient description than the global approach. However, these local master equations are believed to generate inconsistencies with the laws of thermodynamics when intersubsystem interactions exist. Here we develop an alternative local master equation by virtue of similar approximations used in deriving the traditional Gorini-Kossakowski-Lindblad-Sudarshan master equation. In particular, we stick to using eigenstates of each subsystem to construct quantum jump operators, and the secular approximation is also employed to modify the intersubsystem interactions. Our results show that violations of thermodynamic laws will be avoided after correcting intersubsystem interactions. Finally, we study a two-qubit heat transfer model and this further shows the validity of our modified master equation.
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Affiliation(s)
- Si-Ying Wang
- Department of Physics, School of Science, Tianjin University, Tianjin 300072, China
| | - Qinghong Yang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Fu-Lin Zhang
- Department of Physics, School of Science, Tianjin University, Tianjin 300072, China
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3
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Liu F. Semi-Markov processes in open quantum systems: Connections and applications in counting statistics. Phys Rev E 2022; 106:054152. [PMID: 36559413 DOI: 10.1103/physreve.106.054152] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2022] [Accepted: 11/02/2022] [Indexed: 06/17/2023]
Abstract
Using the age-structure formalism, we definitely establish connections between semi-Markov processes and the dynamics of open quantum systems that satisfy the Markov quantum master equations. A generalized Feynman-Kac formula of the semi-Markov processes is also proposed. In addition to inheriting all statistical properties possessed by the piecewise deterministic processes of wave functions, the semi-Markov processes show their unique advantages in quantum counting statistics. Compared with the conventional method of the tilted quantum master equation, they can be applied to more general counting quantities. In particular, the terms involved in the method have precise probability meanings. We use a driven two-level quantum system to exemplify these results.
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Affiliation(s)
- Fei Liu
- School of Physics, Beihang University, Beijing 100191, China
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4
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Gupt N, Bhattacharyya S, Das B, Datta S, Mukherjee V, Ghosh A. Floquet quantum thermal transistor. Phys Rev E 2022; 106:024110. [PMID: 36109934 DOI: 10.1103/physreve.106.024110] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2022] [Accepted: 06/28/2022] [Indexed: 06/15/2023]
Abstract
We apply periodic control to realize a quantum thermal transistor, which we term as the Floquet quantum thermal transistor. Periodic modulation allows us to control the heat flows and achieve large amplification factors even for fixed bath temperatures. Importantly, this transistor effect persists in the cutoff region, where traditional quantum thermal transistors operating in the absence of periodic modulation, fail to act as viable heat modulation devices.
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Affiliation(s)
- Nikhil Gupt
- Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
| | - Srijan Bhattacharyya
- Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
- Department of Chemistry, University of Colorado, Boulder, Colorado 80309, USA
| | - Bikash Das
- School of Physical Sciences, Indian Association for the Cultivation of Science, 2A and B Raja S. C. Mullick Road, Jadavpur, Kolkata 700032, India
| | - Subhadeep Datta
- School of Physical Sciences, Indian Association for the Cultivation of Science, 2A and B Raja S. C. Mullick Road, Jadavpur, Kolkata 700032, India
| | - Victor Mukherjee
- Department of Physical Sciences, IISER Berhampur, Berhampur 760010, India
| | - Arnab Ghosh
- Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
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5
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Yada T, Yoshioka N, Sagawa T. Quantum Fluctuation Theorem under Quantum Jumps with Continuous Measurement and Feedback. PHYSICAL REVIEW LETTERS 2022; 128:170601. [PMID: 35570443 DOI: 10.1103/physrevlett.128.170601] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Revised: 03/17/2022] [Accepted: 03/23/2022] [Indexed: 06/15/2023]
Abstract
While the fluctuation theorem in classical systems has been thoroughly generalized under various feedback control setups, an intriguing situation in quantum systems, namely under continuous feedback, remains to be investigated. In this work, we derive the generalized fluctuation theorem under quantum jumps with continuous measurement and feedback. The essence for the derivation is to newly introduce the operationally meaningful information, which we call quantum-classical-transfer (QC-transfer) entropy. QC-transfer entropy can be naturally interpreted as the quantum counterpart of transfer entropy that is commonly used in classical time series analysis. We also verify our theoretical results by numerical simulation and propose an experiment-numerics hybrid verification method. Our work reveals a fundamental connection between quantum thermodynamics and quantum information, which can be experimentally tested with artificial quantum systems such as circuit quantum electrodynamics.
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Affiliation(s)
- Toshihiro Yada
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Nobuyuki Yoshioka
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Takahiro Sagawa
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Quantum-Phase Electronics Center (QPEC), The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
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6
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Liu F. Auxiliary open quantum system for the Floquet quantum master equation. Phys Rev E 2021; 103:022116. [PMID: 33736066 DOI: 10.1103/physreve.103.022116] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Accepted: 01/25/2021] [Indexed: 11/07/2022]
Abstract
By directly using the probability formulas of quantum trajectories, we construct an auxiliary open quantum system for a periodically driven open quantum system whose dynamics is governed by the Floquet quantum master equation. This auxiliary system can generate a quantum trajectory ensemble that is consistent with the canonical quantum trajectory ensemble. We find that, at a long time limit, though the Lindblad operators are modified, the coherent dynamics of the auxiliary system is the same as that of the original system. A periodically driven two-level quantum system is used to illustrate this construction.
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Affiliation(s)
- Fei Liu
- School of Physics, Beihang University, Beijing 100191, China
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7
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Mondal S, Bhattacharjee S, Dutta A. Exploring the role of asymmetric-pulse modulation in quantum thermal machines and quantum thermometry. Phys Rev E 2020; 102:022140. [PMID: 32942435 DOI: 10.1103/physreve.102.022140] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2020] [Accepted: 08/13/2020] [Indexed: 11/07/2022]
Abstract
We explore the consequences of periodically modulating a quantum two-level system (TLS) with an asymmetric pulse when the system is in contact with thermal baths. By adopting the Floquet-Lindblad formalism for our analysis, we find that the unequal "up" and "down" time duration of the pulse has two main ramifications. First, the energy gap of the multiple sidebands or photon sectors created as a result of the periodic modulation are renormalized by a term which is dependent on both the modulation strength as well as the fraction of up (or down) time duration. Second, the weights of the different sidebands are no longer symmetrically distributed about the central band or zero photon sector. We illustrate the advantages of these findings in the context of applications in quantum thermal machines and thermometry. For a thermal machine constructed by coupling the TLS to two thermal baths, we demonstrate that the asymmetric pulse provides an extra degree of control over the mode of operation of the thermal machine. Further, by appropriately tuning the weight of the subbands, we also show that an asymmetric pulse may provide superior optimality in a recently proposed protocol for quantum thermometry, where dynamical control has been shown to enhance the precision of measurement.
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Affiliation(s)
- Saikat Mondal
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Sourav Bhattacharjee
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Amit Dutta
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India
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8
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Liu F, Su S. Stochastic Floquet quantum heat engines and stochastic efficiencies. Phys Rev E 2020; 101:062144. [PMID: 32688492 DOI: 10.1103/physreve.101.062144] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Accepted: 06/12/2020] [Indexed: 06/11/2023]
Abstract
Based on the notion of quantum trajectory, we present a stochastic theoretical framework for Floquet quantum heat engines. As an application, the large deviation functions of two types of stochastic efficiencies for a two-level Floquet quantum heat engine are investigated. We find that the statistics of one efficiency agree well with the predictions of the universal theory of efficiency fluctuations developed by Verley et al. [Phys. Rev. E 90, 052145 (2014)10.1103/PhysRevE.90.052145], whereas the statistics of the other efficiency do not. The reason for this discrepancy is attributed to the lack of fluctuation theorems for the latter type of efficiency.
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Affiliation(s)
- Fei Liu
- School of Physics, Beihang University, Beijing 100191, China
| | - Shanhe Su
- Department of Physics, Xiamen University, Xiamen 361005, China
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9
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Seah S, Nimmrichter S, Scarani V. Maxwell's Lesser Demon: A Quantum Engine Driven by Pointer Measurements. PHYSICAL REVIEW LETTERS 2020; 124:100603. [PMID: 32216402 DOI: 10.1103/physrevlett.124.100603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Accepted: 02/21/2020] [Indexed: 06/10/2023]
Abstract
We discuss a self-contained spin-boson model for a measurement-driven engine, in which a demon generates work from thermal excitations of a quantum spin via measurement and feedback control. Instead of granting it full direct access to the spin state and to Landauer's erasure strokes for optimal performance, we restrict this demon's action to pointer measurements, i.e., random or continuous interrogations of a damped mechanical oscillator that assumes macroscopically distinct positions depending on the spin state. The engine can reach simultaneously the power and efficiency benchmarks and operate in temperature regimes where quantum Otto engines would fail.
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Affiliation(s)
- Stella Seah
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore
| | - Stefan Nimmrichter
- Max Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany
| | - Valerio Scarani
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
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10
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Engelhardt G, Platero G, Cao J. Discontinuities in Driven Spin-Boson Systems due to Coherent Destruction of Tunneling: Breakdown of the Floquet-Gibbs Distribution. PHYSICAL REVIEW LETTERS 2019; 123:120602. [PMID: 31633942 DOI: 10.1103/physrevlett.123.120602] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2019] [Indexed: 06/10/2023]
Abstract
If an open quantum system is periodically driven with high frequency and the driving commutes with the system-bath coupling operator, it is known that the system approaches a Floquet-Gibbs state, a generalization of Gibbs states to periodically driven systems. Here, we investigate the stationary state of an ac-driven system when the driving and dissipation are noncommutative. Then, the resulting stationary state does not obey the Floquet-Gibbs distribution, and the system dynamics is determined by inelastic scattering processes of the driving field. Based on the Floquet-Redfield formalism, we show that the probability distribution can exhibit population inversion and discontinuities, i.e., jumps, for parameters at which coherent destruction of tunneling takes place. These discontinuities can be observed as intensity jumps in the emission into the bath.
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Affiliation(s)
- Georg Engelhardt
- Beijing Computational Science Research Center, Beijing 100193, People's Republic of China
| | - Gloria Platero
- Instituto de Ciencia de Materiales de Madrid, CSIC, 28049 Madrid, Spain
| | - Jianshu Cao
- Beijing Computational Science Research Center, Beijing 100193, People's Republic of China
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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11
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Abstract
A comprehensive approach to modeling open quantum systems consistent with thermodynamics is presented. The theory of open quantum systems is employed to define system bath partitions. The Markovian master equation defines an isothermal partition between the system and bath. Two methods to derive the quantum master equation are described: the weak coupling limit and the repeated collision model. The role of the eigenoperators of the free system dynamics is highlighted, in particular, for driven systems. The thermodynamical relations are pointed out. Models that lead to loss of coherence, i.e., dephasing are described. The implication of the laws of thermodynamics to simulating transport and spectroscopy is described. The indications for self-averaging in large quantum systems and thus its importance in modeling are described. Basic modeling by the surrogate Hamiltonian is described, as well as thermal boundary conditions using the repeated collision model and their use in the stochastic surrogate Hamiltonian. The problem of modeling with explicitly time dependent driving is analyzed. Finally, the use of the stochastic surrogate Hamiltonian for modeling ultrafast spectroscopy and quantum control is reviewed.
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Affiliation(s)
- Ronnie Kosloff
- The Institute of Chemistry and The Fritz Haber Centre for Theoretical Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
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12
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Guo BQ, Liu T, Yu CS. Multifunctional quantum thermal device utilizing three qubits. Phys Rev E 2019; 99:032112. [PMID: 30999448 DOI: 10.1103/physreve.99.032112] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2018] [Indexed: 06/09/2023]
Abstract
Quantum thermal devices which can manage heat as their electronic analogs for the electronic currents have attracted increasing attention. Here a three-terminal quantum thermal device is designed by three coupling qubits interacting with three heat baths with different temperatures. Based on the steady-state behavior solved from the dynamics of this system, it is demonstrated that such a device integrates multiple interesting thermodynamic functions. It can serve as a heat current transistor to use the weak heat current at one terminal to effectively amplify the currents through the other two terminals, to continuously modulate them ranging in a large amplitude, and even to switch on or off the heat currents. It is also found that the three currents are not sensitive to the fluctuation of the temperature at the low-temperature terminal, so it can behave as a thermal stabilizer. In addition, we can utilize one terminal temperature to ideally turn off the heat current at any one terminal and to allow the heat currents through the other two terminals, so it can be used as a thermal valve. Finally, we illustrate that this thermal device can control the heat currents to flow unidirectionally, so it has the function of a thermal rectifier.
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Affiliation(s)
- Bao-Qing Guo
- School of Physics, Dalian University of Technology, Dalian 116024, China
| | - Tong Liu
- School of Physics, Dalian University of Technology, Dalian 116024, China
| | - Chang-Shui Yu
- School of Physics, Dalian University of Technology, Dalian 116024, China
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13
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Elouard C, Besga B, Auffèves A. Probing the State of a Mechanical Oscillator with an Ultrastrongly Coupled Quantum Emitter. PHYSICAL REVIEW LETTERS 2019; 122:013602. [PMID: 31012721 DOI: 10.1103/physrevlett.122.013602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2018] [Indexed: 06/09/2023]
Abstract
Performing accurate position measurements of a mechanical resonator by coupling it to some optically driven quantum emitter is an important challenge for quantum sensing and metrology. We fully characterize the quantum noise associated with this measurement process, by deriving master equations for the coupled emitter and the resonator valid in the ultrastrong coupling regime. At short timescales, we show that this noise sets a fundamental limit to the readout sensitivity and that the standard quantum limit can be recovered for realistic experimental conditions. At long timescales, the scattering of the mechanical quadratures leads to the decoupling of the emitter from the driving light, switching off the noise source. This method can be used to describe the interaction of any quantum system strongly coupled to a finite size reservoir.
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Affiliation(s)
- Cyril Elouard
- Department of Physics and Astronomy and Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
| | - Benjamin Besga
- Université de Lyon, CNRS, Laboratoire de Physique de l'École Normale Supérieure, UMR5672, 46 Allée d'Italie, 69364 Lyon, France
| | - Alexia Auffèves
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
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14
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Guo BQ, Liu T, Yu CS. Quantum thermal transistor based on qubit-qutrit coupling. Phys Rev E 2018; 98:022118. [PMID: 30253594 DOI: 10.1103/physreve.98.022118] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2018] [Indexed: 11/07/2022]
Abstract
A quantum thermal transistor is designed by the strong coupling between one qubit and one qutrit which are in contact with three heat baths with different temperatures. The thermal behavior is analyzed based on the master equation by both the numerical and the approximately analytic methods. It is shown that the thermal transistor, as a three-terminal device, allows a weak modulation heat current (at the modulation terminal) to switch on and off and effectively modulate the heat current between the other two terminals. In particular, the weak modulation heat current can induce the strong heat current between the other two terminals with the multiple-region amplification of heat current. Furthermore, the heat currents are quite robust to the temperature (current) fluctuation at the lower-temperature terminal within a certain range of temperature, and so it can behave as a heat current stabilizer.
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Affiliation(s)
- Bao-Qing Guo
- School of Physics, Dalian University of Technology, Dalian 116024, China
| | - Tong Liu
- School of Physics, Dalian University of Technology, Dalian 116024, China
| | - Chang-Shui Yu
- School of Physics, Dalian University of Technology, Dalian 116024, China
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15
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Introduction to Quantum Thermodynamics: History and Prospects. FUNDAMENTAL THEORIES OF PHYSICS 2018. [DOI: 10.1007/978-3-319-99046-0_1] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
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16
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Hofer PP, Brask JB, Perarnau-Llobet M, Brunner N. Quantum Thermal Machine as a Thermometer. PHYSICAL REVIEW LETTERS 2017; 119:090603. [PMID: 28949576 DOI: 10.1103/physrevlett.119.090603] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2017] [Indexed: 06/07/2023]
Abstract
We propose the use of a quantum thermal machine for low-temperature thermometry. A hot thermal reservoir coupled to the machine allows for simultaneously cooling the sample while determining its temperature without knowing the model-dependent coupling constants. In its most simple form, the proposed scheme works for all thermal machines that perform at Otto efficiency and can reach Carnot efficiency. We consider a circuit QED implementation that allows for precise thermometry down to ∼15 mK with realistic parameters. Based on the quantum Fisher information, this is close to the optimal achievable performance. This implementation demonstrates that our proposal is particularly promising in systems where thermalization between different components of an experimental setup cannot be guaranteed.
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Affiliation(s)
- Patrick P Hofer
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | - Jonatan Bohr Brask
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | - Martí Perarnau-Llobet
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - Nicolas Brunner
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
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17
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Cavina V, Mari A, Giovannetti V. Slow Dynamics and Thermodynamics of Open Quantum Systems. PHYSICAL REVIEW LETTERS 2017; 119:050601. [PMID: 28949759 DOI: 10.1103/physrevlett.119.050601] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2017] [Indexed: 06/07/2023]
Abstract
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We apply this technique to the analysis of finite-time isothermal processes in which, differently from quasistatic transformations, the state of the system is not able to continuously relax to the equilibrium ensemble. Our approach allows one to formally evaluate perturbations up to arbitrary order to the work and heat exchange associated with an arbitrary process. Within first order in the perturbation expansion, we identify a general formula for the efficiency at maximum power of a finite-time Carnot engine. We also clarify under which assumptions and in which limit one can recover previous phenomenological results as, for example, the Curzon-Ahlborn efficiency.
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Affiliation(s)
- Vasco Cavina
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Andrea Mari
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Vittorio Giovannetti
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
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18
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Liu F, Xi J. Characteristic functions based on a quantum jump trajectory. Phys Rev E 2017; 94:062133. [PMID: 28085337 DOI: 10.1103/physreve.94.062133] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2016] [Indexed: 11/07/2022]
Abstract
Characteristic functions (CFs) provide a very efficient method for evaluating the probability density functions of stochastic thermodynamic quantities and investigating their statistical features in quantum master equations (QMEs). A conventional procedure for obtaining these functions is to resort to a first-principles approach; namely, the evolution equations of the CFs of the combined system and its environment are obtained and then projected into the degrees of freedom of the system. However, the QMEs can be unraveled by a quantum jump trajectory. Thermodynamic quantities such as the heat, work, and entropy production can be well defined along a trajectory. Hence, on the basis of the notion of a trajectory, can we straightforwardly derive these CFs, e.g., their evolution equations? This is essential to establish the self-contained stochastic thermodynamics of a QME. In this paper, we show that it is indeed plausible and also simple. Particularly, these equations are fully consistent with those obtained by the first-principles method. Our results have practical significance; they indicate that the quantum fluctuation relations could be verified by more realistic photocounting experiments.
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Affiliation(s)
- Fei Liu
- School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
| | - Jingyi Xi
- Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, China
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19
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Restrepo S, Cerrillo J, Bastidas VM, Angelakis DG, Brandes T. Driven Open Quantum Systems and Floquet Stroboscopic Dynamics. PHYSICAL REVIEW LETTERS 2016; 117:250401. [PMID: 28036226 DOI: 10.1103/physrevlett.117.250401] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2016] [Indexed: 06/06/2023]
Abstract
We provide an analytic solution to the problem of system-bath dynamics under the effect of high-frequency driving that has applications in a large class of settings, such as driven-dissipative many-body systems. Our method relies on discrete symmetries of the system-bath Hamiltonian and provides the time evolution operator of the full system, including bath degrees of freedom, without weak-coupling or Markovian assumptions. An interpretation of the solution in terms of the stroboscopic evolution of a family of observables under the influence of an effective static Hamiltonian is proposed, which constitutes a flexible simulation procedure of nontrivial Hamiltonians. We instantiate the result with the study of the spin-boson model with time-dependent tunneling amplitude. We analyze the class of Hamiltonians that may be stroboscopically accessed for this example and illustrate the dynamics of system and bath degrees of freedom.
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Affiliation(s)
- S Restrepo
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - J Cerrillo
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - V M Bastidas
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - D G Angelakis
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
- School of Electrical and Computer Engineering, Technical University of Crete, Chania, Crete 73100, Greece
| | - T Brandes
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
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20
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Brandner K, Seifert U. Periodic thermodynamics of open quantum systems. Phys Rev E 2016; 93:062134. [PMID: 27415235 DOI: 10.1103/physreve.93.062134] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2016] [Indexed: 06/06/2023]
Abstract
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.
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Affiliation(s)
- Kay Brandner
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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Unified Quantum Model of Work Generation in Thermoelectric Generators, Solar and Fuel Cells. ENTROPY 2016. [DOI: 10.3390/e18060210] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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22
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Performance of Continuous Quantum Thermal Devices Indirectly Connected to Environments. ENTROPY 2016. [DOI: 10.3390/e18050166] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Chapman A, Miyake A. How an autonomous quantum Maxwell demon can harness correlated information. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062125. [PMID: 26764650 DOI: 10.1103/physreve.92.062125] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2015] [Indexed: 06/05/2023]
Abstract
We study an autonomous quantum system which exhibits refrigeration under an information-work trade-off like a Maxwell demon. The system becomes correlated as a single "demon" qubit interacts sequentially with memory qubits while in contact with two heat reservoirs of different temperatures. Using strong subadditivity of the von Neumann entropy, we derive a global Clausius inequality to show thermodynamic advantages from access to correlated information. It is demonstrated, in a matrix product density operator formalism, that our demon can simultaneously realize refrigeration against a thermal gradient and erasure of information from its memory, which is impossible without correlations. The phenomenon can be even enhanced by the presence of quantum coherence.
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Affiliation(s)
- Adrian Chapman
- Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Akimasa Miyake
- Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
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Abstract
Energy conversion of heat into work at the quantum level is modeled by quantum heat machines (QHMs) generally assumed to operate at weak coupling to the baths. This supposition is grounded in the separability principle between systems and allows the derivation of the evolution equation. In the weak coupling regime, the machine's output is limited by the coupling strength, restricting their application. Seeking to overcome this limitation, we analyze QHMs in the virtually unexplored strong coupling regime here, where separability, as well as other standard thermodynamic assumptions, may no longer hold. We show that strongly coupled QHMs may be as efficient as their weakly coupled counterparts. In addition, we find a novel turnover behavior where their output saturates and disappears in the limit of ultrastrong coupling.
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Affiliation(s)
- David Gelbwaser-Klimovsky
- Department of Chemistry and Chemical Biology, Harvard University , Cambridge, Massachusetts 02138, United States
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University , Cambridge, Massachusetts 02138, United States
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Correa LA, Palao JP, Alonso D. Internal dissipation and heat leaks in quantum thermodynamic cycles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032136. [PMID: 26465455 DOI: 10.1103/physreve.92.032136] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Indexed: 06/05/2023]
Abstract
The direction of the steady-state heat currents across a generic quantum system connected to multiple baths may be engineered to realize virtually any thermodynamic cycle. In spite of their versatility, such continuous energy-conversion systems are generally unable to operate at maximum efficiency due to non-negligible sources of irreversible entropy production. In this paper we introduce a minimal model of irreversible absorption chiller. We identify and characterize the different mechanisms responsible for its irreversibility, namely heat leaks and internal dissipation, and gauge their relative impact in the overall cooling performance. We also propose reservoir engineering techniques to minimize these detrimental effects. Finally, by looking into a known three-qubit embodiment of the absorption cooling cycle, we illustrate how our simple model may help to pinpoint the different sources of irreversibility naturally arising in more complex practical heat devices.
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Affiliation(s)
- Luis A Correa
- Departament de Física, Universitat Autònoma de Barcelona, E08193 Bellaterra, Spain
| | - José P Palao
- IUdEA Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, 38203, Spain and Departamento de Física, Universidad de La Laguna, 38204, Spain
| | - Daniel Alonso
- IUdEA Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, 38203, Spain and Departamento de Física, Universidad de La Laguna, 38204, Spain
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Manzano G, Horowitz JM, Parrondo JMR. Nonequilibrium potential and fluctuation theorems for quantum maps. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032129. [PMID: 26465448 DOI: 10.1103/physreve.92.032129] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2015] [Indexed: 06/05/2023]
Abstract
We derive a general fluctuation theorem for quantum maps. The theorem applies to a broad class of quantum dynamics, such as unitary evolution, decoherence, thermalization, and other types of evolution for quantum open systems. The theorem reproduces well-known fluctuation theorems in a single and simplified framework and extends the Hatano-Sasa theorem to quantum nonequilibrium processes. Moreover, it helps to elucidate the physical nature of the environment that induces a given dynamics in an open quantum system.
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Affiliation(s)
- Gonzalo Manzano
- Departamento de Física Atómica, Molecular y Nuclear and GISC, Universidad Complutense Madrid, 28040 Madrid, Spain
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Jordan M Horowitz
- Department of Physics, University of Massachusetts at Boston, Boston, Massachusetts 02125, USA
| | - Juan M R Parrondo
- Departamento de Física Atómica, Molecular y Nuclear and GISC, Universidad Complutense Madrid, 28040 Madrid, Spain
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Abstract
Quantum thermodynamics supplies a consistent description of quantum heat engines and refrigerators up to a single few-level system coupled to the environment. Once the environment is split into three (a hot, cold, and work reservoir), a heat engine can operate. The device converts the positive gain into power, with the gain obtained from population inversion between the components of the device. Reversing the operation transforms the device into a quantum refrigerator. The quantum tricycle, a device connected by three external leads to three heat reservoirs, is used as a template for engines and refrigerators. The equation of motion for the heat currents and power can be derived from first principles. Only a global description of the coupling of the device to the reservoirs is consistent with the first and second laws of thermodynamics. Optimization of the devices leads to a balanced set of parameters in which the couplings to the three reservoirs are of the same order and the external driving field is in resonance. When analyzing refrigerators, one needs to devote special attention to a dynamical version of the third law of thermodynamics. Bounds on the rate of cooling when Tc→0 are obtained by optimizing the cooling current. All refrigerators as Tc→0 show universal behavior. The dynamical version of the third law imposes restrictions on the scaling as Tc→0 of the relaxation rate γc and heat capacity cV of the cold bath.
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Affiliation(s)
- Ronnie Kosloff
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel;
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Work extraction from heat-powered quantized optomechanical setups. Sci Rep 2015; 5:7809. [PMID: 25589170 PMCID: PMC4295096 DOI: 10.1038/srep07809] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2014] [Accepted: 12/10/2014] [Indexed: 11/30/2022] Open
Abstract
We analyze work extraction from an autonomous (self-contained) heat-powered optomechanical setup. The initial state of the quantized mechanical oscillator plays a key role. As the initial mean amplitude of the oscillator decreases, the resulting efficiency increases. In contrast to laser-powered self-induced oscillations, work extraction from a broadband heat bath does not require coherence or phase-locking: an initial phase-averaged coherent state of the oscillator still yields work, as opposed to an initial Fock-state.
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Correa LA, Palao JP, Adesso G, Alonso D. Optimal performance of endoreversible quantum refrigerators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062124. [PMID: 25615061 DOI: 10.1103/physreve.90.062124] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2014] [Indexed: 06/04/2023]
Abstract
The derivation of general performance benchmarks is important in the design of highly optimized heat engines and refrigerators. To obtain them, one may model phenomenologically the leading sources of irreversibility ending up with results that are model independent, but limited in scope. Alternatively, one can take a simple physical system realizing a thermodynamic cycle and assess its optimal operation from a complete microscopic description. We follow this approach in order to derive the coefficient of performance at maximum cooling rate for any endoreversible quantum refrigerator. At striking variance with the universality of the optimal efficiency of heat engines, we find that the cooling performance at maximum power is crucially determined by the details of the specific system-bath interaction mechanism. A closed analytical benchmark is found for endoreversible refrigerators weakly coupled to unstructured bosonic heat baths: an ubiquitous case study in quantum thermodynamics.
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Affiliation(s)
- Luis A Correa
- School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kindom and Instituto Universitario de Estudios Avanzados en Atómica, Molecular y Fotónica, Universidad de La Laguna, 38203 La Laguna, Spain
| | - José P Palao
- Instituto Universitario de Estudios Avanzados en Atómica, Molecular y Fotónica, Universidad de La Laguna, 38203 La Laguna, Spain and Departamento de Física, Universidad de La Laguna, 38204 La Laguna, Spain
| | - Gerardo Adesso
- School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kindom
| | - Daniel Alonso
- Instituto Universitario de Estudios Avanzados en Atómica, Molecular y Fotónica, Universidad de La Laguna, 38203 La Laguna, Spain and Departamento de Física, Universidad de La Laguna, 38204 La Laguna, Spain
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Liu F. Calculating work in adiabatic two-level quantum Markovian master equations: a characteristic function method. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032121. [PMID: 25314409 DOI: 10.1103/physreve.90.032121] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2014] [Indexed: 06/04/2023]
Abstract
We present a characteristic function method to calculate the probability density functions of the inclusive work in adiabatic two-level quantum Markovian master equations. These systems are steered by some slowly varying parameters and the dissipations may depend on time. Our theory is based on the interpretation of the quantum jump for the master equations. In addition to the calculation, we also find that the fluctuation properties of the work can be described by the symmetry of the characteristic functions, which is exactly the same as in the case of isolated systems. A periodically driven two-level model is used to demonstrate the method.
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Affiliation(s)
- Fei Liu
- School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
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Gelbwaser-Klimovsky D, Kurizki G. Heat-machine control by quantum-state preparation: from quantum engines to refrigerators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022102. [PMID: 25215684 DOI: 10.1103/physreve.90.022102] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2014] [Indexed: 06/03/2023]
Abstract
We explore the dependence of the performance bounds of heat engines and refrigerators on the initial quantum state and the subsequent evolution of their piston, modeled by a quantized harmonic oscillator. Our goal is to provide a fully quantized treatment of self-contained (autonomous) heat machines, as opposed to their prevailing semiclassical description that consists of a quantum system alternately coupled to a hot or a cold heat bath and parametrically driven by a classical time-dependent piston or field. Here, by contrast, there is no external time-dependent driving. Instead, the evolution is caused by the stationary simultaneous interaction of two heat baths (having distinct spectra and temperatures) with a single two-level system that is in turn coupled to the quantum piston. The fully quantized treatment we put forward allows us to investigate work extraction and refrigeration by the tools of quantum-optical amplifier and dissipation theory, particularly, by the analysis of amplified or dissipated phase-plane quasiprobability distributions. Our main insight is that quantum states may be thermodynamic resources and can provide a powerful handle, or control, on the efficiency of the heat machine. In particular, a piston initialized in a coherent state can cause the engine to produce work at an efficiency above the Carnot bound in the linear amplification regime. In the refrigeration regime, the coefficient of performance can transgress the Carnot bound if the piston is initialized in a Fock state. The piston may be realized by a vibrational mode, as in nanomechanical setups, or an electromagnetic field mode, as in cavity-based scenarios.
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Affiliation(s)
| | - G Kurizki
- Weizmann Institute of Science, 76100 Rehovot, Israel
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Liu F. Equivalence of two Bochkov-Kuzovlev equalities in quantum two-level systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042122. [PMID: 24827208 DOI: 10.1103/physreve.89.042122] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2014] [Indexed: 06/03/2023]
Abstract
We present two kinds of Bochkov-Kuzovlev work equalities in a two-level system that is described by a quantum Markovian master equation. One is based on multiple time correlation functions and the other is based on the quantum trajectory viewpoint. We show that these two equalities are indeed equivalent. Importantly, this equivalence provides us a way to calculate the probability density function of the quantum work by solving the evolution equation for its characteristic function. We use a numerical model to verify these results.
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Affiliation(s)
- Fei Liu
- School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
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