1
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Zhang JW, Bu JT, Li JC, Meng W, Ding WQ, Wang B, Yuan WF, Du HJ, Ding GY, Chen WJ, Chen L, Zhou F, Xu Z, Feng M. Single-Atom Verification of the Optimal Trade-Off between Speed and Cost in Shortcuts to Adiabaticity. PHYSICAL REVIEW LETTERS 2024; 132:213602. [PMID: 38856267 DOI: 10.1103/physrevlett.132.213602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2024] [Revised: 03/24/2024] [Accepted: 04/22/2024] [Indexed: 06/11/2024]
Abstract
The approach of shortcuts to adiabaticity enables the effective execution of adiabatic dynamics in quantum information processing with enhanced speed. Owing to the inherent trade-off between dynamical speed and the cost associated with the transitionless driving field, executing arbitrarily fast operations becomes impractical. To understand the accurate interplay between speed and energetic cost in this process, we propose theoretically and verify experimentally a new trade-off, which is characterized by a tightly optimized bound within s-parametrized phase spaces. Our experiment is carried out in a single ultracold ^{40}Ca^{+} ion trapped in a harmonic potential. By exactly operating the quantum states of the ion, we execute the Landau-Zener model as an example, where the quantum speed limit as well as the cost are governed by the spectral gap. We witness that our proposed trade-off is indeed tight in scenarios involving both initially eigenstates and initially thermal equilibrium states. Our work helps understanding the fundamental constraints in shortcuts to adiabaticity and illuminates the potential of underutilized phase spaces that have been traditionally overlooked.
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Affiliation(s)
- J-W Zhang
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
| | - J-T Bu
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - J C Li
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
- Guangzhou Institute of Industrial Intelligence, Guangzhou 511458, China
| | - Weiquan Meng
- School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - W-Q Ding
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - B Wang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - W-F Yuan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - H-J Du
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - G-Y Ding
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - W-J Chen
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - L Chen
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - F Zhou
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - Zhenyu Xu
- School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - M Feng
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China
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2
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Liu W, Niu Z, Cheng W, Li X, Duan CK, Yin Z, Rong X, Du J. Experimental Test of the Jarzynski Equality in a Single Spin-1 System Using High-Fidelity Single-Shot Readouts. PHYSICAL REVIEW LETTERS 2023; 131:220401. [PMID: 38101345 DOI: 10.1103/physrevlett.131.220401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Revised: 10/22/2023] [Accepted: 10/24/2023] [Indexed: 12/17/2023]
Abstract
The Jarzynski equality (JE), which connects the equilibrium free energy with nonequilibrium work statistics, plays a crucial role in quantum thermodynamics. Although practical quantum systems are usually multilevel systems, most tests of the JE were executed in two-level systems. A rigorous test of the JE by directly measuring the work distribution of a physical process in a high-dimensional quantum system remains elusive. Here, we report an experimental test of the JE in a single spin-1 system. We realized nondemolition projective measurement of this three-level system via cascading high-fidelity single-shot readouts and directly measured the work distribution utilizing the two-point measurement protocol. The validity of the JE was verified from the nonadiabatic to adiabatic zone and under different effective temperatures. Our work puts the JE on a solid experimental foundation and makes the nitrogen-vacancy (NV) center system a mature toolbox to perform advanced experiments of stochastic quantum thermodynamics.
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Affiliation(s)
- Wenquan Liu
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China
| | - Zhibo Niu
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Wei Cheng
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xin Li
- Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Chang-Kui Duan
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Zhangqi Yin
- Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Xing Rong
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jiangfeng Du
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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3
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Cao Z, Bao R, Zheng J, Hou Z. Fast Functionalization with High Performance in the Autonomous Information Engine. J Phys Chem Lett 2023; 14:66-72. [PMID: 36566388 DOI: 10.1021/acs.jpclett.2c03335] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Mandal and Jarzynski have proposed a fully autonomous information heat engine, consisting of a demon, a mass, and a memory register interacting with a thermal reservoir. This device converts thermal energy into mechanical work by writing information to a memory register or, conversely, erasing information by consuming mechanical work. Here, we derive a speed limit inequality between the relaxation time of state transformation and the distance between the initial and final distributions, where the combination of the dynamical activity and entropy production plays an important role. Such inequality provides a hint that a speed-performance trade-off relation exists between the relaxation time to a functional state and the average production. To obtain fast functionalization while maintaining the performance, we show that the relaxation dynamics of the information heat engine can be accelerated significantly by devising an optimal initial state of the demon. Our design principle is inspired by the so-called Mpemba effect, where water freezes faster when initially heated.
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Affiliation(s)
- Zhiyu Cao
- Department of Chemical Physics and Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Ruicheng Bao
- Department of Chemical Physics and Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Jiming Zheng
- Department of Chemical Physics and Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Zhonghuai Hou
- Department of Chemical Physics and Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
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4
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Van Vu T, Saito K. Topological Speed Limit. PHYSICAL REVIEW LETTERS 2023; 130:010402. [PMID: 36669213 DOI: 10.1103/physrevlett.130.010402] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2022] [Revised: 11/15/2022] [Accepted: 12/05/2022] [Indexed: 06/17/2023]
Abstract
Any physical system evolves at a finite speed that is constrained not only by the energetic cost but also by the topological structure of the underlying dynamics. In this Letter, by considering such structural information, we derive a unified topological speed limit for the evolution of physical states using an optimal transport approach. We prove that the minimum time required for changing states is lower bounded by the discrete Wasserstein distance, which encodes the topological information of the system, and the time-averaged velocity. The bound obtained is tight and applicable to a wide range of dynamics, from deterministic to stochastic, and classical to quantum systems. In addition, the bound provides insight into the design principles of the optimal process that attains the maximum speed. We demonstrate the application of our results to chemical reaction networks and interacting many-body quantum systems.
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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
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5
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Nakahara M. Counterdiabatic formalism of shortcuts to adiabaticity. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210272. [PMID: 36335939 DOI: 10.1098/rsta.2021.0272] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2022] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
A pedagogical introduction to counterdiabatic formalism of shortcuts to adiabaticity is given so that readers can access some of the more specialized articles in the rest of this theme issue without any barriers. A guide to references is given so that this article also serves as a mini-review. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
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Affiliation(s)
- Mikio Nakahara
- Research Institute for Science and Technology, Kindai University, Higashiosaka, Osaka 577-8502, Japan
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6
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Soriani A, Miranda E, Deffner S, Bonança MVS. Shortcuts to Thermodynamic Quasistaticity. PHYSICAL REVIEW LETTERS 2022; 129:170602. [PMID: 36332265 DOI: 10.1103/physrevlett.129.170602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Revised: 09/16/2022] [Accepted: 09/22/2022] [Indexed: 06/16/2023]
Abstract
The operation of near-term quantum technologies requires the development of feasible, implementable, and robust strategies of controlling complex many body systems. To this end, a variety of techniques, so-called "shortcuts to adiabaticity," have been developed. Many of these shortcuts have already been demonstrated to be powerful and implementable in distinct scenarios. Yet, it is often also desirable to have additional, approximate strategies available that are applicable to a large class of systems. Hence, in this Letter, we take inspiration from thermodynamics and propose to focus on the macrostate, rather than the microstate. Adiabatic dynamics can then be identified as such processes that preserve the equation of state, and systematic corrections are obtained from adiabatic perturbation theory. We demonstrate this approach by improving upon fast quasiadiabatic driving, and by applying the method to the quantum Ising chain in the transverse field.
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Affiliation(s)
- Artur Soriani
- Gleb Wataghin Institute of Physics, University of Campinas, Campinas, São Paulo 13083-950, Brazil
| | - Eduardo Miranda
- Gleb Wataghin Institute of Physics, University of Campinas, Campinas, São Paulo 13083-950, Brazil
| | - Sebastian Deffner
- Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
| | - Marcus V S Bonança
- Gleb Wataghin Institute of Physics, University of Campinas, Campinas, São Paulo 13083-950, Brazil
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7
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Shortcuts to adiabatic population inversion via time-rescaling: stability and thermodynamic cost. Sci Rep 2022; 12:11538. [PMID: 35798967 PMCID: PMC9262946 DOI: 10.1038/s41598-022-15912-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2022] [Accepted: 06/30/2022] [Indexed: 11/08/2022] Open
Abstract
A shortcut to adiabaticity is concerned with the fast and robust manipulation of the dynamics of a quantum system which reproduces the effect of an adiabatic process. In this work, we use the time-rescaling method to study the problem of speeding up the population inversion of a two-level quantum system, and the fidelity of the fast dynamics versus systematic errors in the control parameters. This approach enables the generation of shortcuts from a prescribed slow dynamics by simply rescaling the time variable of the quantum evolution operator. It requires no knowledge of the eigenvalues and eigenstates of the Hamiltonian and, in principle, no additional coupling fields. From a quantum thermodynamic viewpoint, we also demonstrate that the main properties of the distribution of work required to drive the system along the shortcuts are unchanged with respect to the reference (slow) protocol.
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8
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Del Campo A. Probing Quantum Speed Limits with Ultracold Gases. PHYSICAL REVIEW LETTERS 2021; 126:180603. [PMID: 34018797 DOI: 10.1103/physrevlett.126.180603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2020] [Accepted: 03/31/2021] [Indexed: 06/12/2023]
Abstract
Quantum speed limits (QSLs) rule the minimum time for a quantum state to evolve into a distinguishable state in an arbitrary physical process. These fundamental results constrain a notion of distance traveled by the quantum state, known as the Bures angle, in terms of the speed of evolution set by nonadiabatic energy fluctuations. I theoretically propose how to measure QSLs in an ultracold quantum gas confined in a time-dependent harmonic trap. In this highly-dimensional system of continuous variables, quantum tomography is prohibited. Yet, QSLs can be probed whenever the dynamics is self-similar by measuring as a function of time the cloud size of the ultracold gas. This makes it possible to determine the Bures angle and energy fluctuations, as I discuss for various ultracold atomic systems.
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Affiliation(s)
- Adolfo Del Campo
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg; Donostia International Physics Center, E-20018 San Sebastián, Spain; IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain; Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA and Theory Division, Los Alamos National Laboratory, MS-B213, Los Alamos, New Mexico 87545, USA
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9
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Frim AG, Zhong A, Chen SF, Mandal D, DeWeese MR. Engineered swift equilibration for arbitrary geometries. Phys Rev E 2021; 103:L030102. [PMID: 33862711 DOI: 10.1103/physreve.103.l030102] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2020] [Accepted: 02/12/2021] [Indexed: 11/07/2022]
Abstract
Engineered swift equilibration (ESE) is a class of driving protocols that enforce an equilibrium distribution with respect to external control parameters at the beginning and end of rapid state transformations of open, classical nonequilibrium systems. ESE protocols have previously been derived and experimentally realized for Brownian particles in simple, one-dimensional, time-varying trapping potentials; one recent study considered ESE in two-dimensional Euclidean configuration space. Here we extend the ESE framework to generic, overdamped Brownian systems in arbitrary curved configuration space and illustrate our results with specific examples not amenable to previous techniques. Our approach may be used to impose the necessary dynamics to control the full temporal configurational distribution in a wide variety of experimentally realizable settings.
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Affiliation(s)
- Adam G Frim
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
| | - Adrianne Zhong
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
| | - Shi-Fan Chen
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
| | - Dibyendu Mandal
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
| | - Michael R DeWeese
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA.,Redwood Center For Theoretical Neuroscience and Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, California 94720, USA
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10
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Ono K, Shevchenko SN, Mori T, Moriyama S, Nori F. Analog of a Quantum Heat Engine Using a Single-Spin Qubit. PHYSICAL REVIEW LETTERS 2020; 125:166802. [PMID: 33124837 DOI: 10.1103/physrevlett.125.166802] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Accepted: 09/15/2020] [Indexed: 06/11/2023]
Abstract
A quantum two-level system with periodically modulated energy splitting could provide a minimal universal quantum heat machine. We present the experimental realization and the theoretical description of such a two-level system as an impurity electron spin in a silicon tunnel field-effect transistor. In the incoherent regime, the system can behave analogously to either an Otto heat engine or a refrigerator. The coherent regime could be described as a superposition of those two regimes, producing specific interference fringes in the observed source-drain current.
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Affiliation(s)
- K Ono
- Advanced Device Laboratory, RIKEN, Wako-shi, Saitama 351-0198, Japan
- CEMS, RIKEN, Wako-shi, Saitama 351-0198, Japan
| | - S N Shevchenko
- B. Verkin Institute for Low Temperature Physics and Engineering, Kharkov 61103, Ukraine
- V. N. Karazin Kharkiv National University, Kharkov 61022, Ukraine
- Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wako-shi, Saitama 351-0198, Japan
| | - T Mori
- Device Technology Research Institute (D-Tech), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan
| | - S Moriyama
- Department of Electrical and Electronic Engineering, Tokyo Denki University, Adachi-ku, Tokyo 120-8551, Japan
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wako-shi, Saitama 351-0198, Japan
- Department of Physics, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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11
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García-Pintos LP, Hamma A, Del Campo A. Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries. PHYSICAL REVIEW LETTERS 2020; 125:040601. [PMID: 32794781 DOI: 10.1103/physrevlett.125.040601] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
We study the connection between the charging power of quantum batteries and the fluctuations of the extractable work. We prove that in order to have a nonzero rate of change of the extractable work, the state ρ_{W} of the battery cannot be an eigenstate of a "free energy operator," defined by F≡H_{W}+β^{-1}log(ρ_{W}), where H_{W} is the Hamiltonian of the battery and β is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the free energy operator upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine.
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Affiliation(s)
- Luis Pedro García-Pintos
- Joint Center for Quantum Information and Computer Science and Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
| | - Alioscia Hamma
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
| | - Adolfo Del Campo
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
- Donostia International Physics Center, E-20018 San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
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12
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Hino Y, Hayakawa H. Fluctuation relations for adiabatic pumping. Phys Rev E 2020; 102:012115. [PMID: 32795070 DOI: 10.1103/physreve.102.012115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2019] [Accepted: 05/28/2020] [Indexed: 06/11/2023]
Abstract
We derive an extended fluctuation relation for an open system coupled with two reservoirs under adiabatic one-cycle modulation. We confirm that the geometrical phase caused by the Berry-Sinitsyn-Nemenman curvature in the parameter space generates non-Gaussian fluctuations. This non-Gaussianity is enhanced for the instantaneous fluctuation relation when the bias between the two reservoirs disappears.
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Affiliation(s)
- Yuki Hino
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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13
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Funo K, Lambert N, Nori F, Flindt C. Shortcuts to Adiabatic Pumping in Classical Stochastic Systems. PHYSICAL REVIEW LETTERS 2020; 124:150603. [PMID: 32357046 DOI: 10.1103/physrevlett.124.150603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Accepted: 03/18/2020] [Indexed: 06/11/2023]
Abstract
Adiabatic pumping is characterized by a geometric contribution to the pumped charge, which can be nonzero even in the absence of a bias. However, as the driving speed is increased, nonadiabatic excitations gradually reduce the pumped charge, thereby limiting the maximal applicable driving frequencies. To circumvent this problem, we here extend the concept of shortcuts to adiabaticity to construct a control protocol which enables geometric pumping well beyond the adiabatic regime. Our protocol allows for an increase, by more than an order of magnitude, in the driving frequencies, and the method is also robust against moderate fluctuations of the control field. We provide a geometric interpretation of the control protocol and analyze the thermodynamic cost of implementing it. Our findings can be realized using current technology and potentially enable fast pumping of charge or heat in quantum dots, as well as in other stochastic systems from physics, chemistry, and biology.
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Affiliation(s)
- Ken Funo
- Theoretical Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Neill Lambert
- Theoretical Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Franco Nori
- Theoretical Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
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14
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Takahashi K, Fujii K, Hino Y, Hayakawa H. Nonadiabatic Control of Geometric Pumping. PHYSICAL REVIEW LETTERS 2020; 124:150602. [PMID: 32357045 DOI: 10.1103/physrevlett.124.150602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Accepted: 03/17/2020] [Indexed: 06/11/2023]
Abstract
We study nonadiabatic effects of geometric pumping. With arbitrary choices of periodic control parameters, we go beyond the adiabatic approximation to obtain the exact pumping current. We find that a geometrical interpretation for the nontrivial part of the current is possible even in the nonadiabatic regime. The exact result allows us to find a smooth connection between the adiabatic Berry phase theory at low frequencies and the Floquet theory at high frequencies. We also study how to control the geometric current. Using the method of shortcuts to adiabaticity with the aid of an assisting field, we illustrate that it enhances the current.
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Affiliation(s)
- Kazutaka Takahashi
- Institute of Innovative Research, Tokyo Institute of Technology, Kanagawa 226-8503, Japan
| | - Keisuke Fujii
- Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan and iTHEMS Program, RIKEN, Saitama 351-0198, Japan
| | - Yuki Hino
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
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15
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Fogarty T, Deffner S, Busch T, Campbell S. Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit. PHYSICAL REVIEW LETTERS 2020; 124:110601. [PMID: 32242725 DOI: 10.1103/physrevlett.124.110601] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2019] [Accepted: 02/18/2020] [Indexed: 06/11/2023]
Abstract
A remarkable feature of quantum many-body systems is the orthogonality catastrophe that describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body system, whose variance in ground state energy scales with the system size, exhibits the orthogonality catastrophe. Our rigorous findings are demonstrated by two paradigmatic classes of many-body systems-the trapped Fermi gas and the long-range interacting Lipkin-Meshkov-Glick spin model.
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Affiliation(s)
- Thomás Fogarty
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Sebastian Deffner
- Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
| | - Thomas Busch
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Steve Campbell
- School of Physics, University College Dublin, Belfield Dublin 4, Ireland
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16
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Claeys PW, Pandey M, Sels D, Polkovnikov A. Floquet-Engineering Counterdiabatic Protocols in Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2019; 123:090602. [PMID: 31524451 DOI: 10.1103/physrevlett.123.090602] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2019] [Revised: 07/17/2019] [Indexed: 05/26/2023]
Abstract
Counterdiabatic (CD) driving presents a way of generating adiabatic dynamics at an arbitrary pace, where excitations due to nonadiabaticity are exactly compensated by adding an auxiliary driving term to the Hamiltonian. While this CD term is theoretically known and given by the adiabatic gauge potential, obtaining and implementing this potential in many-body systems is a formidable task, requiring knowledge of the spectral properties of the instantaneous Hamiltonians and control of highly nonlocal multibody interactions. We show how an approximate gauge potential can be systematically built up as a series of nested commutators, remaining well defined in the thermodynamic limit. Furthermore, the resulting CD driving protocols can be realized up to arbitrary order without leaving the available control space using tools from periodically driven (Floquet) systems. This is illustrated on few- and many-body quantum systems, where the resulting Floquet protocols significantly suppress dissipation and provide a drastic increase in fidelity.
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Affiliation(s)
- Pieter W Claeys
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Mohit Pandey
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Dries Sels
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
- Theory of Quantum and Complex Systems, Universiteit Antwerpen, B-2610 Antwerpen, Belgium
| | - Anatoli Polkovnikov
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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17
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Çakmak B, Müstecaplıoğlu ÖE. Spin quantum heat engines with shortcuts to adiabaticity. Phys Rev E 2019; 99:032108. [PMID: 30999442 DOI: 10.1103/physreve.99.032108] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2018] [Indexed: 06/09/2023]
Abstract
We consider a finite-time quantum Otto cycle with single- and two spin-1/2 systems as its working medium. To mimic adiabatic dynamics at a finite time, we employ a shortcut-to-adiabaticity technique and evaluate the performance of the engine including the cost of the shortcut. We compare our results with the true adiabatic and nonadiabatic performances of the same cycle. Our findings indicate that the use of the shortcut-to-adiabaticity scheme significantly enhances the performance of the quantum Otto engine as compared to its adiabatic and nonadiabatic counterparts for different figures of merit.
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Affiliation(s)
- Barış Çakmak
- Department of Physics, Koç University, İstanbul, Sarıyer 34450, Turkey
- College of Engineering and Natural Sciences, Bahçeşehir University, Beşiktaş, Istanbul 34353, Turkey
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18
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Abah O, Paternostro M. Shortcut-to-adiabaticity Otto engine: A twist to finite-time thermodynamics. Phys Rev E 2019; 99:022110. [PMID: 30934342 DOI: 10.1103/physreve.99.022110] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2018] [Indexed: 06/09/2023]
Abstract
We consider a finite-time Otto engine operating on a quantum harmonic oscillator and driven by shortcut-to-adiabaticity (STA) techniques to speed up its cycle. We study its efficiency and power when internal friction, time-averaged work, and work fluctuations are used as quantitative figures of merit, showing that time-averaged efficiency and power are useful cost functions for the characterization of the performance of the engine. We then use the minimum allowed time for validity of STA protocol relation to establish a physically relevant bound to the efficiency at maximum power of the STA-driven cycle.
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Affiliation(s)
- Obinna Abah
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Mauro Paternostro
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
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19
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Quantum Information Remote Carnot Engines and Voltage Transformers. ENTROPY 2019; 21:e21020127. [PMID: 33266843 PMCID: PMC7514606 DOI: 10.3390/e21020127] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/03/2019] [Revised: 01/24/2019] [Accepted: 01/28/2019] [Indexed: 11/17/2022]
Abstract
A physical system out of thermal equilibrium is a resource for obtaining useful work when a heat bath at some temperature is available. Information Heat Engines are the devices which generalize the Szilard cylinders and make use of the celebrated Maxwell demons to this end. In this paper, we consider a thermo-chemical reservoir of electrons which can be exchanged for entropy and work. Qubits are used as messengers between electron reservoirs to implement long-range voltage transformers with neither electrical nor magnetic interactions between the primary and secondary circuits. When they are at different temperatures, the transformers work according to Carnot cycles. A generalization is carried out to consider an electrical network where quantum techniques can furnish additional security.
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20
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Tajima H, Shiraishi N, Saito K. Uncertainty Relations in Implementation of Unitary Operations. PHYSICAL REVIEW LETTERS 2018; 121:110403. [PMID: 30265087 DOI: 10.1103/physrevlett.121.110403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2017] [Indexed: 06/08/2023]
Abstract
The underlying mechanism in the implementation of unitary operation on a system with an external apparatus is studied. We implement the unitary time evolution in the system as a physical phenomenon that results from the interaction between the system and the apparatus. We investigate the fundamental limitation of an accurate implementation for the desired unitary time evolution. This limitation is manifested in the form of trade-off relations between the accuracy of the implementation and quantum fluctuation of energy in the external apparatus. Our relations clearly show that an accurate unitary operation requires a large energy fluctuation inside the apparatus originated from the quantum fluctuation.
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Affiliation(s)
- Hiroyasu Tajima
- Department of Communication Engineering and Informatics, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, 182-8585, Japan
| | - Naoto Shiraishi
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Yokohama, 223-8522, Japan
| | - Keiji Saito
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Yokohama, 223-8522, Japan
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21
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Shiraishi N, Funo K, Saito K. Speed Limit for Classical Stochastic Processes. PHYSICAL REVIEW LETTERS 2018; 121:070601. [PMID: 30169075 DOI: 10.1103/physrevlett.121.070601] [Citation(s) in RCA: 63] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2018] [Indexed: 05/10/2023]
Abstract
We consider the speed limit for classical stochastic Markov processes with and without the local detailed balance condition. We find that, for both cases, a trade-off inequality exists between the speed of the state transformation and the entropy production. The dynamical activity is related to a time scale and plays a crucial role in the inequality. For the dynamics without the local detailed balance condition, we use the Hatano-Sasa entropy production instead of the standard entropy production. Our inequalities consist of the quantities that are commonly used in stochastic thermodynamics and explicitly show underlying physical mechanisms.
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Affiliation(s)
- Naoto Shiraishi
- Department of Physics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 2288521, Japan
| | - Ken Funo
- School of Physics, Peking University, Beijing 100871, China
| | - Keiji Saito
- Department of Physics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 2288521, Japan
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22
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Campaioli F, Pollock FA, Binder FC, Modi K. Tightening Quantum Speed Limits for Almost All States. PHYSICAL REVIEW LETTERS 2018; 120:060409. [PMID: 29481279 DOI: 10.1103/physrevlett.120.060409] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2017] [Indexed: 06/08/2023]
Abstract
Conventional quantum speed limits perform poorly for mixed quantum states: They are generally not tight and often significantly underestimate the fastest possible evolution speed. To remedy this, for unitary driving, we derive two quantum speed limits that outperform the traditional bounds for almost all quantum states. Moreover, our bounds are significantly simpler to compute as well as experimentally more accessible. Our bounds have a clear geometric interpretation; they arise from the evaluation of the angle between generalized Bloch vectors.
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Affiliation(s)
- Francesco Campaioli
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Felix A Pollock
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Felix C Binder
- School of Physical & Mathematical Sciences, Nanyang Technological University, 637371 Singapore, Singapore
| | - Kavan Modi
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
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23
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Jaramillo JD, Deng J, Gong J. Quantum work fluctuations in connection with the Jarzynski equality. Phys Rev E 2018; 96:042119. [PMID: 29347528 DOI: 10.1103/physreve.96.042119] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2017] [Indexed: 11/07/2022]
Abstract
A result of great theoretical and experimental interest, the Jarzynski equality predicts a free energy change ΔF of a system at inverse temperature β from an ensemble average of nonequilibrium exponential work, i.e., 〈e^{-βW}〉=e^{-βΔF}. The number of experimental work values needed to reach a given accuracy of ΔF is determined by the variance of e^{-βW}, denoted var(e^{-βW}). We discover in this work that var(e^{-βW}) in both harmonic and anharmonic Hamiltonian systems can systematically diverge in nonadiabatic work protocols, even when the adiabatic protocols do not suffer from such divergence. This divergence may be regarded as a type of dynamically induced phase transition in work fluctuations. For a quantum harmonic oscillator with time-dependent trapping frequency as a working example, any nonadiabatic work protocol is found to yield a diverging var(e^{-βW}) at sufficiently low temperatures, markedly different from the classical behavior. The divergence of var(e^{-βW}) indicates the too-far-from-equilibrium nature of a nonadiabatic work protocol and makes it compulsory to apply designed control fields to suppress the quantum work fluctuations in order to test the Jarzynski equality.
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Affiliation(s)
- Juan D Jaramillo
- Department of Physics, National University of Singapore, Singapore 117546
| | - Jiawen Deng
- NUS Graduate School for Integrative Science and Engineering, Singapore 117597
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore 117546.,NUS Graduate School for Integrative Science and Engineering, Singapore 117597
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24
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Ito K, Hayashi M. Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond independent-and-identical-distribution scaling. Phys Rev E 2018; 97:012129. [PMID: 29448373 DOI: 10.1103/physreve.97.012129] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2017] [Indexed: 06/08/2023]
Abstract
In quantum thermodynamics, effects of finiteness of the baths have been less considered. In particular, there is no general theory which focuses on finiteness of the baths of multiple conserved quantities. Then, we investigate how the optimal performance of generalized heat engines with multiple conserved quantities alters in response to the size of the baths. In the context of general theories of quantum thermodynamics, the size of the baths has been given in terms of the number of identical copies of a system, which does not cover even such a natural scaling as the volume. In consideration of the asymptotic extensivity, we deal with a generic scaling of the baths to naturally include the volume scaling. Based on it, we derive a bound for the performance of generalized heat engines reflecting finite-size effects of the baths, which we call fine-grained generalized Carnot bound. We also construct a protocol to achieve the optimal performance of the engine given by this bound. Finally, applying the obtained general theory, we deal with simple examples of generalized heat engines. As for an example of non-independent-and-identical-distribution scaling and multiple conserved quantities, we investigate a heat engine with two baths composed of an ideal gas exchanging particles, where the volume scaling is applied. The result implies that the mass of the particle explicitly affects the performance of this engine with finite-size baths.
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Affiliation(s)
- Kosuke Ito
- Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8602, Japan
| | - Masahito Hayashi
- Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8602, Japan
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
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25
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Bravetti A, Tapias D. Thermodynamic cost for classical counterdiabatic driving. Phys Rev E 2017; 96:052107. [PMID: 29347640 DOI: 10.1103/physreve.96.052107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2017] [Indexed: 06/07/2023]
Abstract
Motivated by the recent growing interest about the thermodynamic cost of shortcuts to adiabaticity, we consider the cost of driving a classical system by the so-called counterdiabatic driving (CD). To do so, we proceed in three steps: first we review a general definition recently put forward in the literature for the thermodynamic cost of driving a Hamiltonian system; then we provide a new complementary definition of cost, which is of particular relevance for cases where the average excess work vanishes; finally, we apply our general framework to the case of CD. Interestingly, we find that in such a case our results are the exact classical counterparts of those reported by Funo et al. [Phys. Rev. Lett. 118, 100602 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.100602]. In particular we show that a universal trade-off between speed and cost for CD also exists in the classical case. To illustrate our points we consider the example of a time-dependent harmonic oscillator subject to different strategies of adiabatic control.
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Affiliation(s)
- Alessandro Bravetti
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México 04510, Mexico
| | - Diego Tapias
- Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México 04510, Mexico
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26
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Campbell S, Deffner S. Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity. PHYSICAL REVIEW LETTERS 2017; 118:100601. [PMID: 28339279 DOI: 10.1103/physrevlett.118.100601] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2016] [Indexed: 05/25/2023]
Abstract
Achieving effectively adiabatic dynamics is a ubiquitous goal in almost all areas of quantum physics. Here, we study the speed with which a quantum system can be driven when employing transitionless quantum driving. As a main result, we establish a rigorous link between this speed, the quantum speed limit, and the (energetic) cost of implementing such a shortcut to adiabaticity. Interestingly, this link elucidates a trade-off between speed and cost, namely, that instantaneous manipulation is impossible as it requires an infinite cost. These findings are illustrated for two experimentally relevant systems-the parametric oscillator and the Landau-Zener model-which reveal that the spectral gap governs the quantum speed limit as well as the cost for realizing the shortcut.
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Affiliation(s)
- Steve Campbell
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
- Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milan, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, 20133 Milan, Italy
| | - Sebastian Deffner
- Department of Physics, University of Maryland Baltimore County, Baltimore, Maryland 21250, USA
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