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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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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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Funo K, Zhang JN, Chatou C, Kim K, Ueda M, Del Campo A. Universal Work Fluctuations During Shortcuts to Adiabaticity by Counterdiabatic Driving. PHYSICAL REVIEW LETTERS 2017; 118:100602. [PMID: 28339228 DOI: 10.1103/physrevlett.118.100602] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2016] [Indexed: 06/06/2023]
Abstract
Counterdiabatic driving (CD) exploits auxiliary control fields to tailor the nonequilibrium dynamics of a quantum system, making possible the suppression of dissipated work in finite-time thermodynamics and the engineering of optimal thermal machines with no friction. We show that while the mean work done by the auxiliary controls vanishes, CD leads to a broadening of the work distribution. We derive a fundamental inequality that relates nonequilibrium work fluctuations to the operation time and quantifies the thermodynamic cost of CD in both critical and noncritical systems.
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Affiliation(s)
- Ken Funo
- School of Physics, Peking University, Beijing 100871, China
| | - Jing-Ning Zhang
- Center for Quantum Information, Institute for the Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Cyril Chatou
- Université Paris 13, Sorbonne Paris Cité, 99 Avenue J.-B. Clément, F-93430 Villetaneuse, France
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
| | - Kihwan Kim
- Center for Quantum Information, Institute for the Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Masahito Ueda
- Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| | - Adolfo Del Campo
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
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Deng J, Tan AM, Hänggi P, Gong J. Merits and qualms of work fluctuations in classical fluctuation theorems. Phys Rev E 2017; 95:012106. [PMID: 28208437 DOI: 10.1103/physreve.95.012106] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2016] [Indexed: 11/07/2022]
Abstract
Work is one of the most basic notions in statistical mechanics, with work fluctuation theorems being one central topic in nanoscale thermodynamics. With Hamiltonian chaos commonly thought to provide a foundation for classical statistical mechanics, here we present general salient results regarding how (classical) Hamiltonian chaos generically impacts on nonequilibrium work fluctuations. For isolated chaotic systems prepared with a microcanonical distribution, work fluctuations are minimized and vanish altogether in adiabatic work protocols. For isolated chaotic systems prepared at an initial canonical distribution at inverse temperature β, work fluctuations depicted by the variance of e^{-βW} are also minimized by adiabatic work protocols. This general result indicates that, if the variance of e^{-βW} diverges for an adiabatic work protocol, it diverges for all nonadiabatic work protocols sharing the same initial and final Hamiltonians. Such divergence is hence not an isolated event and thus greatly impacts on the efficiency of using Jarzynski's equality to simulate free-energy differences. Theoretical results are illustrated in a Sinai model. Our general insights shall boost studies in nanoscale thermodynamics and are of fundamental importance in designing useful work protocols.
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Affiliation(s)
- Jiawen Deng
- NUS Graduate School for Integrative Science and Engineering, Singapore 117597
| | - Alvis Mazon Tan
- Department of Physics, National University of Singapore, Singapore 117546
| | - Peter Hänggi
- Department of Physics, National University of Singapore, Singapore 117546.,Institute of Physics, University of Augsburg, Universitätsstraße 1, D-86135 Augsburg, Germany
| | - Jiangbin Gong
- NUS Graduate School for Integrative Science and Engineering, Singapore 117597.,Department of Physics, National University of Singapore, Singapore 117546
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