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Whitelam S. Free-energy estimates from nonequilibrium trajectories under varying-temperature protocols. Phys Rev E 2024; 110:014142. [PMID: 39160951 DOI: 10.1103/physreve.110.014142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2023] [Accepted: 07/10/2024] [Indexed: 08/21/2024]
Abstract
The Jarzynski equality allows the calculation of free-energy differences using values of work measured from nonequilibrium trajectories. The number of trajectories required to accurately estimate free-energy differences in this way grows sharply with the size of work fluctuations, motivating the search for protocols that perform desired transformations with minimum work. However, protocols of this nature can involve varying temperature, to which the Jarzynski equality does not apply. We derive a variant of the Jarzynski equality that applies to varying-temperature protocols, and show that it can have better convergence properties than the standard version of the equality. We derive this modified equality and the associated fluctuation relation within the framework of Markovian stochastic dynamics, complementing related derivations done within the framework of Hamiltonian dynamics.
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Kamba M, Aikawa K. Revealing the Velocity Uncertainties of a Levitated Particle in the Quantum Ground State. PHYSICAL REVIEW LETTERS 2023; 131:183602. [PMID: 37977629 DOI: 10.1103/physrevlett.131.183602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Revised: 08/02/2023] [Accepted: 09/28/2023] [Indexed: 11/19/2023]
Abstract
We demonstrate time-of-flight measurements for an ultracold levitated nanoparticle and reveal its velocity for the translational motion brought to the quantum ground state. We discover that the velocity distributions obtained with repeated release-and-recapture measurements are significantly broadened via librational motions of the nanoparticle. Under feedback cooling on all the librational motions, we recover the velocity distributions in reasonable agreement with an expectation from the occupation number, with approximately twice the width of the quantum limit. The strong impact of librational motions on the translational motions is understood as a result of the deviation between the libration center and the center of mass, induced by the asymmetry of the nanoparticle. Our results elucidate the importance of the control over librational motions and establish the basis for exploring quantum mechanical properties of levitated nanoparticles in terms of their velocity.
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Affiliation(s)
- M Kamba
- Department of Physics, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, 152-8550 Tokyo, Japan
| | - K Aikawa
- Department of Physics, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, 152-8550 Tokyo, Japan
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Pires LB, Goerlich R, da Fonseca AL, Debiossac M, Hervieux PA, Manfredi G, Genet C. Optimal Time-Entropy Bounds and Speed Limits for Brownian Thermal Shortcuts. PHYSICAL REVIEW LETTERS 2023; 131:097101. [PMID: 37721846 DOI: 10.1103/physrevlett.131.097101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 07/20/2023] [Indexed: 09/20/2023]
Abstract
By controlling the variance of the radiation pressure exerted on an optically trapped microsphere in real time, we engineer temperature protocols that shortcut thermal relaxation when transferring the microsphere from one thermal equilibrium state to another. We identify the entropic footprint of such accelerated transfers and derive optimal temperature protocols that either minimize the production of entropy for a given transfer duration or accelerate the transfer for a given entropic cost as much as possible. Optimizing the trade-off yields time-entropy bounds that put speed limits on thermalization schemes. We further show how optimization expands the possibilities for accelerating Brownian thermalization down to its fundamental limits. Our approach paves the way for the design of optimized, finite-time thermodynamics for Brownian engines. It also offers a platform for investigating fundamental connections between information geometry and finite-time processes.
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Affiliation(s)
- Luís Barbosa Pires
- University of Strasbourg and CNRS, CESQ and ISIS, UMR 7006, F-67000 Strasbourg, France
| | - Rémi Goerlich
- University of Strasbourg and CNRS, CESQ and ISIS, UMR 7006, F-67000 Strasbourg, France
- University of Strasbourg and CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, France
| | - Arthur Luna da Fonseca
- University of Strasbourg and CNRS, CESQ and ISIS, UMR 7006, F-67000 Strasbourg, France
- Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, Rio de Janeiro, 21941-972, Brazil
| | - Maxime Debiossac
- Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, A-1090 Vienna, Austria
| | - Paul-Antoine Hervieux
- University of Strasbourg and CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, France
| | - Giovanni Manfredi
- University of Strasbourg and CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, France
| | - Cyriaque Genet
- University of Strasbourg and CNRS, CESQ and ISIS, UMR 7006, F-67000 Strasbourg, France
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Raynal D, de Guillebon T, Guéry-Odelin D, Trizac E, Lauret JS, Rondin L. Shortcuts to Equilibrium with a Levitated Particle in the Underdamped Regime. PHYSICAL REVIEW LETTERS 2023; 131:087101. [PMID: 37683149 DOI: 10.1103/physrevlett.131.087101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Accepted: 07/24/2023] [Indexed: 09/10/2023]
Abstract
We report on speeding-up equilibrium recovery in the previously unexplored general case of the underdamped regime using an optically levitated particle. We accelerate the convergence toward equilibrium by an order of magnitude compared to the natural relaxation time. We then discuss the efficiency of the studied protocols, especially for a multidimensional system. These results pave the way for optimizing realistic nanomachines with application to sensing and developing efficient nanoheat engines.
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Affiliation(s)
- Damien Raynal
- Université Paris-Saclay, ENS Paris-Saclay, CNRS, CentraleSupélec, LuMIn, 91405 Orsay Cedex, France
| | - Timothée de Guillebon
- Université Paris-Saclay, ENS Paris-Saclay, CNRS, CentraleSupélec, LuMIn, 91405 Orsay Cedex, France
| | - David Guéry-Odelin
- Université Paul Sabatier-Toulouse 3, CNRS, LCAR, 31062 Toulouse Cedex 9, France
| | - Emmanuel Trizac
- Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay Cedex, France
- Univ Lyon, ENS de Lyon, F-69342 Lyon, France
| | - Jean-Sébastien Lauret
- Université Paris-Saclay, ENS Paris-Saclay, CNRS, CentraleSupélec, LuMIn, 91405 Orsay Cedex, France
| | - Loïc Rondin
- Université Paris-Saclay, ENS Paris-Saclay, CNRS, CentraleSupélec, LuMIn, 91405 Orsay Cedex, France
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Barker PF. Scalable optical levitation. NATURE NANOTECHNOLOGY 2023; 18:7. [PMID: 36411373 DOI: 10.1038/s41565-022-01242-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Affiliation(s)
- P F Barker
- Department of Physics and Astronomy, University College London, London, UK.
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Sheng J, Yang C, Wu H. Nonequilibrium thermodynamics in cavity optomechanics. FUNDAMENTAL RESEARCH 2023; 3:75-86. [PMID: 38933566 PMCID: PMC11197698 DOI: 10.1016/j.fmre.2022.09.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Revised: 08/23/2022] [Accepted: 09/12/2022] [Indexed: 11/30/2022] Open
Abstract
Classical thermodynamics has been a great achievement in dealing with systems that are in equilibrium or near equilibrium. As an emerging field, nonequilibrium thermodynamics provides a general framework for understanding the nonequilibrium processes, particularly in small systems that are typically far-from-equilibrium and are dominated by thermal or quantum fluctuations. Cavity optomechanical systems hold great promise among the various experimental platforms for studying nonequilibrium thermodynamics owing to their high controllability, excellent mechanical performance, and ability to operate deep in the quantum regime. Here, we present an overview of the recent advances in nonequilibrium thermodynamics with cavity optomechanical systems. The experimental results in entropy production assessment, fluctuation theorems, heat transfer, and heat engines are highlighted.
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Affiliation(s)
- Jiteng Sheng
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
- Chongqing Key Laboratory of Precision Optics, Chongqing Institute of East China Normal University, Chongqing 401120, China
| | - Cheng Yang
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Haibin Wu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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