Quantum Features and Signatures of Quantum Thermal Machines

The aim of this book chapter is to indicate how quantum phenomena are affecting the operation of microscopic thermal machines, such as engines and refrigerators. As converting heat to work is one of the fundamental concerns in thermodynamics, the platform of quantum thermal machines sheds light on thermodynamics in the quantum regime. This chapter focuses on the basic features of quantum mechanics, such as energy quantization, the uncertainty principle, quantum coherence and correlations, and their manifestation in microscopic thermal devices. In addition to indicating the peculiar behaviors of thermal-machines due to their non-classical aspects, we present quantum-thermodynamic signatures of these machines. Any violation of the classical thermodynamic bounds observed in the outcome of measurements on theses machines is a sufficient condition to conclude that quantum effects are present in the operation of that thermal machine. Experimental setups demonstrating some of these results are also presented.

[1]  Alán Aspuru-Guzik,et al.  Strongly Coupled Quantum Heat Machines. , 2015, The journal of physical chemistry letters.

[2]  Gernot Schaller,et al.  Fermionic reaction coordinates and their application to an autonomous Maxwell demon in the strong coupling regime , 2017, 1711.08914.

[3]  Normal-metal-superconductor tunnel junction as a Brownian refrigerator. , 2007, Physical review letters.

[4]  Alán Aspuru-Guzik,et al.  Single-Atom Heat Machines Enabled by Energy Quantization. , 2017, Physical Review Letters.

[5]  L. Ballentine,et al.  Quantum Theory: Concepts and Methods , 1994 .

[6]  S. Popescu,et al.  Thermodynamics and the measure of entanglement , 1996, quant-ph/9610044.

[7]  M. Plenio,et al.  Colloquium: quantum coherence as a resource , 2016, 1609.02439.

[8]  Antonio Acín,et al.  Entanglement generation is not necessary for optimal work extraction. , 2013, Physical review letters.

[9]  Srihari Keshavamurthy,et al.  Annual Review of Physical Chemistry, 2015 , 2016 .

[10]  J. Rossnagel,et al.  A single-atom heat engine , 2015, Science.

[11]  G. Kurizki,et al.  Work extraction from heat-powered quantized optomechanical setups , 2014, Scientific Reports.

[12]  R. Kosloff,et al.  Speed limits in Liouville space for open quantum systems , 2016, 1607.00941.

[13]  G. Kurizki,et al.  Heat-machine control by quantum-state preparation: from quantum engines to refrigerators. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Ronnie Kosloff,et al.  Quantum absorption refrigerator. , 2011, Physical review letters.

[15]  R. Zambrini,et al.  Quantum Otto cycle with inner friction: finite-time and disorder effects , 2015, 1507.03417.

[16]  P. Horodecki,et al.  Quantum redundancies and local realism , 1994 .

[17]  David Gelbwaser-Klimovsky,et al.  Non-equilibrium quantum heat machines , 2015, 1507.01660.

[18]  Gershon Kurizki,et al.  Work extraction via quantum nondemolition measurements of qubits in cavities: Non-Markovian effects , 2012, 1211.1772.

[19]  Paul Skrzypczyk,et al.  Entanglement enhances cooling in microscopic quantum refrigerators. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Pingxing Chen,et al.  Four-level entangled quantum heat engines , 2007 .

[21]  Tao Wang,et al.  Effects of reservoir squeezing on quantum systems and work extraction. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  S. Harris,et al.  Electromagnetically induced transparency and quantum heat engines , 2016, 1611.01218.

[23]  S. Mukamel Principles of Nonlinear Optical Spectroscopy , 1995 .

[24]  Aharon Brodutch,et al.  Quantum discord, local operations, and Maxwell's demons , 2010 .

[25]  K. Funo,et al.  Universal Work Fluctuations During Shortcuts to Adiabaticity by Counterdiabatic Driving. , 2016, Physical review letters.

[26]  J. Åberg Catalytic coherence. , 2013, Physical Review Letters.

[27]  Ronnie Kosloff,et al.  Quantum Flywheel , 2016, 1602.04322.

[28]  Gerardo Adesso,et al.  Testing the Validity of the 'Local' and 'Global' GKLS Master Equations on an Exactly Solvable Model , 2017, Open Syst. Inf. Dyn..

[29]  Wojciech Hubert Zurek Quantum discord and Maxwell's demons , 2003 .

[30]  On thermodynamic inconsistencies in several photosynthetic and solar cell models and how to fixthem , 2017 .

[31]  E. Sudarshan,et al.  Completely Positive Dynamical Semigroups of N Level Systems , 1976 .

[32]  D. Poletti,et al.  Work and efficiency of quantum Otto cycles in power-law trapping potentials. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  M. Esposito,et al.  Quantum thermodynamics: a nonequilibrium Green's function approach. , 2014, Physical review letters.

[34]  Jonatan Bohr Brask,et al.  Small quantum absorption refrigerator in the transient regime: Time scales, enhanced cooling, and entanglement. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  W. Case,et al.  Wigner functions and Weyl transforms for pedestrians , 2008 .

[36]  M. Gurtin,et al.  The Mechanics and Thermodynamics of Continua , 2010 .

[37]  G'eraldine Haack,et al.  Markovian master equations for quantum thermal machines: local versus global approach , 2017, 1707.09211.

[38]  J. Parrondo,et al.  Entropy production and thermodynamic power of the squeezed thermal reservoir. , 2015, Physical review. E.

[39]  Mark A Ratner,et al.  Stochastic surrogate Hamiltonian. , 2008, The Journal of chemical physics.

[40]  L. Correa,et al.  Multistage quantum absorption heat pumps. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  D. Segal Two-level system in spin baths: non-adiabatic dynamics and heat transport. , 2014, The Journal of chemical physics.

[42]  E. Wigner On the quantum correction for thermodynamic equilibrium , 1932 .

[43]  Ronnie Kosloff,et al.  A quantum-mechanical heat engine operating in finite time. A model consisting of spin-1/2 systems as the working fluid , 1992 .

[44]  Hao Wang,et al.  Thermal entanglement in two-atom cavity QED and the entangled quantum Otto engine. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  Yi Gao,et al.  Molecular Heat Engines: Quantum Coherence Effects , 2017, Entropy.

[46]  G. Kurizki,et al.  Minimal universal quantum heat machine. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[48]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[49]  Ronnie Kosloff,et al.  Quantum lubrication: suppression of friction in a first-principles four-stroke heat engine. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  M. Partovi,et al.  Entanglement versus Stosszahlansatz: disappearance of the thermodynamic arrow in a high-correlation environment. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  runden Tisch,et al.  AM , 2020, Catalysis from A to Z.

[52]  T. Brandes,et al.  Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping , 2016, 1602.01340.

[53]  G. Look,et al.  Thermodynamics of a simple rubber‐band heat engine , 1975 .

[55]  The low density limit for anN-level system interacting with a free bose or fermi gas , 1985 .

[56]  Shaul Mukamel,et al.  Heat fluctuations and coherences in a quantum heat engine , 2012 .

[57]  George C. Schatz,et al.  The journal of physical chemistry letters , 2009 .

[58]  Herbert Walther,et al.  Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence , 2003, Science.

[59]  M. Horodecki,et al.  The entanglement of purification , 2002, quant-ph/0202044.

[60]  Marlan O Scully,et al.  Quantum heat engine power can be increased by noise-induced coherence , 2011, Proceedings of the National Academy of Sciences.

[61]  Ronnie Kosloff,et al.  Equivalence of Quantum Heat Machines, and Quantum-Thermodynamic Signatures , 2015 .

[62]  Gleb Maslennikov,et al.  Quantum absorption refrigerator with trapped ions , 2017, Nature Communications.

[63]  Daniel A. Lidar,et al.  Distance bounds on quantum dynamics , 2008, 0803.4268.

[64]  David Jennings,et al.  Description of quantum coherence in thermodynamic processes requires constraints beyond free energy , 2014, Nature Communications.

[65]  E. Lutz,et al.  Generalized clausius inequality for nonequilibrium quantum processes. , 2010, Physical review letters.

[66]  Ronnie Kosloff,et al.  The local approach to quantum transport may violate the second law of thermodynamics , 2014, 1402.3825.

[67]  David Jennings,et al.  The extraction of work from quantum coherence , 2015, 1506.07875.

[68]  H. Callen Thermodynamics and an Introduction to Thermostatistics , 1988 .

[69]  Florian Mintert,et al.  Performance of a quantum heat engine at strong reservoir coupling. , 2016, Physical review. E.

[70]  J. Rossnagel,et al.  Nanoscale heat engine beyond the Carnot limit. , 2013, Physical review letters.

[71]  Ronnie Kosloff,et al.  Quantum Heat Machines Equivalence, Work Extraction beyond Markovianity, and Strong Coupling via Heat Exchangers , 2016, Entropy.

[72]  J. Herskowitz,et al.  Proceedings of the National Academy of Sciences, USA , 1996, Current Biology.

[73]  Javier Prior,et al.  Coherence-assisted single-shot cooling by quantum absorption refrigerators , 2015, 1504.01593.

[74]  S. Du,et al.  Quantum Heat Engine Using Electromagnetically Induced Transparency. , 2017, Physical review letters.

[75]  S. Paolucci Continuum Mechanics and Thermodynamics of Matter: Mechanics and thermodynamics , 2016 .

[76]  J. Oppenheim,et al.  Thermodynamical approach to quantifying quantum correlations. , 2001, Physical review letters.

[77]  Paul Skrzypczyk,et al.  Extracting work from correlations , 2014, 1407.7765.

[78]  Craig A. Tracy,et al.  Communications in Mathematical Physics The Pearcey Process , 2006 .

[79]  E. O. Schulz-DuBois,et al.  Three-Level Masers as Heat Engines , 1959 .

[80]  A. E. Allahverdyan,et al.  Maximal work extraction from finite quantum systems , 2004 .

[81]  R. Kosloff,et al.  The multilevel four-stroke swap engine and its environment , 2014, 1404.6182.

[82]  C. Blanc,et al.  Nanoscale phase engineering of thermal transport with a Josephson heat modulator. , 2015, Nature nanotechnology.

[83]  David Jennings,et al.  Exchange fluctuation theorem for correlated quantum systems. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[84]  A. Wehrl General properties of entropy , 1978 .

[85]  C. Lubich,et al.  Error Bounds for Exponential Operator Splittings , 2000 .

[86]  Ronnie Kosloff,et al.  Discrete four-stroke quantum heat engine exploring the origin of friction. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[87]  J. G. Muga,et al.  Shortcuts to Adiabaticity , 2012, 1212.6343.

[88]  Milburn,et al.  Intrinsic decoherence in quantum mechanics. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[89]  G. Lindblad Expectations and entropy inequalities for finite quantum systems , 1974 .

[90]  S. V. Titov,et al.  Wigner function approach to the quantum Brownian motion of a particle in a potential. , 2007, Physical chemistry chemical physics : PCCP.

[91]  Bernhard H. Haak,et al.  Open Quantum Systems , 2019, Tutorials, Schools, and Workshops in the Mathematical Sciences.

[92]  Paul Skrzypczyk,et al.  The role of quantum information in thermodynamics—a topical review , 2015, 1505.07835.

[93]  D. Griffiths,et al.  Introduction to Quantum Mechanics , 1960 .

[94]  T. Rudolph,et al.  Entanglement and the thermodynamic arrow of time. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[95]  J. G. Muga,et al.  Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity. , 2009, Physical review letters.

[96]  G. Strang On the Construction and Comparison of Difference Schemes , 1968 .

[97]  R. Zambrini,et al.  Irreversible work and inner friction in quantum thermodynamic processes. , 2014, Physical review letters.

[98]  Ronnie Kosloff,et al.  Quantum refrigerators and the third law of thermodynamics. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[99]  D. Poletti,et al.  Quantum statistics and the performance of engine cycles. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[100]  Gerardo Adesso,et al.  Performance bound for quantum absorption refrigerators. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[101]  Paul Skrzypczyk,et al.  Thermodynamic cost of creating correlations , 2014, 1404.2169.

[102]  E. Lutz,et al.  When is a quantum heat engine quantum? , 2015, 1508.04128.

[103]  Ronnie Kosloff,et al.  Quantum heat engines and refrigerators: continuous devices. , 2013, Annual review of physical chemistry.

[104]  J. G. Muga,et al.  Noise resistant quantum control using dynamical invariants , 2017, 1711.09439.

[105]  Sebastian Deffner,et al.  Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity. , 2016, Physical review letters.

[106]  T. Paterek,et al.  The classical-quantum boundary for correlations: Discord and related measures , 2011, 1112.6238.

[107]  P. Corkum,et al.  Journal of Physics B: atomic, molecular and optical physics , 2015 .

[108]  Gershon Kurizki,et al.  On the operation of machines powered by quantum non-thermal baths , 2015, 1508.06519.

[109]  R. Farris Rubber Heat Engines, Analyses and Theory , 1977 .

[110]  U. Seifert,et al.  Universal Coherence-Induced Power Losses of Quantum Heat Engines in Linear Response. , 2017, Physical review letters.

[111]  Franco Nori,et al.  Quantum feedback: theory, experiments, and applications , 2014, 1407.8536.

[112]  Kavan Modi,et al.  Quantacell: powerful charging of quantum batteries , 2015, 1503.07005.

[113]  A. Allahverdyan,et al.  Work extremum principle: structure and function of quantum heat engines. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[114]  Jianshu Cao,et al.  Polaron effects on the performance of light-harvesting systems: a quantum heat engine perspective , 2015, 1508.04708.

[115]  M. Horodecki,et al.  Fundamental limitations for quantum and nanoscale thermodynamics , 2011, Nature Communications.

[116]  Ronnie Kosloff,et al.  The Quantum Harmonic Otto Cycle , 2016, Entropy.

[117]  M. Lewenstein,et al.  Quantum Entanglement , 2020, Quantum Mechanics.

[118]  Geva,et al.  Three-level quantum amplifier as a heat engine: A study in finite-time thermodynamics. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[119]  G. Lindblad On the existence of quantum subdynamics , 1996 .

[120]  E. Ott,et al.  The goodness of ergodic adiabatic invariants , 1987 .

[121]  Gian Luca Giorgi,et al.  Correlation approach to work extraction from finite quantum systems , 2014, 1404.7785.

[122]  Rafael Sánchez,et al.  Three-terminal energy harvester with coupled quantum dots. , 2015, Nature nanotechnology.

[123]  Massimiliano Esposito,et al.  Quantum-dot Carnot engine at maximum power. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[124]  Feldmann,et al.  Performance of discrete heat engines and heat pumps in finite time , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[125]  Franco Nori,et al.  Quantum thermodynamic cycles and quantum heat engines. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[126]  R. Stephenson A and V , 1962, The British journal of ophthalmology.

[127]  J M Gordon,et al.  Quantum thermodynamic cooling cycle. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[128]  Mark Fannes,et al.  Entanglement boost for extractable work from ensembles of quantum batteries. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[129]  G. Kurizki,et al.  Work and energy gain of heat-pumped quantized amplifiers , 2013, 1306.1472.

[130]  L. Di'osi,et al.  Continuous quantum measurement and itô formalism , 1988, 1812.11591.

[131]  Gershon Kurizki,et al.  Thermodynamics of quantum systems under dynamical control , 2015, 1503.01195.

[132]  E. Davies,et al.  Markovian master equations , 1974 .

[133]  M. Paternostro,et al.  More bang for your buck: Super-adiabatic quantum engines , 2013, Scientific Reports.