Advertisement

Physical Implementations of Quantum Absorption Refrigerators

  • Mark T. MitchisonEmail author
  • Patrick P. Potts
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 195)

Abstract

Absorption refrigerators are autonomous thermal machines that harness the spontaneous flow of heat from a hot bath into the environment in order to perform cooling. Here we discuss quantum realizations of absorption refrigerators in two different settings: namely, cavity and circuit quantum electrodynamics. We first provide a unified description of these machines in terms of the concept of virtual temperature. Next, we describe the two different physical setups in detail and compare their properties and performance. We conclude with an outlook on future work and open questions in this field of research.

Notes

Acknowledgements

MTM acknowledges funding from the ERC Synergy grant BioQ and the EU project QUCHIP. PPP acknowledges support from the Swiss National Science foundation, the NCCR Quantum Science and Technology (QSIT), the Swedish Research Council, and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 796700. We also acknowledge the COST MP1209 network “Thermodynamics in the quantum regime” which fostered the research described in this chapter.

References

  1. 1.
    R. Kosloff, A. Levy, Quantum heat engines and refrigerators: continuous devices. Annu. Rev. Phys. Chem. 65(1), 365 (2014).  https://doi.org/10.1146/annurev-physchem-040513-103724
  2. 2.
    D. Gelbwaser-Klimovsky, W. Niedenzu, G. Kurizki, Thermodynamics of quantum systems under dynamical control. Adv. At. Mol. Opt. Phys. 64, 329 (2015).  https://doi.org/10.1016/bs.aamop.2015.07.002ADSCrossRefGoogle Scholar
  3. 3.
    J. Goold, M. Huber, A. Riera, L. del Rio, P. Skrzypczyk, The role of quantum information in thermodynamics–a topical review. J. Phys. A: Math. Theor. 49(14), 143001 (2016).  https://doi.org/10.1088/1751-8113/49/14/143001
  4. 4.
    S. Vinjanampathy, J. Anders, Quantum thermodynamics. Contemp. Phys. 57(4), 545 (2016).  https://doi.org/10.1080/00107514.2016.1201896
  5. 5.
    G. Benenti, G. Casati, K. Saito, R.S. Whitney, Fundamental aspects of steady-state conversion of heat to work at the nanoscale. Phys. Rep. 694(1), (2017).  https://doi.org/10.1016/j.physrep.2017.05.008
  6. 6.
    R. Kosloff, Quantum thermodynamics: A dynamical viewpoint. Entropy 15(6), 2100 (2013).  https://doi.org/10.3390/e15062100
  7. 7.
    J.B. Brask, G. Haack, N. Brunner, M. Huber, Autonomous quantum thermal machine for generating steady-state entanglement. New J. Phys. 17(11), 113029 (2015).  https://doi.org/10.1088/1367-2630/17/11/113029
  8. 8.
    P.P. Hofer, J.B. Brask, M. Perarnau-Llobet, N. Brunner, Quantum thermal machine as a thermometer. Phys. Rev. Lett. 119(9), 090603 (2017). https://doi.org/10.1103/PhysRevLett. 119.090603
  9. 9.
    P. Erker, M.T. Mitchison, R. Silva, M.P. Woods, N. Brunner, M. Huber, Autonomous quantum clocks: does thermodynamics limit our ability to measure time? Phys. Rev. X 7(3), 031022 (2017).  https://doi.org/10.1103/PhysRevX.7.031022CrossRefGoogle Scholar
  10. 10.
    F. Clivaz, R. Silva, G. Haack, J.B. Brask, N. Brunner, M. Huber, Unifying paradigms of quantum refrigeration: how resource-control determines fundamental limits arXiv:1710.11624, [quant-ph] (2017)
  11. 11.
    M.P. Woods, R. Silva, J. Oppenheim, Autonomous quantum machines and finite sized clocks. Ann. Henri Poincaré. 20(1), 125–128 (2019).  https://doi.org/10.1007/s00023-018-0736-9
  12. 12.
    K.E. Dorfman, D.V. Voronine, S. Mukamel, M.O. Scully, Photosynthetic reaction center as a quantum heat engine. Proc. Natl. Acad. Sci. U. S. A. 110(8), 2746–2751 (2013).  https://doi.org/10.1073/pnas.1212666110
  13. 13.
    C. Creatore, M.A. Parker, S. Emmott, A.W. Chin, Efficient biologically inspired photocell enhanced by delocalized quantum states. Phys. Rev. Lett. 111(25), 253601 (2013).  https://doi.org/10.1103/PhysRevLett.111.253601
  14. 14.
    N. Killoran, S.F. Huelga, M.B. Plenio, Enhancing light-harvesting power with coherent vibrational interactions: A quantum heat engine picture. J. Chem. Phys. 143(15), 155102 (2015).  https://doi.org/10.1063/1.4932307
  15. 15.
    J.P. Palao, R. Kosloff, J.M. Gordon, Quantum thermodynamic cooling cycle. Phys. Rev. E 64(5), 056130 (2001).  https://doi.org/10.1103/PhysRevE.64.056130ADSCrossRefGoogle Scholar
  16. 16.
    N. Linden, S. Popescu, P. Skrzypczyk, How small can thermal machines be? The smallest possible refrigerator. Phys. Rev. Lett. 105(13), 130401 (2010). https://doi.org/10.1103/PhysRevLett. 105.130401
  17. 17.
    A. Levy, R. Kosloff, Quantum Absorption Refrigerator. Phys. Rev. Lett. 108(7), 070604 (2012). https://doi.org/10.1103/PhysRevLett. 108.070604
  18. 18.
    Y.-X. Chen, S.-W. Li, Quantum refrigerator driven by current noise. EPL (Europhys. Lett.) 97(4), 40003 (2012).  https://doi.org/10.1209/0295-5075/97/40003
  19. 19.
    A. Mari, J. Eisert, Cooling by heating: Very hot thermal light can significantly cool quantum systems. Phys. Rev. Lett. 108(12), 120602 (2012). https://doi.org/10.1103/PhysRevLett. 108.120602
  20. 20.
    D. Venturelli, R. Fazio, V. Giovannetti, Minimal self-contained quantum refrigeration machine based on four quantum dots. Phys. Rev. Lett. 110(25), 256801 (2013). https://doi.org/10.1103/PhysRevLett. 110.256801
  21. 21.
    M.T. Mitchison, M. Huber, J. Prior, M.P. Woods, M.B. Plenio, Realising a quantum absorption refrigerator with an atom-cavity system. Quantum Sci. Technol. 1(1), 015001 (2016).  https://doi.org/10.1088/2058-9565/1/1/015001
  22. 22.
    P.P. Hofer, M. Perarnau-Llobet, J.B. Brask, R. Silva, M. Huber, N. Brunner, Autonomous quantum refrigerator in a circuit QED architecture based on a Josephson junction. Phys. Rev. B 94(23), 235420 (2016).  https://doi.org/10.1103/PhysRevB.94.235420ADSCrossRefGoogle Scholar
  23. 23.
    G. Maslennikov, S. Ding, R. Hablutzel, J. Gan, A. Roulet, S. Nimmrichter, J. Dai, V. Scarani, D. Matsukevich, Quantum absorption refrigerator with trapped ions. Nat. Comm. 10, 202 (2019).  https://doi.org/10.1038/s41467-018-08090-0
  24. 24.
    N. Brunner, N. Linden, S. Popescu, P. Skrzypczyk, Virtual qubits, virtual temperatures, and the foundations of thermodynamics. Phys. Rev. E 85(5), 051117 (2012).  https://doi.org/10.1103/PhysRevE.85.051117ADSCrossRefGoogle Scholar
  25. 25.
    P. Skrzypczyk, R. Silva, N. Brunner, Passivity, complete passivity, and virtual temperatures. Phys. Rev. E 91(5), 052133 (2015).  https://doi.org/10.1103/PhysRevE.91.052133ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    L.A. Correa, J.P. Palao, D. Alonso, Internal dissipation and heat leaks in quantum thermodynamic cycles. Phys. Rev. E 92(3), 032136 (2015).  https://doi.org/10.1103/PhysRevE.92.032136ADSCrossRefGoogle Scholar
  27. 27.
    L.A. Correa, J.P. Palao, G. Adesso, D. Alonso, Performance bound for quantum absorption refrigerators. Phys. Rev. E 87(4), 042131 (2013).  https://doi.org/10.1103/PhysRevE.87.042131ADSCrossRefGoogle Scholar
  28. 28.
    P.P. Hofer, M. Perarnau-Llobet, L.D.M. Miranda, G. Haack, R. Silva, J.B. Brask, N. Brunner, Markovian master equations for quantum thermal machines: local versus global approach. New J. Phys. 19(12), 123037 (2017).  https://doi.org/10.1088/1367-2630/aa964f
  29. 29.
    J.O. González, L.A. Correa, G. Nocerino, J.P. Palao, D. Alonso, G. Adesso, Testing the validity of the ‘local’ and ‘global’ GKLS master equations on an exactly solvable model. Open Syst. Inf. Dyn. 24(04), 1740010 (2017).  https://doi.org/10.1142/s1230161217400108
  30. 30.
    S. Seah, S. Nimmrichter, V. Scarani, Refrigeration beyond weak internal coupling. Phys. Rev. E 98(1), 012131 (2018).  https://doi.org/10.1103/PhysRevE.98.012131
  31. 31.
    H.E.D. Scovil, E.O. Schulz-DuBois, Three-level masers as heat engines. Phys. Rev. Lett. 2(6), 262–263 (1959). https://doi.org/10.1103/PhysRevLett. 2.262
  32. 32.
    P. Skrzypczyk, N. Brunner, N. Linden, S. Popescu, The smallest refrigerators can reach maximal efficiency. J. Phys. A: Math. Theor. 44(49), 492002 (2011).  https://doi.org/10.1088/1751-8113/44/49/492002
  33. 33.
    J.B. Brask, N. Brunner, Small quantum absorption refrigerator in the transient regime: Time scales, enhanced cooling, and entanglement. Phys. Rev. E 92(6), 062101 (2015).  https://doi.org/10.1103/PhysRevE.92.062101ADSCrossRefGoogle Scholar
  34. 34.
    M.T. Mitchison, M.P. Woods, J. Prior, M. Huber, Coherence-assisted single-shot cooling by quantum absorption refrigerators. New J. Phys. 17(11), 115013 (2015).  https://doi.org/10.1088/1367-2630/17/11/115013
  35. 35.
    R. Miller, T.E. Northup, K.M. Birnbaum, A. Boca, A.D. Boozer, H.J. Kimble, Trapped atoms in cavity QED: coupling quantized light and matter. J. Phys. B 38(9), S551 (2005).  https://doi.org/10.1088/0953-4075/38/9/007
  36. 36.
    H. Walther, B.T.H. Varcoe, B.-G. Englert, T. Becker, Cavity quantum electrodynamics. Rep. Prog. Phys. 69(5), 1325–1382 (2006).  https://doi.org/10.1088/0034-4885/69/5/r02
  37. 37.
    S. Haroche, Nobel Lecture: Controlling photons in a box and exploring the quantum to classical boundary. Rev. Mod. Phys. 85(3), 1083–1102 (2013).  https://doi.org/10.1103/revmodphys.85.1083
  38. 38.
    D. Leibfried, R. Blatt, C. Monroe, D. Wineland, Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75(1), 281–324 (2003). https://doi.org/10.1103/RevModPhys. 75.281
  39. 39.
    C.A. Blockley, D.F. Walls, H. Risken, Quantum collapses and revivals in a quantized trap. EPL (Europhys. Lett.) 17(6), 509–514 (1992).  https://doi.org/10.1209/0295-5075/17/6/006
  40. 40.
    V. Bužek, G. Drobný, M.S. Kim, G. Adam, P.L. Knight, Cavity QED with cold trapped ions. Phys. Rev. A 56(3), 2352–2360 (1997).  https://doi.org/10.1103/physreva.56.2352
  41. 41.
    E.T. Jaynes, F.W. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE 51(1), 89–109 (1963).  https://doi.org/10.1109/proc.1963.1664
  42. 42.
    B.W. Shore, P.L. Knight, The jaynes-cummings model. J. Mod. Opt. 40(7), 1195–1238 (1993).  https://doi.org/10.1080/09500349314551321
  43. 43.
    R. Winston, Light collection within the framework of geometrical optics. J. Opt. Soc. Am. 60(2), 245 (1970).  https://doi.org/10.1364/josa.60.000245
  44. 44.
    R. Alicki, D. Gelbwaser-Klimovsky, Non-equilibrium quantum heat machines. New J. Phys. 17(11), 115012 (2015).  https://doi.org/10.1088/1367-2630/17/11/115012
  45. 45.
    W. Martienssen, E. Spiller, Coherence and fluctuations in light beams. Am. J. Phys. 32(12), 919–926 (1964).  https://doi.org/10.1119/1.1970023
  46. 46.
    F.T. Arecchi, Measurement of the statistical distribution of Gaussian and laser sources. Phys. Rev. Lett. 15(24), 912–916 (1965).  https://doi.org/10.1103/physrevlett.15.912
  47. 47.
    P.F. Herskind, A. Dantan, J.P. Marler, M. Albert, M. Drewsen, Realization of collective strong coupling with ion Coulomb crystals in an optical cavity. Nat. Phys. 5(7), 494–498 (2009).  https://doi.org/10.1038/nphys1302
  48. 48.
    E.D. Black, An introduction to Pound-Drever-Hall laser frequency stabilization. Am. J. Phys. 69(1), 79–87 (2001).  https://doi.org/10.1119/1.1286663
  49. 49.
    P.P. Hofer, J.-R. Souquet, A.A. Clerk, Quantum heat engine based on photon-assisted Cooper pair tunneling. Phys. Rev. B 93(4), 041418(R) (2016).  https://doi.org/10.1103/PhysRevB.93.041418ADSCrossRefGoogle Scholar
  50. 50.
    R.J. Schoelkopf, S.M. Girvin, Wiring up quantum systems. Nature 451(7179), 664 (2008).  https://doi.org/10.1038/451664a
  51. 51.
    U. Vool, M. Devoret, Introduction to quantum electromagnetic circuits. Int. J. Theor. Appl. 45(7), 897 (2017).  https://doi.org/10.1002/cta.2359
  52. 52.
    A.D. Armour, M.P. Blencowe, E. Brahimi, A.J. Rimberg, Universal quantum fluctuations of a cavity mode driven by a Josephson junction. Phys. Rev. Lett. 111(24), 247001 (2013). https://doi.org/10.1103/PhysRevLett. 111.247001
  53. 53.
    V. Gramich, B. Kubala, S. Rohrer, J. Ankerhold, From Coulomb-Blockade to Nonlinear Quantum Dynamics in a Superconducting Circuit with a Resonator. Phys. Rev. Lett. 111(24), 247002 (2013). https://doi.org/10.1103/PhysRevLett. 111.247002
  54. 54.
    W.A. Al-Saidi, D. Stroud, Eigenstates of a small Josephson junction coupled to a resonant cavity. Phys. Rev. B 65(1), 014512 (2001).  https://doi.org/10.1103/PhysRevB.65.014512ADSCrossRefGoogle Scholar
  55. 55.
    G.-L. Ingold, Y.V. Nazarov, Charge tunneling rates in ultrasmall junctions, in Single Charge Tunneling, ed. by H. Grabert, M.H. Devoret (Springer, Berlin, 1992).  https://doi.org/10.1007/978-1-4757-2166-9
  56. 56.
    D.V. Averin, Y.V. Nazarov, A.A. Odintsov, Incoherent tunneling of the Cooper pairs and magnetic flux quanta in ultrasmall Josephson junctions. Phys. B 165, 945 (1990).  https://doi.org/10.1016/S0921-4526(09)80058-6ADSCrossRefGoogle Scholar
  57. 57.
    T. Holst, D. Esteve, C. Urbina, M.H. Devoret, Effect of a transmission line resonator on a small capacitance tunnel junction. Phys. Rev. Lett. 73(25), 3455 (1994). https://doi.org/10.1103/PhysRevLett. 73.3455
  58. 58.
    J. Basset, H. Bouchiat, R. Deblock, Emission and absorption quantum noise measurement with an on-chip resonant circuit. Phys. Rev. Lett. 105(16), 166801 (2010). https://doi.org/10.1103/PhysRevLett. 105.166801
  59. 59.
    M. Hofheinz, F. Portier, Q. Baudouin, P. Joyez, D. Vion, P. Bertet, P. Roche, D. Esteve, Bright side of the Coulomb Blockade. Phys. Rev. Lett. 106(21), 217005 (2011). https://doi.org/10.1103/PhysRevLett. 106.217005
  60. 60.
    J.-R. Souquet, A.A. Clerk, Fock-state stabilization and emission in superconducting circuits using dc-biased Josephson junctions. Phys. Rev. A 93(6), 060301 (2016).  https://doi.org/10.1103/PhysRevA.93.060301ADSCrossRefGoogle Scholar
  61. 61.
    S. Dambach, B. Kubala, V. Gramich, J. Ankerhold, Time-resolved statistics of nonclassical light in Josephson photonics. Phys. Rev. B 92(5), 054508 (2015).  https://doi.org/10.1103/PhysRevB.92.054508ADSCrossRefGoogle Scholar
  62. 62.
    J. Leppäkangas, G. Johansson, M. Marthaler, M. Fogelström, Nonclassical photon pair production in a voltage-biased Josephson junction. Phys. Rev. Lett. 110(26), 267004 (2013). https://doi.org/10.1103/PhysRevLett. 110.267004
  63. 63.
    A.D. Armour, B. Kubala, J. Ankerhold, Josephson photonics with a two-mode superconducting circuit. Phys. Rev. B 91(18), 184508 (2015).  https://doi.org/10.1103/PhysRevB.91.184508
  64. 64.
    M. Trif, P. Simon, Photon cross-correlations emitted by a Josephson junction in two microwave cavities. Phys. Rev. B 92(1), 014503 (2015).  https://doi.org/10.1103/PhysRevB.92.014503ADSCrossRefGoogle Scholar
  65. 65.
    S. Dambach, B. Kubala, J. Ankerhold, Generating entangled quantum microwaves in a Josephson-photonics device. New J. Phys. 19(2), 023027 (2017).  https://doi.org/10.1088/1367-2630/aa5bb6
  66. 66.
    O. Dmytruk, M. Trif, P. Simon, Josephson effect in topological superconducting rings coupled to a microwave cavity. Phys. Rev. B 94(11), 115423 (2016).  https://doi.org/10.1103/PhysRevB.94.115423ADSCrossRefGoogle Scholar
  67. 67.
    M. Westig, B. Kubala, O. Parlavecchio, Y. Mukharsky, C. Altimiras, P. Joyez, D. Vion, P. Roche, D. Esteve, M. Hofheinz, M. Trif, P. Simon, J. Ankerhold, F. Portier, Emission of nonclassical radiation by inelastic Cooper pair tunneling. Phys. Rev. Lett. 119(13), 137001 (2017). https://doi.org/10.1103/PhysRevLett. 119.137001
  68. 68.
    F. Chen, J. Li, A.D. Armour, E. Brahimi, J. Stettenheim, A.J. Sirois, R.W. Simmonds, M.P. Blencowe, A.J. Rimberg, Realization of a single-Cooper-pair Josephson laser. Phys. Rev. B 90(2), 020506 (2014).  https://doi.org/10.1103/PhysRevB.90.020506ADSCrossRefGoogle Scholar
  69. 69.
    S. Jebari, F. Blanchet, A. Grimm, D. Hazra, R. Albert, P. Joyez, D. Vion, D. Estève, F. Portier, M. Hofheinz, Near-quantum-limited amplification from inelastic Cooper-pair tunnelling. Nat. Electron 1(4), 223 (2018).  https://doi.org/10.1038/s41928-018-0055-7
  70. 70.
    S. Nimmrichter, J. Dai, A. Roulet, V. Scarani, Quantum and classical dynamics of a three-mode absorption refrigerator. Quantum 1, 37 (2017). https://doi.org/10.22331/q-2017-12-11-37
  71. 71.
    N. Lörch, C. Bruder, N. Brunner, P.P. Hofer, Optimal work extraction from quantum states by photo-assisted Cooper pair tunneling. Quantum Sci. Technol. 3, 035014 (2018).  https://doi.org/10.1088/2058-9565/aacbf3ADSCrossRefGoogle Scholar
  72. 72.
    C. Gogolin, J. Eisert, Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems. Rep. Prog. Phys. 79(5), 056001 (2016).  https://doi.org/10.1088/0034-4885/79/5/056001
  73. 73.
    N. Brunner, M. Huber, N. Linden, S. Popescu, R. Silva, P. Skrzypczyk, Entanglement enhances cooling in microscopic quantum refrigerators. Phys. Rev. E 89(3), 032115 (2014).  https://doi.org/10.1103/PhysRevE.89.032115ADSCrossRefGoogle Scholar
  74. 74.
    L.A. Correa, J.P. Palao, G. Adesso, D. Alonso, Optimal performance of endoreversible quantum refrigerators. Phys. Rev. E 90(6), 062124 (2014).  https://doi.org/10.1103/PhysRevE.90.062124ADSCrossRefGoogle Scholar
  75. 75.
    A. Levy, L. Diósi, R. Kosloff, Quantum flywheel. Phys. Rev. A 93(5), 052119 (2016).  https://doi.org/10.1103/PhysRevA.93.052119ADSCrossRefGoogle Scholar
  76. 76.
    C. Elouard, D. Herrera-Martí, B. Huard, A. Auffèves, Extracting Work from quantum measurement in Maxwell’s Demon engines. Phys. Rev. Lett. 118(26), 260603 (2017). https://doi.org/10.1103/PhysRevLett. 118.260603
  77. 77.
    M.H. Mohammady, J. Anders, A quantum Szilard engine without heat from a thermal reservoir. New J. Phys. 19(11), 113026 (2017).  https://doi.org/10.1088/1367-2630/aa8ba1
  78. 78.
    J.M.R. Parrondo, J.M. Horowitz, T. Sagawa, Thermodynamics of information. Nat. Phys. 11(2), 131–139 (2015).  https://doi.org/10.1038/nphys3230
  79. 79.
    A.S.L. Malabarba, A.J. Short, P. Kammerlander, Clock-driven quantum thermal engines. New J. Phys. 17(4), 045027 (2015).  https://doi.org/10.1088/1367-2630/17/4/045027
  80. 80.
    A.C. Barato, U. Seifert, Cost and precision of Brownian clocks. Phys. Rev. X 6(4), 041053 (2016).  https://doi.org/10.1103/physrevx.6.041053

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institut für Theoretische Physik, Universität UlmUlmGermany
  2. 2.Department of Applied PhysicsUniversity of GenevaGenevaSwitzerland
  3. 3.Physics Department and NanoLundLund UniversityLundSweden

Personalised recommendations