Advertisement

Quantum Rotor Engines

  • Stella SeahEmail author
  • Stefan Nimmrichter
  • Alexandre Roulet
  • Valerio Scarani
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 195)

Abstract

This chapter presents autonomous quantum engines that generate work in the form of directed motion for a rotor. We first formulate a prototypical clock-driven model in a time-dependent framework and demonstrate how it can be translated into an autonomous engine with the introduction of a planar rotor degree of freedom. The rotor plays both the roles of internal engine clock and of work repository. Using the example of a single-qubit piston engine, the thermodynamic performance is then reviewed. We evaluate the extractable work in terms of ergotropy, the kinetic energy associated to net directed rotation, as well as the intrinsic work based on the exerted torque under autonomous operation; and we compare them with the actual energy output to an external dissipative load. The chapter closes with a quantum-classical comparison of the engine’s dynamics. For the single-qubit piston example, we propose two alternative representations of the qubit in an entirely classical framework: (i) a coin flip model and (ii) a classical magnetic moment, showing subtle differences between the quantum and classical descriptions

Notes

Acknowledgements

This research is supported by the Singapore Ministry of Education through the Academic Research Fund Tier 3 (Grant No. MOE2012-T3-1-009); and by the same MoE and the National Research Foundation, Prime Minister’s Office, Singapore, under the Research Centres of Excellence programme. In addition, this work was financially supported by the Swiss SNF and the NCCR Quantum Science and Technology.

References

  1. 1.
    A. Roulet, S. Nimmrichter, J.M. Arrazola, S. Seah, V. Scarani, Phys. Rev. E 95, 062131 (2017).  https://doi.org/10.1103/PhysRevE.95.062131ADSCrossRefGoogle Scholar
  2. 2.
    S. Seah, S. Nimmrichter, V. Scarani, New J. Phys. 20(4), 043045 (2018).  https://doi.org/10.1088/1367-2630/aab704ADSCrossRefGoogle Scholar
  3. 3.
    A. Roulet, S. Nimmrichter, J.M. Taylor, Quantum Sci. Technol. 3, 035008 (2018).  https://doi.org/10.1088/2058-9565/aac40d
  4. 4.
    F. Tonner, G. Mahler, Phys. Rev. E 72, 066118 (2005).  https://doi.org/10.1103/PhysRevE.72.066118ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    M. Youssef, G. Mahler, A.S. Obada, Phys. E 42(3), 454 (2010).  https://doi.org/10.1016/j.physe.2009.06.032CrossRefGoogle Scholar
  6. 6.
    N. Brunner, N. Linden, S. Popescu, P. Skrzypczyk, Phys. Rev. E 85, 051117 (2012).  https://doi.org/10.1103/PhysRevE.85.051117ADSCrossRefGoogle Scholar
  7. 7.
    L. Gilz, E.P. Thesing, J.R. Anglin (2013), arXiv:1304.3222
  8. 8.
    A. Mari, A. Farace, V. Giovannetti, J. Phys. B 48(17), 175501 (2015).  https://doi.org/10.1088/0953-4075/48/17/175501
  9. 9.
    A. Levy, L. Diósi, R. Kosloff, Phys. Rev. A 93, 052119 (2016).  https://doi.org/10.1103/PhysRevA.93.052119ADSCrossRefGoogle Scholar
  10. 10.
    A.U.C. Hardal, N. Aslan, C.M. Wilson, Ö.E. Müstecaplıoğlu, Phys. Rev. E 96, 062120 (2017).  https://doi.org/10.1103/PhysRevE.96.062120
  11. 11.
    R. Alicki, D. Gelbwaser-Klimovsky, A. Jenkins, Ann. Phys. 378, 71 (2017).  https://doi.org/10.1016/j.aop.2017.01.003ADSCrossRefGoogle Scholar
  12. 12.
    R. Kosloff, J. Chem. Phys. 80(4), 1625 (1984).  https://doi.org/10.1063/1.446862ADSCrossRefGoogle Scholar
  13. 13.
    M.O. Scully, M.S. Zubairy, G.S. Agarwal, H. Walther, Science 299(5608), 862 (2003).  https://doi.org/10.1126/science.1078955ADSCrossRefGoogle Scholar
  14. 14.
    Y. Rezek, R. Kosloff, New J. Phys. 8(5), 83 (2006).  https://doi.org/10.1088/1367-2630/8/5/083
  15. 15.
    R. Alicki, Open Syst. Inf. Dyn. 21(01n02), 1440002 (2014).  https://doi.org/10.1142/S1230161214400022
  16. 16.
    K. Zhang, F. Bariani, P. Meystre, Phys. Rev. Lett. 112, 150602 (2014).  https://doi.org/10.1103/PhysRevLett.112.150602
  17. 17.
    R. Uzdin, A. Levy, R. Kosloff, Entropy 18(4) (2016).  https://doi.org/10.3390/e18040124
  18. 18.
    R. Alicki, J. Phys. A Math. Gen. 12(5), L103 (1979).  https://doi.org/10.1088/0305-4470/12/5/007ADSCrossRefGoogle Scholar
  19. 19.
    X.L. Huang, T. Wang, X.X. Yi, Phys. Rev. E 86, 051105 (2012).  https://doi.org/10.1103/PhysRevE.86.051105ADSCrossRefGoogle Scholar
  20. 20.
    O. Abah, E. Lutz, EPL (Europhys. Lett.) 106(2), 20001 (2014).  https://doi.org/10.1209/0295-5075/106/20001
  21. 21.
    J. Roßnagel, O. Abah, F. Schmidt-Kaler, K. Singer, E. Lutz, Phys. Rev. Lett. 112, 030602 (2014).  https://doi.org/10.1103/PhysRevLett.112.030602ADSCrossRefGoogle Scholar
  22. 22.
    W. Niedenzu, D. Gelbwaser-Klimovsky, A.G. Kofman, G. Kurizki, New J. Phys. 18(8), 083012 (2016). https://doi.org/10.1088/1367-2630/18/8/083012
  23. 23.
    J. Klaers, S. Faelt, A. Imamoglu, E. Togan, Phys. Rev. X 7, 031044 (2017).  https://doi.org/10.1103/PhysRevX.7.031044CrossRefGoogle Scholar
  24. 24.
    R. Wulfert, M. Oechsle, T. Speck, U. Seifert, Phys. Rev. E 95, 050103 (2017).  https://doi.org/10.1103/PhysRevE.95.050103ADSCrossRefGoogle Scholar
  25. 25.
    A. Rivas, A.D.K. Plato, S.F. Huelga, M.B. Plenio, New J. Phys. 12(11), 113032 (2010).  https://doi.org/10.1088/1367-2630/12/11/113032ADSCrossRefGoogle Scholar
  26. 26.
    A. Levy, R. Kosloff, Europhys. Lett. 107(2), 20004 (2014).  https://doi.org/10.1209/0295-5075/107/20004ADSCrossRefGoogle Scholar
  27. 27.
    P.P. Hofer, M. Perarnau-Llobet, L.D.M. Miranda, G. Haack, R. Silva, J.B. Brask, N. Brunner, New J. Phys. 19, 123037 (2017).  https://doi.org/10.1088/1367-2630/aa964fADSCrossRefGoogle Scholar
  28. 28.
    J.O. González, L.A. Correa, G. Nocerino, J.P. Palao, D. Alonso, G. Adesso, Open Syst. Inf. Dyn. 24, 1740010 (2017).  https://doi.org/10.1142/S1230161217400108MathSciNetCrossRefGoogle Scholar
  29. 29.
    J. Johansson, P. Nation, F. Nori, Comput. Phys. Commun. 184(4), 1234 (2013).  https://doi.org/10.1016/j.cpc.2012.11.019
  30. 30.
    A.E. Allahverdyan, R. Balian, T.M. Nieuwenhuizen, Europhys. Lett. 67(4), 565 (2004).  https://doi.org/10.1209/epl/i2004-10101-2
  31. 31.
    J. Goold, M. Huber, A. Riera, L. del Rio, P. Skrzypczyk, J. Phys. A 49(14), 143001 (2016).  https://doi.org/10.1088/1751-8113/49/14/143001
  32. 32.
    B.A. Stickler, B. Schrinski, K. Hornberger, Phys. Rev. Lett. 121, 040401 (2018).  https://doi.org/10.1103/PhysRevLett.121.040401ADSCrossRefGoogle Scholar
  33. 33.
    A. Caldeira, A. Leggett, Phys. A 121(3), 587 (1983).  https://doi.org/10.1016/0378-4371(83)90013-4MathSciNetCrossRefGoogle Scholar
  34. 34.
    H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).  https://doi.org/10.1093/acprof:oso/9780199213900.001.0001
  35. 35.
    S. Nimmrichter, J. Dai, A. Roulet, V. Scarani, Quantum 1, 37 (2017).  https://doi.org/10.22331/q-2017-12-11-37
  36. 36.
    N.I. Fisher, Statistical Analysis of Circular Data (Cambridge University Press, Cambridge, 1995).  https://doi.org/10.1002/bimj.4710380307
  37. 37.
    J.L. García-Palacios, On the Statics and Dynamics of Magnetoanisotropic Nanoparticles (Wiley-Blackwell, New Jercy, 2007), pp. 1–210.  https://doi.org/10.1002/9780470141717.ch1

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Stella Seah
    • 1
    Email author
  • Stefan Nimmrichter
    • 2
  • Alexandre Roulet
    • 3
  • Valerio Scarani
    • 1
    • 2
  1. 1.Department of PhysicsNational University of SingaporeSingaporeSingapore
  2. 2.Centre for Quantum TechnologiesNational University of SingaporeSingaporeSingapore
  3. 3.Department of PhysicsUniversity of BaselBaselSwitzerland

Personalised recommendations