- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Wave-particle duality in a quantum heat engine

Marcelo Janovitch*, Matteo Brunelli, and Patrick P. Potts†

  • Department of Physics and Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland

  • *m.janovitch@unibas.ch
  • †patrick.potts@unibas.ch
PDF

Phys. Rev. Research 5, L042007 – Published 5 October, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L042007

Abstract

According to the wave-particle duality (WPD), quantum systems show both particlelike and wavelike behavior and cannot be described using only one of these classical concepts. Identifying quantum features that cannot be reproduced by any classical means is key for quantum technology. This task is often pursued by comparing the quantum system of interest with a suitable classical counterpart. However, the WPD implies that a comparison with a single classical model is generally insufficient; at least one wave model and one particle model should be considered. Here we exploit this insight and contrast a bosonic quantum heat engine with two classical counterparts, one based on waves and one based on particles. While both classical models reproduce the average output power of the quantum engine, neither reproduces its fluctuations. The wave model fails to capture the vacuum fluctuations, while the particle model cannot reproduce bunching to its full extent. We find regimes where wave and particle descriptions agree with the quantum one, as well as a regime where neither classical model is adequate, revealing the role of the WPD in nonequilibrium bosonic transport.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (50)

  1. A. Einstein, On a heuristic point of view concerning the production and transformation of light, Ann. Phys. (Berlin) 322, 132 (1905).
  2. A. Einstein, On the present status of the radiation problem, Phys. Z. 10, 185 (1909).
  3. S. Weinberg, Lectures on Quantum Mechanics, 2nd ed. (Cambridge University Press, Cambridge, 2015).
  4. A. H. Compton, A quantum theory of the scattering of x-rays by light elements, Phys. Rev. 21, 483 (1923).
  5. C. Davisson and L. H. Germer, Diffraction of electrons by a crystal of nickel, Phys. Rev. 30, 705 (1927).
  6. W. D. Oliver, J. Kim, R. C. Liu, and Y. Yamamoto, Hanbury Brown and Twiss-type experiment with electrons, Science 284, 299 (1999).
  7. W. K. Wootters and W. H. Zurek, Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr's principle, Phys. Rev. D 19, 473 (1979).
  8. B.-G. Englert, Fringe visibility and which-way information: An inequality, Phys. Rev. Lett. 77, 2154 (1996).
  9. C. Dittel, G. Dufour, G. Weihs, and A. Buchleitner, Wave-particle duality of many-body quantum states, Phys. Rev. X 11, 031041 (2021).
  10. K. Wang, Q. Xu, S. Zhu, and X.-s. Ma, Quantum wave-particle superposition in a delayed-choice experiment, Nat. Photonics 13, 872 (2019).
  11. M. T. Mitchison, M. P. Woods, J. Prior, and M. Huber, Coherence-assisted single-shot cooling by quantum absorption refrigerators, New J. Phys. 17, 115013 (2015).
  12. S. Nimmrichter, J. Dai, A. Roulet, and V. Scarani, Quantum and classical dynamics of a three-mode absorption refrigerator, Quantum 1, 37 (2017).
  13. A. A. S. Kalaee, A. Wacker, and P. P. Potts, Violating the thermodynamic uncertainty relation in the three-level maser, Phys. Rev. E 104, L012103 (2021).
  14. K. Korzekwa and M. Lostaglio, Quantum advantage in simulating stochastic processes, Phys. Rev. X 11, 021019 (2021).
  15. K. Prech, P. Johansson, E. Nyholm, G. T. Landi, C. Verdozzi, P. Samuelsson, and P. P. Potts, Entanglement and thermokinetic uncertainty relations in coherent mesoscopic transport, Phys. Rev. Res. 5, 023155 (2023).
  16. W. G. Unruh and W. H. Zurek, Reduction of a wave packet in quantum Brownian motion, Phys. Rev. D 40, 1071 (1989).
  17. W. H. Zurek, S. Habib, and J. P. Paz, Coherent States via Decoherence, Phys. Rev. Lett. 70, 1187 (1993).
  18. W. H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys. 75, 715 (2003).
  19. R. W. Spekkens, Evidence for the epistemic view of quantum states: A toy theory, Phys. Rev. A 75, 032110 (2007).
  20. R. W. Spekkens, Quasi-quantization: Classical statistical theories with an epistemic restriction, in Quantum Theory: Informational Foundations and Foils, edited by G. Chiribella and R. W. Spekkens (Springer, Dordrecht, 2016), pp. 83–135.
  21. A. W. Harrow and A. Montanaro, Quantum computational supremacy, Nature (London) 549, 203 (2017).
  22. L. Mandel, Non-classical states of the electromagnetic field, Phys. Scr. T12, 34 (1986).
  23. A. Ghosh, W. Niedenzu, V. Mukherjee, and G. Kurizki, Thermodynamic principles and implementations of quantum machines, in Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, edited by F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (Springer International, Cham, Switzerland, 2018), pp. 37–66.
  24. T. Kerremans, P. Samuelsson, and P. Potts, Probabilistically violating the first law of thermodynamics in a quantum heat engine, SciPost Phys. 12, 168 (2022).
  25. R. Kosloff, A quantum mechanical open system as a model of a heat engine, J. Chem. Phys. 80, 1625 (1984).
  26. P. P. Hofer, J.-R. Souquet, and A. A. Clerk, Quantum heat engine based on photon-assisted Cooper pair tunneling, Phys. Rev. B 93, 041418(R) (2016).
  27. R. Alicki and R. Kosloff, Introduction to quantum thermodynamics: History and prospects, in Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, edited by F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (Springer International, Cham, Switzerland, 2018), pp. 1–33.
  28. 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, and F. Portier, Emission of nonclassical radiation by inelastic Cooper pair tunneling, Phys. Rev. Lett. 119, 137001 (2017).
  29. A. Peugeot, G. Ménard, S. Dambach, M. Westig, B. Kubala, Y. Mukharsky, C. Altimiras, P. Joyez, D. Vion, P. Roche, D. Esteve, P. Milman, J. Leppäkangas, G. Johansson, M. Hofheinz, J. Ankerhold, and F. Portier, Generating two continuous entangled microwave beams using a dc-biased Josephson junction, Phys. Rev. X 11, 031008 (2021).
  30. G. C. Menard, A. Peugeot, C. Padurariu, C. Rolland, B. Kubala, Y. Mukharsky, Z. Iftikhar, C. Altimiras, P. Roche, H. L. Sueur, P. Joyez, D. Vion, D. Esteve, J. Ankerhold, and F. Portier, Emission of Photon Multiplets by a dc-Biased Superconducting Circuit, Phys. Rev. X 12, 021006 (2022).
  31. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  32. J. Monsel, N. Dashti, S. K. Manjeshwar, J. Eriksson, H. Ernbrink, E. Olsson, E. Torneus, W. Wieczorek, and J. Splettstoesser, Optomechanical cooling with coherent and squeezed light: The thermodynamic cost of opening the heat valve, Phys. Rev. A 103, 063519 (2021).
  33. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L042007 for detailed calculations of the average current and noise in each model and a short note on the connection between power and work variance.
  34. C. W. Gardiner and M. J. Collett, Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation, Phys. Rev. A 31, 3761 (1985).
  35. C. W. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods With Applications to Quantum Optics (Springer, New York, 2004).
  36. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Generation of optical harmonics, Phys. Rev. Lett. 7, 118 (1961).
  37. Y. V. G. S. Murti and C. Vijayan, A phenomenological view of nonlinear optics, in Physics of Nonlinear Optics (Springer International, Cham, Switzerland, 2021), pp. 9–25.
  38. C. W. Gardiner, Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences (Springer, New York, 2004).
  39. L. Isserlis, On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables, Biometrika 12, 134 (1918).
  40. C. Flindt, T. Novotny, A. Braggio, and A.-P. Jauho, Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects, Phys. Rev. B 82, 155407 (2010).
  41. Y. Blanter and M. Büttiker, Shot noise in mesoscopic conductors, Phys. Rep. 336, 1 (2000).
  42. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys. 82, 1155 (2010).
  43. F. Brange, P. Menczel, and C. Flindt, Photon counting statistics of a microwave cavity, Phys. Rev. B 99, 085418 (2019).
  44. L. Basano, P. Ottonello, and B. Torre, Bunching, antibunching, and the Poisson limit of Bose-Einstein processes at low-degeneracy parameters, J. Opt. Soc. Am. B 22, 1314 (2005).
  45. A. Kronwald, M. Ludwig, and F. Marquardt, Full photon statistics of a light beam transmitted through an optomechanical system, Phys. Rev. A 87, 013847 (2013).
  46. A. C. Barato and U. Seifert, Thermodynamic uncertainty relation for biomolecular processes, Phys. Rev. Lett. 114, 158101 (2015).
  47. T. R. Gingrich, J. M. Horowitz, N. Perunov, and J. L. England, Dissipation bounds all steady-state current fluctuations, Phys. Rev. Lett. 116, 120601 (2016).
  48. J. M. Horowitz and T. R. Gingrich, Thermodynamic uncertainty relations constrain non-equilibrium fluctuations, Nat. Phys. 16, 15 (2020).
  49. S. Saryal, H. M. Friedman, D. Segal, and B. K. Agarwalla, Thermodynamic uncertainty relation in thermal transport, Phys. Rev. E 100, 042101 (2019).
  50. T. R. Gingrich, G. M. Rotskoff, and J. M. Horowitz, Inferring dissipation from current fluctuations, J. Phys. A: Math. Theor. 50, 184004 (2017).

Outline

Information

Phys. Rev. Research 5, L042007– Published 5 October, 2023
  • Received 31 March 2023
  • Accepted 12 September 2023
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation