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Thermodynamics of a phaseonium-driven optomechanical Otto engine

Federico Amato1,2,*, Gerardo Adesso2,†, G. Massimo Palma3, Salvatore Lorenzo3, and Rosario Lo Franco1,‡

  • *Contact author: federico.amato01@unipa.it
  • †Contact author: gerardo.adesso@nottingham.ac.uk
  • ‡Contact author: rosario.lofranco@unipa.it
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Phys. Rev. A 114, 052202 – Published 2 November, 2026

DOI: https://doi.org/10.1103/hl39-wfbr

Abstract

We study an optomechanical Otto engine whose working medium is a single-mode cavity driven by beams of coherently prepared three-level phaseonium atoms. The atoms are not thermal reservoirs in the Gibbs sense; rather, their populations and ground-state coherence set the detailed-balance ratio of the cavity collision map, so that the field relaxes to a Gibbs state at an operational apparent temperature. We combine the finite-time collision-model dynamics with radiation-pressure work extraction and compare three reservoir preparations: a thermal reference at the same apparent temperatures, an incoherent atomic beam with the same populations, and the coherent phaseonium beam. We show that the phaseonium isochore charges the cavity passively: the cavity ergotropy and energy-basis coherence remain zero up to numerical precision, while the state converges to the Gibbs fixed point selected by the apparent detailed balance. We further estimate lower bounds on the cost of preparing the atomic populations and coherence, showing that the relevant advantage of phaseonium is a resource-preparation tradeoff rather than a cost-free enhancement over a thermal bath at the same temperature. Finally, we assess the finite-time performance of a two-cavity cascade with additive mechanical work accounting. Over the investigated coherence-phase range, the cascade produces approximately 47%–52% more power than the single-cavity engine while requiring only 65%–68% of the hot and cold phaseonium atoms needed by two independent engines, resulting in a 9%–15% enhancement of power per injected atom over a complete cycle.

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References (43)

  1. A. Streltsov, G. Adesso, and M. B. Plenio, Colloquium: Quantum coherence as a resource, Rev. Mod. Phys. 89, 041003 (2017).
  2. Edited by F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso, Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, Fundamental Theories of Physics Vol. 195 (Springer, Cham, 2018).
  3. S. Aimet and H. Kwon, Engineering a heat engine purely driven by quantum coherence, Phys. Rev. A 107, 012221 (2023).
  4. R. Alicki and D. Gelbwaser-Klimovsky, Non-equilibrium quantum heat machines, New J. Phys. 17, 115012 (2015).
  5. C. L. Latune, I. Sinayskiy, and F. Petruccione, Apparent temperature: Demystifying the relation between quantum coherence, correlations, and heat flows, Quantum Sci. Technol. 4, 025005 (2019).
  6. C. L. Latune, I. Sinayskiy, and F. Petruccione, Roles of quantum coherences in thermal machines, Eur. Phys. J. Spec. Top. 230, 841 (2021).
  7. C. L. Latune, I. Sinayskiy, and F. Petruccione, Quantum coherence, many-body correlations, and non-thermal effects for autonomous thermal machines, Sci. Rep. 9, 3191 (2019).
  8. C. Dağ, W. Niedenzu, Ö. Müstecaplıoğlu, and G. Kurizki, Multiatom quantum coherences in micromasers as fuel for thermal and nonthermal machines, Entropy 18, 244 (2016).
  9. M. O. Scully, From lasers and masers to phaseonium and phasers, Phys. Rep. 219, 191 (1992).
  10. V. V. Kozlov and J. H. Eberly, Ultrashort pulses in phaseonium: The interplay between SIT and EIT, Opt. Commun. 179, 85 (2000).
  11. D. M. Nguyen, C. Soci, and C. H. Ooi, Coherently tunable triangular trefoil phaseonium metamaterial, Sci. Rep. 6, 21083 (2016).
  12. U. Rathea, M. Fleischhauer, and M. O. Scully, Optical nonlinearities and the Kerr-effect in phaseonium, in Frontiers in Nonlinear Optics, The Sergei Akhmanov Memorial Volume (CRC Press, Boca Raton, FL, 2021), pp. 17–25.
  13. M. O. Scully, Extracting work from a single heat bath via vanishing quantum coherence II: Microscopic model, AIP Conf. Proc. 643, 83 (2002).
  14. F. Amato, C. Pellitteri, G. M. Palma, S. Lorenzo, and R. Lo Franco, Heating and cooling processes via phaseonium-driven dynamics of cascade systems, Phys. Rev. A 109, 043705 (2024).
  15. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  16. H. T. Quan, P. Zhang, and C. P. Sun, Quantum-classical transition of photon-Carnot engine induced by quantum decoherence, Phys. Rev. E 73, 036122 (2006).
  17. F. Ciccarello, S. Lorenzo, V. Giovannetti, and G. M. Palma, Quantum collision models: Open system dynamics from repeated interactions, Phys. Rep. 954, 1 (2022).
  18. H.-P. Breuer, F. Petruccione, et al., The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
  19. A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Maximal work extraction from finite quantum systems, Europhys. Lett. 67, 565 (2004).
  20. W. Pusz and S. L. Woronowicz, Passive states and KMS states for general quantum systems, Commun. Math. Phys. 58, 273 (1978).
  21. A. Lenard, Thermodynamical proof of the Gibbs formula for elementary quantum systems, J. Stat. Phys. 19, 575 (1978).
  22. G. T. Landi and M. Paternostro, Irreversible entropy production: From classical to quantum, Rev. Mod. Phys. 93, 035008 (2021).
  23. M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, J. Tura, and A. Acín, Most energetic passive states, Phys. Rev. E 92, 042147 (2015).
  24. C. K. Law, Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation, Phys. Rev. A 51, 2537 (1995).
  25. A. Tejero, D. Manzano, and P. I. Hurtado, Atom-doped photon engine: Extracting mechanical work from a quantum system via radiation pressure, Phys. Rev. E 109, 024141 (2024).
  26. R. Alicki, The quantum open system as a model of the heat engine, J. Phys. A: Math. Gen. 12, L103 (1979).
  27. F. G. S. L. Brandão, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens, Resource theory of quantum states out of thermal equilibrium, Phys. Rev. Lett. 111, 250404 (2013).
  28. P. Skrzypczyk, A. J. Short, and S. Popescu, Work extraction and thermodynamics for individual quantum systems, Nat. Commun. 5, 4185 (2014).
  29. T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying coherence, Phys. Rev. Lett. 113, 140401 (2014).
  30. M. Lostaglio, D. Jennings, and T. Rudolph, Description of quantum coherence in thermodynamic processes requires constraints beyond free energy, Nat. Commun. 6, 6383 (2015).
  31. F. L. Curzon and B. Ahlborn, Efficiency of a Carnot engine at maximum power output, Am. J. Phys. 43, 22 (1975).
  32. L. M. Cangemi, C. Bhadra, and A. Levy, Quantum engines and refrigerators, Phys. Rep. 1087, 1 (2024).
  33. W. H. Zurek, Information transfer in quantum measurements: Irreversibility and amplification, in Quantum Optics, Experimental Gravity, and Measurement Theory, edited by P. Meystre and M. O. Scully (Springer, Berlin, 1983), pp. 87–116.
  34. L. A. S. Machado, P. A. Maia Neto, and C. Farina, Quantum radiation pressure on a moving mirror at finite temperature, Phys. Rev. D 66, 105016 (2002).
  35. E. Cavalcanti and A. P. C. Malbouisson, Quantum forces in cavities, Phys. Rev. D 106, 025005 (2022).
  36. S. Butera, Corrections to the optomechanical Hamiltonian from quadratic fluctuations of a moving mirror, Phys. Rev. A 111, 043524 (2025).
  37. S. Kuhr, S. Gleyzes, C. Guerlin, J. Bernu, U. B. Hoff, S. Deléglise, S. Osnaghi, M. Brune, J.-M. Raimond, S. Haroche, E. Jacques, P. Bosland, and B. Visentin, Ultrahigh finesse Fabry-Pérot superconducting resonator, Appl. Phys. Lett. 90, 164101 (2007).
  38. K. J. Vahala, Optical microcavities, Nature (London) 424, 839 (2003).
  39. F. Famà, S. Zhou, B. Heizenreder, M. Tang, S. Bennetts, S. B. Jäger, S. A. Schäffer, and F. Schreck, Continuous cavity QED with an atomic beam, Phys. Rev. A 110, 063721 (2024).
  40. Q. Qiao, J. Lin, R. Gao, J. Guan, C. Li, G. Zhao, X. Zheng, M. Li, Q. Hou, X. Luo, Y. Qiu, L. Qiao, M. Wang, and Y. Cheng, Integrated high-Q cascaded Fabry–Perot resonators based on lithium niobate Sagnac loop reflectors, Opt. Lett. 50, 2370 (2025).
  41. A. Suleymanzade, A. Anferov, M. Stone, R. K. Naik, A. Oriani, J. Simon, and D. Schuster, A tunable high-Q millimeter wave cavity for hybrid circuit and cavity QED experiments, Appl. Phys. Lett. 116, 104001 (2020).
  42. T. Zhang, M. Wu, S. R. Cohen, L. Xin, D. Das, K. K. S. Multani, N. Peard, A.-M. Valente-Feliciano, P. B. Welander, A. H. Safavi-Naeini, E. A. Nanni, and M. Schleier-Smith, Optically accessible high-finesse millimeter-wave resonator for cavity quantum electrodynamics with atom arrays, Phys. Rev. Appl. 24, L041001 (2025).
  43. F. Amato, G. Adesso, G. M. Palma, S. Lorenzo, and R. Lo Franco, Selected numerical data for a phaseonium-driven optomechanical Otto engine, version 1.0.0, Zenodo, 2026, https://doi.org/10.5281/zenodo.23726312.

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Phys. Rev. A 114, 052202– Published 2 November, 2026
  • Received 6 March 2026
  • Revised 2 August 2026
  • Accepted 15 October 2026
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