- Physical Review Journals
All JournalsPhysics Magazine

Physical Review E

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
  • Open Access

Energy storage in a continuous-variable quantum battery with nonlinear coupling

C. A. Downing1,* and M. S. Ukhtary2

  • *Contact author: c.a.downing@exeter.ac.uk
PDF

Phys. Rev. E 112, 044143 – Published 24 October, 2025

DOI: https://doi.org/10.1103/73zl-yn4h

Abstract

In the quantum world, the process of energy storage can be enhanced thanks to various nonclassical phenomena. This inspiring fact suggests quantum batteries as plausible sources of power for future quantum devices, at least in principle. However, thermodynamically not all of the energy stored in a quantum battery is useful for doing work. By considering a class of models based upon quantum continuous variables, here we show how the maximum extractable energy from a bosonic quantum battery can be intimately related to Heisenberg's uncertainty principle. We found that realizing minimum uncertainty essentially guarantees that all of the energy stored in a Gaussian quantum battery can be withdrawn and used to do work. For a standard system where the charger and battery are coupled linearly, this criterion is satisfied rather trivially. However, our theoretical results demonstrate that—for a quantum battery with nonlinear coupling—a state of minimum uncertainty can also be achieved nontrivially via the generation of quantum squeezing. We characterize the charging performance of our proposed continuous-variable quantum batteries in detail, and we hope that our theory may be useful in the design of a new generation of efficient quantum batteries harnessing bosonic excitations, such as those built with photonic architectures.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (58)

  1. J. Q. Quach, G. Cerullo, and T. Virgili, Quantum batteries: The future of energy storage? Joule 7, 2195 (2023).
  2. F. Campaioli, S. Gherardini, J. Q. Quach, M. Polini, and G. M. Andolina, Colloquium: Quantum batteries, Rev. Mod. Phys. 96, 031001 (2024).
  3. D. Rossini, G. M. Andolina, D. Rosa, M. Carrega, and M. Polini, Quantum advantage in the charging process of Sachdev-Ye-Kitaev batteries, Phys. Rev. Lett. 125, 236402 (2020).
  4. G. M. Andolina, V. Stanzione, V. Giovannetti, and M. Polini, Genuine quantum advantage in nonlinear bosonic quantum batteries, Phys. Rev. Lett. 134, 240403 (2025).
  5. J. Q. Quach, K. E. McGhee, L. Ganzer, D. M. Rouse, B. W. Lovett, E. M. Gauger, J. Keeling, G. Cerullo, D. G. Lidzey, and T. Virgili, Superabsorption in an organic microcavity: Toward a quantum battery, Sci. Adv. 8, eabk3160 (2022).
  6. J. Joshi and T. S. Mahesh, Experimental investigation of a quantum battery using star-topology NMR spin systems, Phys. Rev. A 106, 042601 (2022).
  7. C.-K. Hu, J. Qiu, P. J. P. Souza, J. Yuan, Y. Zhou, L. Zhang, J. Chu, X. Pan, L. Hu, J. Li, Y. Xu, Y. Zhong, S. Liu, F. Yan, D. Tan, R. Bachelard, C. J. Villas-Boas, A. C. Santos, and D. Yu, Optimal charging of a superconducting quantum battery, Quantum Sci. Technol. 7, 045018 (2022).
  8. Y. Ge, X. Yu, W. Xin, Z. Wang, Y. Zhang, W. Zheng, S. Li, D. Lan, and Y. Yu, Efficient charging and discharging of a superconducting quantum battery through frequency-modulated driving, Appl. Phys. Lett. 123, 154002 (2023).
  9. D. Qu, X. Zhan, H. Lin, and P. Xue, Experimental optimization of charging quantum batteries through a catalyst system, Phys. Rev. B 108, L180301 (2023).
  10. X. Huang, K. Wang, L. Xiao, L. Gao, H. Lin, and P. Xue, Demonstration of the charging progress of quantum batteries, Phys. Rev. A 107, L030201 (2023).
  11. Z. Niu, Y. Wu, Y. Wang, X. Rong, and J. Due, Experimental investigation of coherent ergotropy in a single spin system, Phys. Rev. Lett. 133, 180401 (2024).
  12. B. Donelli, S. Gherardini, R. Marino, F. Campaioli, and L. Buffoni, Charging a quantum spin network with superextensive precision, Phys. Rev. E 111, L062102 (2025).
  13. K. Hymas, J. B. Muir, D. Tibben, J. van Embden, T. Hirai, C. J. Dunn, D. E. Gómez, J. A. Hutchison, T. A. Smith, and J. Q. Quach, Experimental demonstration of a scalable room-temperature quantum battery, arXiv:2501.16541.
  14. Y. Kurman, K. Hymas, A. Fedorov, W. J. Munro, and J. Quach, Quantum computation with quantum batteries, arXiv:2503.23610.
  15. A. C. Santos, B. Çakmak, S. Campbell, and N. T. Zinner, Stable adiabatic quantum batteries, Phys. Rev. E 100, 032107 (2019).
  16. A. C. Santos, A. Saguia, and M. S. Sarandy, Stable and charge-switchable quantum batteries, Phys. Rev. E 101, 062114 (2020).
  17. F. H. Kamin, F. T. Tabesh, S. Salimi, and A. C. Santos, Entanglement, coherence, and charging process of quantum batteries, Phys. Rev. E 102, 052109 (2020).
  18. F. H. Kamin, S. Salimi, and A. C. Santos, Exergy of passive states: Waste energy after ergotropy extraction, Phys. Rev. E 104, 034134 (2021).
  19. A. C. Santos, Quantum advantage of two-level batteries in the self-discharging process, Phys. Rev. E 103, 042118 (2021).
  20. M. B. Arjmandi, H. Mohammadi, and A. C. Santos, Enhancing self-discharging process with disordered quantum batteries, Phys. Rev. E 105, 054115 (2022).
  21. M. B. Arjmandi, H. Mohammadi, A. Saguia, M. S. Sarandy, and A. C. Santos, Localization effects in disordered quantum batteries, Phys. Rev. E 108, 064106 (2023).
  22. B. Mojaveri, R. Jafarzadeh Bahrbeig, and M. A. Fasihi, Charging a quantum battery mediated by parity-deformed fields, Phys. Rev. E 110, 064107 (2024).
  23. Z. K. Wang, K. Xu, Z. D. Wei, W. Han, Y. J. Zhang, Z. X. Man, and Y. J. Xia, Classical-driving-assisted qubit-array quantum battery, Phys. Rev. E 111, 014121 (2025).
  24. R. R. Rodríguez, B. Ahmadi, P. Mazurek, S. Barzanjeh, R. Alicki, and P. Horodecki, Catalysis in charging quantum batteries, Phys. Rev. A 107, 042419 (2023).
  25. K. Gangwar and A. Pathak, Coherently driven quantum harmonic oscillator battery, Adv. Quantum Technol. 7, 2400069 (2024).
  26. B. Ahmadi, P. Mazurek, P. Horodecki, and S. Barzanjeh, Nonreciprocal quantum batteries, Phys. Rev. Lett. 132, 210402 (2024).
  27. A. Bhattacharyya, P. Dongre, and U. Sen, Nonlinearity-assisted advantage for open Dicke-quantum batteries, arXiv:2410.00618.
  28. D. F. Walls, Squeezed states of light, Nature (London) 306, 141 (1983).
  29. R. Loudon and P. L. Knight, Squeezed light, J. Mod. Opt. 34, 709 (1987).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/73zl-yn4h for further details of the calculations and for various analyses supporting the main text.
  31. N. Friis and M. Huber, Precision and work fluctuations in Gaussian battery charging, Quantum 2, 61 (2018).
  32. F. Centrone, L. Mancino, and M. Paternostro, Charging batteries with quantum squeezing, Phys. Rev. A 108, 052213 (2023).
  33. C. A. Downing and M. S. Ukhtary, Energetics of a pulsed quantum battery, Europhys. Lett. 146, 10001 (2024).
  34. T. K. Konar, A. Patra, R. Gupta, S. Ghosh, and A. Sen, Multimode advantage in continuous-variable quantum batteries, Phys. Rev. A 110, 022226 (2024).
  35. A. Ferraro, S. Olivares, and M. Paris, Gaussian states in quantum information (Bibliopolis, Napoli, 2005) See also: arXiv:quant-ph/0503237.
  36. S. Olivares, Quantum optics in the phase space: A tutorial on Gaussian states, Eur. Phys. J. Spec. Top. 203, 3 (2012).
  37. C. A. Downing and M. S. Ukhtary, Two-photon charging of a quantum battery with a Gaussian pulse envelope, Phys. Lett. A 518, 129693 (2024).
  38. A. E. Allahverdyan, R. Balian, and Th M. Nieuwenhuizen, Maximal work extraction from finite quantum systems, Europhys. Lett. 67, 565 (2004).
  39. R. Alicki and M. Fannes, Entanglement boost for extractable work from ensembles of quantum batteries, Phys. Rev. E 87, 042123 (2013).
  40. A. Lenard, Thermodynamical proof of the Gibbs formula for elementary quantum systems, J. Stat. Phys. 19, 575 (1978).
  41. W. Pusz and S. L. Woronowicz, Passive states and KMS states for general quantum systems, Commun. Math. Phys. 58, 273 (1978).
  42. D. Farina, G. M. Andolina, A. Mari, M. Polini, and V. Giovannetti, Charger-mediated energy transfer for quantum batteries: An open-system approach, Phys. Rev. B 99, 035421 (2019).
  43. C. A. Downing and M. S. Ukhtary, A quantum battery with quadratic driving, Commun. Phys. 6, 322 (2023).
  44. G. M. Andolina, D. Farina, A. Mari, V. Pellegrini, V. Giovannetti, and M. Polini, Charger-mediated energy transfer in exactly solvable models for quantum batteries, Phys. Rev. B 98, 205423 (2018).
  45. G. M. Andolina, M. Keck, A. Mari, V. Giovannetti, and M. Polini, Quantum versus classical many-body batteries, Phys. Rev. B 99, 205437 (2019).
  46. C. A. Downing and M. S. Ukhtary, Hyperbolic enhancement of a quantum battery, Phys. Rev. A 109, 052206 (2024).
  47. R. Shastri, C. Jiang, G. H. Xu, B. P. Venkatesh, and G. Watanabe, Dephasing enabled fast charging of quantum batteries, npj quantum inf. 11, 9 (2025).
  48. H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, New York, 2002).
  49. C. A. Downing and O. I. R. Fox, Unbalanced gain and loss in a quantum photonic system, J. Opt. 25, 095201 (2023).
  50. C. A. Downing and V. A. Saroka, A first encounter with exceptional points in a quantum model, Am J. Phys. 93, 396 (2025).
  51. X. Guo, C. L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, Parametric down-conversion photon-pair source on a nanophotonic chip, Light Sci. Appl. 6, e16249 (2017).
  52. C. W. Sandbo Chang, C. Sabin, P. Forn-Diaz, F. Quijandria, A. M. Vadiraj, I. Nsanzineza, G. Johansson, and C. M. Wilson, Observation of three-photon spontaneous parametric down–conversion in a superconducting parametric cavity, Phys. Rev. X 10, 011011 (2020).
  53. R. Kubo, Generalized cumulant expansion method, J. Phys. Soc. Jpn. 17, 1100 (1962).
  54. R. Kubo, Stochastic Liouville equations, J. Math. Phys. 4, 174 (1963).
  55. S. H. Strogatz, Nonlinear Dynamics and Chaos (Westview Press, New York, 2001).
  56. J. R. Johansson, P. D. Nation, and F. Nori, QuTiP: An open-source python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 183, 1760 (2012).
  57. B. M. Gomes, J. F. R. Moutinho, and M. H. Braga, A perspective on the building blocks of a solid-state battery: From solid electrolytes to quantum power harvesting and storage, J. Mater. Chem. A 12, 690 (2024).
  58. A. Camposeo, T. Virgili, F. Lombardi, G. Cerullo, D. Pisignano, and M. Polini, Quantum batteries: A materials science perspective, Adv. Mater. 37, 2415073 (2025).

Outline

Information

Phys. Rev. E 112, 044143– Published 24 October, 2025
  • Received 1 May 2025
  • Accepted 30 September 2025
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