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Impact of quenched disorder and multiphoton interaction on the dynamics of a quantum battery

Azam Mirzaei

Hamid Reza Baghshahi*

Mohammad Javad Faghihi†

  • *Contact author: baghshahi@vru.ac.ir
  • †Contact author: mjfaghihi@outlook.com
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Phys. Rev. E 114, 054107 – Published 5 November, 2026

DOI: https://doi.org/10.1103/hshg-bcn7

Abstract

Quantum batteries (QBs) represent a promising and emerging class of energy storage devices that exploit the principles of quantum mechanics to achieve superior performance compared to conventional, classical batteries. In this work, we investigate the charging dynamics of a QB in a bipartite system composed of two qubits, where one qubit acts as a charger and the other as the battery, each embedded in an independent cavity reservoir. The model incorporates multiphoton atom-cavity interactions as well as quenched disorder (QD) in the system-reservoir coupling, including discrete, uniform, Gaussian, and Cauchy-Lorentz distributions. The resulting dynamics are analyzed in both weak- and strong-coupling regimes. We examine how the multiphoton order affects the internal energies of the charger and the battery, and show that increasing the multiphoton order leads to enhanced dissipation and a reduction of the energy transferred to the battery. By comparing different disorder statistics, we find that uniform and discrete QDs can partially mitigate decoherence and yield higher charging efficiency compared to Gaussian and Cauchy-Lorentz QDs. Furthermore, our results demonstrate that strong system-reservoir coupling induces non-Markovian dynamics accompanied by rapid energy loss and suppression of ergotropy and efficiency. In contrast, efficient charging and partial revival features are predominantly observed in the weak-coupling, Markovian regime, where coherent dynamics are preserved.

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References (77)

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2010).
  2. G. M. Andolina, M. Keck, M. Campisi, A. Mari, V. Giovannetti, and M. Polini, Extractable work, the role of correlations, and asymptotic freedom in quantum batteries, Phys. Rev. Lett. 122, 047702 (2019).
  3. Y. Yao and X. Q. Shao, Stable charging of a Rydberg quantum battery in an open system, Phys. Rev. E 104, 044116 (2021).
  4. F. Campaioli, F. A. Pollock, F. C. Binder, L. Céleri, J. Goold, S. Vinjanampathy, and K. Modi, Enhancing the charging power of quantum batteries, Phys. Rev. Lett. 118, 150601 (2017).
  5. Y.-Y. Zhang, T.-R. Yang, L. Fu, and X. Wang, Powerful harmonic charging in a quantum battery, Phys. Rev. E 99, 052106 (2019).
  6. T. P. Le, J. Levinsen, K. Modi, M. M. Parish, and F. A. Pollock, Spin-chain model of a many-body quantum battery, Phys. Rev. A 97, 022106 (2018).
  7. L. Peng, W.-B. He, S. Chesi, H.-Q. Lin, and X.-W. Guan, Lower and upper bounds of quantum battery power in multiple central spin systems, Phys. Rev. A 103, 052220 (2021).
  8. F. Caravelli, G. Coulter-De Wit, L. P. García-Pintos, and A. Hamma, Random quantum batteries, Phys. Rev. Res. 2, 023095 (2020).
  9. V. P. Patil, I. C. V. Kos, M. Ravnik, and J. Dunkel, Discharging dynamics of topological batteries, Phys. Rev. Res. 2, 043196 (2020).
  10. D. Ferraro, M. Campisi, G. M. Andolina, V. Pellegrini, and M. Polini, High-power collective charging of a solid-state quantum battery, Phys. Rev. Lett. 120, 117702 (2018).
  11. A. Crescente, M. Carrega, M. Sassetti, and D. Ferraro, Ultrafast charging in a two-photon Dicke quantum battery, Phys. Rev. B 102, 245407 (2020).
  12. G. M. Andolina, M. Keck, A. Mari, V. Giovannetti, and M. Polini, Quantum versus classical many-body batteries, Phys. Rev. B 99, 205437 (2019).
  13. J. Liu, D. Segal, and G. Hanna, Loss-free excitonic quantum battery, J. Phys. Chem. C 123, 18303 (2019).
  14. Z. Li, P. Yang, W.-L. You, and N. Wu, Dynamics of the homogeneous two-qubit XXZ central spin model with the spin bath prepared in superpositions of symmetric Dicke states, Phys. Rev. A 102, 032409 (2020).
  15. 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).
  16. C. A. Downing and M. S. Ukhtary, A quantum battery with quadratic driving, Commun. Phys. 6, 322 (2023).
  17. F. Barra, Dissipative charging of a quantum battery, Phys. Rev. Lett. 122, 210601 (2019).
  18. F. Pirmoradian and K. Mølmer, Aging of a quantum battery, Phys. Rev. A 100, 043833 (2019).
  19. T. F. F. Santos, Y. V. de Almeida, and M. F. Santos, Vacuum-enhanced charging of a quantum battery, Phys. Rev. A 107, 032203 (2023).
  20. F. C. Binder, S. Vinjanampathy, K. Modi, and J. Goold, Quantacell: Powerful charging of quantum batteries, New J. Phys. 17, 075015 (2015).
  21. 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).
  22. X. Q. Yan and Z. L. Yue, Dynamics of quantum and classical correlations of a two-atom system in thermal reservoirs, Chaos Solit. Fractals 57, 117 (2013).
  23. Z. Dahbi, M. Mansour, and A. El Allati, Dynamics of quantum correlations in two 2-level atoms coupled to thermal reservoirs, Phys. Scr. 98, 015102 (2023).
  24. K. K. Rajagopal and G. Ibragimov, Non-equilibrium dynamics of a double-well Bose–Einstein condensate-dual reservoir system, Braz. J. Phys. 51, 944 (2021).
  25. F. Petiziol and A. Eckardt, Cavity-based reservoir engineering for Floquet-engineered superconducting circuits, Phys. Rev. Lett. 129, 233601 (2022).
  26. X.-Y. Yao, H. Ali, F.-L. Li, and P.-B. Li, Nonreciprocal phonon blockade in a spinning acoustic ring cavity coupled to a two-level system, Phys. Rev. Appl. 17, 054004 (2022).
  27. F. T. Tabesh, F. H. Kamin, and S. Salimi, Environment-mediated charging process of quantum batteries, Phys. Rev. A 102, 052223 (2020).
  28. F. H. Kamin, F. T. Tabesh, S. Salimi, F. Kheirandish, and A. C. Santos, Non-Markovian effects on charging and self-discharging process of quantum batteries, New J. Phys. 22, 083007 (2020).
  29. S. Zakavati, F. T. Tabesh, and S. Salimi, Bounds on charging power of open quantum batteries, Phys. Rev. E 104, 054117 (2021).
  30. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
  31. H.-P. Breuer, E.-M. Laine, J. Piilo, and B. Vacchini, Colloquium: Non-Markovian dynamics in open quantum systems, Rev. Mod. Phys. 88, 021002 (2016).
  32. Y. Aiache, C. Seida, K. El Anouz, and A. El Allati, Non-Markovian enhancement of nonequilibrium quantum thermometry, Phys. Rev. E 110, 024132 (2024).
  33. R. Gutzler, M. Garg, C. R. Ast, K. Kuhnke, and K. Kern, Light–matter interaction at atomic scales, Nat. Rev. Phys. 3, 441 (2021).
  34. A. Ghoshal, S. Das, A. Sen(De), and U. Sen, Population inversion and entanglement in single and double glassy Jaynes–Cummings models, Phys. Rev. A 101, 053805 (2020).
  35. J. H. Warnes, F. M. de Paula, N. C. Costa, and O. P. de Sá Neto, Dynamics of quantum coherence in the Jaynes–Cummings model with quenched disorder, Phys. Open 15, 100146 (2023).
  36. M. Brune, J. M. Raimond, P. Goy, L. Davidovich, and S. Haroche, Realization of a two-photon maser oscillator, Phys. Rev. Lett. 59, 1899 (1987).
  37. M. Brune, J. M. Raimond, and S. Haroche, Theory of the Rydberg-atom two-photon micromaser, Phys. Rev. A 35, 154 (1987).
  38. M. Koch, C. Sames, M. Balbach, H. Chibani, A. Kubanek, K. Murr, T. Wilk, and G. Rempe, Three-photon correlations in a strongly driven atom-cavity system, Phys. Rev. Lett. 107, 023601 (2011).
  39. T. G. Rudolph, H. S. Freedhoff, and Z. Ficek, Multiphoton ac Stark effect in a bichromatically driven two-level atom, Phys. Rev. A 58, 1296 (1998).
  40. A. Hayat and M. Orenstein, Photon conversion processes in dispersive microcavities: Quantum-field model, Phys. Rev. A 77, 013830 (2008).
  41. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  42. I. Vilkoviskiy and D. A. Abanin, Bound on approximating non-Markovian dynamics by tensor networks in the time domain, Phys. Rev. B 109, 205126 (2024).
  43. K. Saito, S. Takesue, and S. Miyashita, Energy transport in the integrable system in contact with various types of phonon reservoirs, Phys. Rev. E 61, 2397 (2000).
  44. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 2012).
  45. F. Kahlert, V. Link, R. Hartmann, and W. T. Strunz, Simulating the Landau–Zener sweep in deeply sub-Ohmic environments, J. Chem. Phys. 161, 184108 (2024).
  46. E. Ghasemian and M. K. Tavassoly, Generation of nonclassical optomagnonic states under the influences of Stokes scattering process and thermal noise, Sci. Rep. 15, 27717 (2025).
  47. M. Hadipour, S. Haseli, H. Dolatkhah, and M. Rashidi, Study the charging process of moving quantum batteries inside cavity, Sci. Rep. 13, 10672 (2023).
  48. M. Hadipour and S. Haseli, Enhancing the efficiency of open quantum batteries via adjusting the classical driving field, Results Phys. 64, 107928 (2024).
  49. R. Alicki and M. Fannes, Entanglement boost for extractable work from ensembles of quantum batteries, Phys. Rev. E 87, 042123 (2013).
  50. A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Maximal work extraction from finite quantum systems, Europhys. Lett. 67, 565 (2004).
  51. B. Çakmak, Ergotropy from coherences in an open quantum system, Phys. Rev. E 102, 042111 (2020).
  52. F. Hatami Kamin and S. Salimi, Exergy and Quantum Batteries (Books on Demand, Norderstedt, 2024), Chap. 4, pp. 61–68.
  53. C.-J. Wang and F.-Q. Dou, Ergotropy in quantum batteries, Chinese Phys. Lett. 43, 060602 (2026).
  54. M. A. Fasihi, R. Jafarzadeh Bahrbeig, B. Mojaveri, and R. Haji Mohammadzadeh, Fast stable adiabatic charging of open quantum batteries, Phys. Rev. E 112, 024117 (2025).
  55. X. Yang, Y.-H. Yang, M. Alimuddin, R. Salvia, S.-M. Fei, L.-M. Zhao, S. Nimmrichter, and M.-X. Luo, Battery capacity of energy-storing quantum systems, Phys. Rev. Lett. 131, 030402 (2023).
  56. K. Xu, H.-J. Zhu, G.-F. Zhang, and W.-M. Liu, Enhancing the performance of an open quantum battery via environment engineering, Phys. Rev. E 104, 064143 (2021).
  57. Z. Wang, H. Yu, and J. Wang, Driven-dissipative quantum battery with non-equilibrium reservoirs, J. Phys. Chem. Lett. 16, 12018 (2025).
  58. A. Shokri, E. Faizi, and M. B. Arjmandi, Entanglement-assisted charging of quantum batteries within optomechanical framework, Phys. Rev. E 111, 064117 (2025).
  59. C. A. Downing and M. S. Ukhtary, Charging a quantum battery from the Bloch sphere, Ann. Phys. (Leipzig) 538, e00638 (2026).
  60. J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Monroe, Many-body localization in a quantum simulator with programmable random disorder, Nat. Phys. 12, 907 (2016).
  61. K. Xu, J.-J. Chen, Y. Zeng, Y.-R. Zhang, C. Song, W. Liu, Q. Guo, P. Zhang, D. Xu, H. Deng, K. Huang, H. Wang, X. Zhu, D. Zheng, and H. Fan, Emulating many-body localization with a superconducting quantum processor, Phys. Rev. Lett. 120, 050507 (2018).
  62. H.-Y. Yang, H.-L. Shi, Q.-K. Wan, K. Zhang, X.-H. Wang, and W.-L. Yang, Optimal energy storage in the Tavis–Cummings quantum battery, Phys. Rev. A 109, 012204 (2024).
  63. S. Ghosh, T. Chanda, and A. Sen(De), Enhancement in the performance of a quantum battery by ordered and disordered interactions, Phys. Rev. A 101, 032115 (2020).
  64. A. Ali, S. Al-Kuwari, M. I. Hussain, T. Byrnes, M. T. Rahim, J. Q. Quach, M. Ghominejad, and S. Haddadi, Ergotropy and capacity optimization in Heisenberg spin-chain quantum batteries, Phys. Rev. A 110, 052404 (2024).
  65. B. Mojaveri, R. Jafarzadeh Bahrbeig, and M. A. Fasihi, Extracting ergotropy from nonequilibrium steady states of an XYZ spin-chain quantum battery, Phys. Rev. A 109, 042619 (2024).
  66. F.-Q. Dou, H. Zhou, and J.-A. Sun, Cavity Heisenberg-spin-chain quantum battery, Phys. Rev. A 106, 032212 (2022).
  67. W. Zhang, S. Wang, C. Wu, and G. Wang, Quantum battery based on dipole-dipole interaction and external driving field, Phys. Rev. E 107, 054125 (2023).
  68. D.-L. Yang, F.-M. Yang, and F.-Q. Dou, Three-level Dicke quantum battery, Phys. Rev. B 109, 235432 (2024).
  69. A. Canzio, V. Cavina, M. Polini, and V. Giovannetti, Single-atom dissipation and dephasing in Dicke and Tavis–Cummings quantum batteries, Phys. Rev. A 111, 022222 (2025).
  70. F.-Q. Dou and F.-M. Yang, Superconducting transmon qubit-resonator quantum battery, Phys. Rev. A 107, 023725 (2023).
  71. S. Elghaayda, A. Ali, S. Al-Kuwari, A. Czerwinski, M. Mansour, and S. Haddadi, Performance of a superconducting quantum battery, Adv. Quantum Technol. 8, 2400651 (2025).
  72. N. Taşaltın and D. E. Yıldız, Quantum batteries: Energy storage models and physical approaches via quantum systems, J. Energy Storage 162, 122088 (2026).
  73. F.-Q. Dou, Y.-Q. Lu, Y.-J. Wang, and J.-A. Sun, Extended Dicke quantum battery with interatomic interactions and driving field, Phys. Rev. B 105, 115405 (2022).
  74. Y. Yao and X. Q. Shao, Optimal charging of open spin-chain quantum batteries via homodyne-based feedback control, Phys. Rev. E 106, 014138 (2022).
  75. D. Koutromanos, D. Stefanatos, and E. Paspalakis, Efficient charging of driven cavity-Heisenberg spin-1/2 chain quantum battery with deep learning methods, Phys. Rev. Appl. 25, 054053 (2026).
  76. P.-Y. Sun, H. Zhou, and F.-Q. Dou, Cavity-Heisenberg spin-j chain quantum battery and reinforcement learning optimization, New J. Phys. 27, 124513 (2025).
  77. S.-C. Zhao, Z.-R. Zhao, and N.-Y. Zhuang, Non-Markovian N-spin chain quantum battery in thermal charging process, Phys. Rev. E 112, 024129 (2025).

Outline

Information

Phys. Rev. E 114, 054107– Published 5 November, 2026
  • Received 3 February 2026
  • Revised 19 August 2026
  • Accepted 2 October 2026
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