{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T07:07:17Z","timestamp":1775891237773,"version":"3.50.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2025,7,31]],"date-time":"2025-07-31T00:00:00Z","timestamp":1753920000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,7,31]],"date-time":"2025-07-31T00:00:00Z","timestamp":1753920000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-025-04854-y","type":"journal-article","created":{"date-parts":[[2025,7,31]],"date-time":"2025-07-31T05:47:35Z","timestamp":1753940855000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Charging a quantum battery with interacting spin baths in a trio coherent state"],"prefix":"10.1007","volume":"24","author":[{"given":"M. Y.","family":"Abd-Rabbou","sequence":"first","affiliation":[]},{"given":"H.","family":"Allhibi","sequence":"additional","affiliation":[]},{"given":"F.","family":"Aljuaydi","sequence":"additional","affiliation":[]},{"given":"A.-B. A.","family":"Mohamed","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,31]]},"reference":[{"issue":"10","key":"4854_CR1","doi-asserted-by":"publisher","first-page":"1801","DOI":"10.1021\/acs.jchemed.8b00479","volume":"95","author":"K Schmidt-Rohr","year":"2018","unstructured":"Schmidt-Rohr, K.: How batteries store and release energy: explaining basic electrochemistry. J. Chem. Educ. 95(10), 1801\u20131810 (2018)","journal-title":"J. Chem. Educ."},{"issue":"11","key":"4854_CR2","doi-asserted-by":"publisher","first-page":"20499","DOI":"10.3390\/molecules201119711","volume":"20","author":"F Pan","year":"2015","unstructured":"Pan, F., Wang, Q.: Redox species of redox flow batteries: a review. Molecules 20(11), 20499\u201320517 (2015)","journal-title":"Molecules"},{"issue":"20","key":"4854_CR3","doi-asserted-by":"publisher","first-page":"200601","DOI":"10.1103\/PhysRevLett.116.200601","volume":"116","author":"K Joulain","year":"2016","unstructured":"Joulain, K., Drevillon, J., Ezzahri, Y., Ordonez-Miranda, J.: Quantum thermal transistor. Phys. Rev. Lett. 116(20), 200601 (2016)","journal-title":"Phys. Rev. Lett."},{"issue":"3","key":"4854_CR4","doi-asserted-by":"publisher","first-page":"036801","DOI":"10.1103\/PhysRevLett.100.036801","volume":"100","author":"PK Shukla","year":"2008","unstructured":"Shukla, P.K., Eliasson, B.: Nonlinear theory for a quantum diode in a dense fermi magnetoplasma. Phys. Rev. Lett. 100(3), 036801 (2008)","journal-title":"Phys. Rev. Lett."},{"issue":"2","key":"4854_CR5","doi-asserted-by":"publisher","first-page":"023849","DOI":"10.1103\/PhysRevA.90.023849","volume":"90","author":"HZ Shen","year":"2014","unstructured":"Shen, H.Z., Zhou, Y.H., Yi, X.X.: Quantum optical diode with semiconductor microcavities. Phys. Rev. A 90(2), 023849 (2014)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"4854_CR6","doi-asserted-by":"publisher","first-page":"042123","DOI":"10.1103\/PhysRevE.87.042123","volume":"87","author":"R Alicki","year":"2013","unstructured":"Alicki, R., Fannes, M.: Entanglement boost for extractable work from ensembles of quantum batteries. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 87(4), 042123 (2013)","journal-title":"Phys. Rev. E Stat. Nonlinear Soft Matter Phys."},{"issue":"3","key":"4854_CR7","doi-asserted-by":"publisher","first-page":"032115","DOI":"10.1103\/PhysRevA.101.032115","volume":"101","author":"S Ghosh","year":"2020","unstructured":"Ghosh, S., Chanda, T., Sen, A.: Enhancement in the performance of a quantum battery by ordered and disordered interactions. Phys. Rev. A 101(3), 032115 (2020)","journal-title":"Phys. Rev. A"},{"issue":"11","key":"4854_CR8","doi-asserted-by":"publisher","first-page":"115142","DOI":"10.1103\/PhysRevB.100.115142","volume":"100","author":"D Rossini","year":"2019","unstructured":"Rossini, D., Andolina, G.M., Polini, M.: Many-body localized quantum batteries. Phys. Rev. B 100(11), 115142 (2019)","journal-title":"Phys. Rev. B"},{"issue":"5","key":"4854_CR9","doi-asserted-by":"publisher","first-page":"052109","DOI":"10.1103\/PhysRevE.102.052109","volume":"102","author":"FH Kamin","year":"2020","unstructured":"Kamin, F.H., Tabesh, F.T., Salimi, S., Santos, A.C.: Entanglement, coherence, and charging process of quantum batteries. Phys. Rev. E 102(5), 052109 (2020)","journal-title":"Phys. Rev. E"},{"key":"4854_CR10","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.aop.2019.02.015","volume":"404","author":"K Araya-Sossa","year":"2019","unstructured":"Araya-Sossa, K., Mundarain, D.: Geometrical correlations as a resource for nonlocal extractable work. Ann. Phys. 404, 81\u201392 (2019)","journal-title":"Ann. Phys."},{"key":"4854_CR11","doi-asserted-by":"publisher","first-page":"117702","DOI":"10.1103\/PhysRevLett.120.117702","volume":"120","author":"D Ferraro","year":"2018","unstructured":"Ferraro, D., Campisi, M., Andolina, G.M., Pellegrini, V., Polini, M.: High-power collective charging of a solid-state quantum battery. Phys. Rev. Lett. 120, 117702 (2018)","journal-title":"Phys. Rev. Lett."},{"key":"4854_CR12","doi-asserted-by":"publisher","first-page":"022106","DOI":"10.1103\/PhysRevA.97.022106","volume":"97","author":"TP Le","year":"2018","unstructured":"Le, T.P., Levinsen, J., Modi, K., Parish, M.M., Pollock, F.A.: Spin-chain model of a many-body quantum battery. Phys. Rev. A 97, 022106 (2018)","journal-title":"Phys. Rev. A"},{"key":"4854_CR13","doi-asserted-by":"publisher","first-page":"180401","DOI":"10.1103\/PhysRevLett.134.180401","volume":"134","author":"L Zhi-Guang","year":"2025","unstructured":"Zhi-Guang, L., Tian, G., L\u00fc, X.-Y., Shang, C.: Topological quantum batteries. Phys. Rev. Lett. 134, 180401 (2025)","journal-title":"Phys. Rev. Lett."},{"key":"4854_CR14","doi-asserted-by":"publisher","first-page":"2400651","DOI":"10.1002\/qute.202400651","volume":"24","author":"S Elghaayda","year":"2025","unstructured":"Elghaayda, S., Ali, A., Al-Kuwari, S., Czerwinski, A., Mansour, M., Haddadi, S.: Performance of a superconducting quantum battery. Adv. Quantum Technol. 24, 2400651 (2025)","journal-title":"Adv. Quantum Technol."},{"issue":"4","key":"4854_CR15","doi-asserted-by":"publisher","first-page":"047702","DOI":"10.1103\/PhysRevLett.122.047702","volume":"122","author":"GM Andolina","year":"2019","unstructured":"Andolina, G.M., Keck, M., Mari, A., Campisi, M., Giovannetti, V., Polini, M.: Extractable work, the role of correlations, and asymptotic freedom in quantum batteries. Phys. Rev. Lett. 122(4), 047702 (2019)","journal-title":"Phys. Rev. Lett."},{"key":"4854_CR16","doi-asserted-by":"publisher","first-page":"065501","DOI":"10.1088\/1361-6455\/adbc56","volume":"58","author":"AA Zahia","year":"2025","unstructured":"Zahia, A.A., Abd-Rabbou, M.Y., Megahed, A.M.: Entanglement-driven energy exchange in a two-qubit quantum battery. J. Phys. B 58, 065501 (2025)","journal-title":"J. Phys. B"},{"issue":"4","key":"4854_CR17","doi-asserted-by":"publisher","first-page":"042333","DOI":"10.1103\/PhysRevA.100.042333","volume":"100","author":"C Radhakrishnan","year":"2019","unstructured":"Radhakrishnan, C., L\u00fc, Z., Jing, J., Byrnes, T.: Dynamics of quantum coherence in a spin-star system: bipartite initial state and coherence distribution. Phys. Rev. A 100(4), 042333 (2019)","journal-title":"Phys. Rev. A"},{"issue":"2","key":"4854_CR18","doi-asserted-by":"publisher","first-page":"025101","DOI":"10.1088\/1402-4896\/ada206","volume":"100","author":"AA Zahia","year":"2025","unstructured":"Zahia, A.A., Abd-Rabbou, M.Y., Megahed, A.M.: Explicit and implicit quantum correlation dynamics of qubits interacting with thermal baths. Phys. Scr. 100(2), 025101 (2025)","journal-title":"Phys. Scr."},{"issue":"2","key":"4854_CR19","doi-asserted-by":"publisher","first-page":"022115","DOI":"10.1103\/PhysRevA.69.022115","volume":"69","author":"H-P Breuer","year":"2004","unstructured":"Breuer, H.-P.: Exact quantum jump approach to open systems in bosonic and spin baths. Phys. Rev. A 69(2), 022115 (2004)","journal-title":"Phys. Rev. A"},{"key":"4854_CR20","doi-asserted-by":"crossref","unstructured":"Yuan, X.-Z., Goan, H.-S., Zhu, K.-D.: Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment. Phys. Rev. B Condens. Matter Mater. Phys. 75(4), 045331 (2007)","DOI":"10.1103\/PhysRevB.75.045331"},{"key":"4854_CR21","doi-asserted-by":"crossref","unstructured":"Hutton, A., Bose, S.: Mediated entanglement and correlations in a star network of interacting spins. Phys. Rev. A At. Mol. Opt. Phys. 69(4), 042312 (2004)","DOI":"10.1103\/PhysRevA.69.042312"},{"key":"4854_CR22","volume-title":"Interacting Electrons and Quantum Magnetism","author":"A Auerbach","year":"2012","unstructured":"Auerbach, A.: Interacting Electrons and Quantum Magnetism. Springer (2012)"},{"issue":"12","key":"4854_CR23","doi-asserted-by":"publisher","first-page":"1098","DOI":"10.1103\/PhysRev.58.1098","volume":"58","author":"T Holstein","year":"1940","unstructured":"Holstein, T., Primakoff, H.: Field dependence of the intrinsic domain magnetization of a ferromagnet. Phys. Rev. 58(12), 1098 (1940)","journal-title":"Phys. Rev."},{"key":"4854_CR24","volume-title":"The Theory of Open Quantum Systems","author":"H-P Breuer","year":"2002","unstructured":"Breuer, H.-P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)"},{"key":"4854_CR25","doi-asserted-by":"crossref","unstructured":"Lidar, D.A., Whaley, K.B.: Decoherence-free subspaces and subsystems. In: Irreversible Quantum Dynamics, pp. 83\u2013120. Springer (2003)","DOI":"10.1007\/3-540-44874-8_5"},{"key":"4854_CR26","doi-asserted-by":"publisher","first-page":"3289","DOI":"10.1103\/PhysRevA.45.3289","volume":"45","author":"J Peng","year":"1992","unstructured":"Peng, J., Li, G.: Phase fluctuations in the Jaynes\u2013Cummings model with and without the rotating-wave approximation. Phys. Rev. A 45, 3289\u20133293 (1992)","journal-title":"Phys. Rev. A"},{"issue":"3","key":"4854_CR27","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1088\/0305-4470\/4\/3\/009","volume":"4","author":"JM Radcliffe","year":"1971","unstructured":"Radcliffe, J.M.: Some properties of coherent spin states. J. Phys. A 4(3), 313 (1971)","journal-title":"J. Phys. A"},{"issue":"1","key":"4854_CR28","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1088\/1464-4266\/4\/1\/313","volume":"4","author":"NB An","year":"2002","unstructured":"An, N.B., Duc, T.M.: Trio coherent states. J. Opt. B 4(1), 80 (2002)","journal-title":"J. Opt. B"},{"key":"4854_CR29","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1134\/S1054660X08020072","volume":"18","author":"S Abdel-Khalek","year":"2008","unstructured":"Abdel-Khalek, S., Khalil, E.M., Ali, S.I.: Entanglement of a two-level atom papered in a finite trio-coherent state. Laser Phys. 18, 135\u2013143 (2008)","journal-title":"Laser Phys."},{"issue":"3","key":"4854_CR30","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1088\/1464-4266\/4\/3\/310","volume":"4","author":"NB An","year":"2002","unstructured":"An, N.B.: Multimode higher-order antibunching and squeezing in trio coherentstates. J. Opt. B 4(3), 222 (2002)","journal-title":"J. Opt. B"},{"key":"4854_CR31","doi-asserted-by":"publisher","first-page":"022320","DOI":"10.1103\/PhysRevA.88.022320","volume":"88","author":"TM Duc","year":"2013","unstructured":"Duc, T.M., Dat, T.Q., An, N.B., Kim, J.: Scheme for the generation of freely traveling optical trio coherent states. Phys. Rev. A 88, 022320 (2013)","journal-title":"Phys. Rev. A"},{"key":"4854_CR32","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.4.020319","volume":"4","author":"JM Gertler","year":"2023","unstructured":"Gertler, J.M., van Geldern, S., Shirol, S., Jiang, L., Wang, C.: Experimental realization and characterization of stabilized pair-coherent states. PRX Quantum 4, 020319 (2023)","journal-title":"PRX Quantum"},{"issue":"8","key":"4854_CR33","doi-asserted-by":"publisher","first-page":"1760","DOI":"10.1016\/j.cpc.2012.02.021","volume":"183","author":"JR Johansson","year":"2012","unstructured":"Johansson, J.R., Nation, P.D., Nori, F.: QuTiP: an open-source Python framework for the dynamics of open quantum systems. Comput. Phys. Commun. 183(8), 1760\u20131772 (2012)","journal-title":"Comput. Phys. Commun."},{"issue":"2","key":"4854_CR34","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.107.023725","volume":"107","author":"F-Q Dou","year":"2023","unstructured":"Dou, F.-Q., Yang, F.-M.: Superconducting transmon qubit-resonator quantum battery. Phys. Rev. A 107(2), 023725 (2023)","journal-title":"Phys. Rev. A"},{"issue":"15","key":"4854_CR35","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1063\/5.0161354","volume":"123","author":"Y Ge","year":"2023","unstructured":"Ge, Y., Yu, X., Xin, W., Wang, Z., Zhang, Y., Zheng, W., Li, S., Lan, D., Yu, Y.: Efficient charging and discharging of a superconducting quantum battery through frequency-modulated driving. Appl. Phys. Lett. 123(15), 25\u201368 (2023)","journal-title":"Appl. Phys. Lett."},{"issue":"15","key":"4854_CR36","doi-asserted-by":"publisher","first-page":"150601","DOI":"10.1103\/PhysRevLett.118.150601","volume":"118","author":"F Campaioli","year":"2017","unstructured":"Campaioli, F., Pollock, F.A., Binder, F.C., C\u00e9leri, L., Goold, J., Vinjanampathy, S., Modi, K.: Enhancing the charging power of quantum batteries. Phys. Rev. Lett. 118(15), 150601 (2017)","journal-title":"Phys. Rev. Lett."},{"issue":"6","key":"4854_CR37","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.107.064109","volume":"107","author":"K Koshihara","year":"2023","unstructured":"Koshihara, K., Yuasa, K.: Quantum ergotropy and quantum feedback control. Phys. Rev. E 107(6), 064109 (2023)","journal-title":"Phys. Rev. E"},{"issue":"18","key":"4854_CR38","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.125.180603","volume":"125","author":"G Francica","year":"2020","unstructured":"Francica, G., Binder, F.C., Guarnieri, G., Mitchison, M.T., Goold, J., Plastina, F.: Quantum coherence and ergotropy. Phys. Rev. Lett. 125(18), 180603 (2020)","journal-title":"Phys. Rev. Lett."},{"issue":"5","key":"4854_CR39","doi-asserted-by":"publisher","first-page":"612","DOI":"10.3390\/e23050612","volume":"23","author":"A Delmonte","year":"2021","unstructured":"Delmonte, A., Crescente, A., Carrega, M., Ferraro, D., Sassetti, M.: Characterization of a two-photon quantum battery: initial conditions, stability and work extraction. Entropy 23(5), 612 (2021)","journal-title":"Entropy"},{"issue":"4","key":"4854_CR40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.102.042111","volume":"102","author":"B \u00c7akmak","year":"2020","unstructured":"\u00c7akmak, B.: Ergotropy from coherences in an open quantum system. Phys. Rev. E 102(4), 042111 (2020)","journal-title":"Phys. Rev. E"},{"issue":"6","key":"4854_CR41","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.106.062609","volume":"106","author":"MB Arjmandi","year":"2022","unstructured":"Arjmandi, M.B., Shokri, A., Faizi, E., Mohammadi, H.: Performance of quantum batteries with correlated and uncorrelated chargers. Phys. Rev. A 106(6), 062609 (2022)","journal-title":"Phys. Rev. A"},{"issue":"13","key":"4854_CR42","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.129.130602","volume":"129","author":"H-L Shi","year":"2022","unstructured":"Shi, H.-L., Ding, S., Wan, Q.-K., Wang, X.-H., Yang, W.-L.: Entanglement, coherence, and extractable work in quantum batteries. Phys. Rev. Lett. 129(13), 130602 (2022)","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"4854_CR43","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1116\/5.0184903","volume":"6","author":"J-Y Gyhm","year":"2024","unstructured":"Gyhm, J.-Y., Fischer, U.R.: Beneficial and detrimental entanglement for quantum battery charging. AVS Quantum Sci. 6(1), 579\u2013598 (2024)","journal-title":"AVS Quantum Sci."},{"key":"4854_CR44","doi-asserted-by":"crossref","unstructured":"Petz, D.: Entropy, von Neumann and the von Neumann entropy: dedicated to the memory of Alfred Wehrl. In: John von Neumann and the Foundations of Quantum Physics, pp. 83\u201396. Springer (2001)","DOI":"10.1007\/978-94-017-2012-0_7"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04854-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-025-04854-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04854-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T08:25:17Z","timestamp":1757319917000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-025-04854-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,31]]},"references-count":44,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["4854"],"URL":"https:\/\/doi.org\/10.1007\/s11128-025-04854-y","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-6376526\/v1","asserted-by":"object"}]},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,31]]},"assertion":[{"value":"4 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 July 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"245"}}