Modulator-Assisted Zeno Control of Energy Transfer in Quantum Batteries
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AbstractEfficient operation of quantum batteries requires not only fast energy transfer but also the ability to halt the charging process to prevent reverse flow. Existing approaches typically rely on direct control of the charger-battery interaction, which can be experimentally demanding. Here we propose a modulator-assisted quantum battery protocol that enables indirect control of energy transfer while keeping the interaction always on. By applying repeated local unitary operations to an auxiliary modulator qubit, we exploit a Zeno-like mechanism to dynamically reshape the effective Hamiltonian and switch the charger-battery coupling on and off. We demonstrate this mechanism in a minimal three-body model and show that it remains effective beyond the ideal fast-control limit. We further extend the protocol to a collective many-body architecture, where it preserves the characteristic enhancement of charging power, scaling as $N^{3/2}$ with the number of battery units. We also discuss a possible implementation in an NV-${}^{13}$C spin platform. Our results establish modulator-assisted Zeno control as a scalable route to regulating energy transfer in quantum batteries.Featured image: Left side: A schematic representation of the modulator-assisted quantum battery, where the battery-charger coupling is always on. The effective coupling strength is modified through adding kicks to an external modulator, which only interacts locally with the battery. Right side: A schematic illustration of our modulator-assisted battery charging protocol when extended to $N$ batteries. Panel (a): Parallel-charging benchmark. An array of identical modulator-assisted Jaynes-Cummings quantum battery. Panel (b): Collective charging. A modulator-assisted Tavis-Cummings quantum battery.Popular summaryQuantum batteries can charge faster as they scale, because collective quantum effects enhance their charging power. But this quantum advantage comes with a fundamental challenge: quantum evolution is reversible. Once the battery is fully charged, the transfer must be stopped before the energy begins to flow back. Existing methods typically halt charging by directly tuning the battery, the charger, or the interaction between them. Such control requires direct access to the main energy-transfer components and becomes increasingly difficult in large or spatially separated systems. We introduce a new control strategy that leaves the physical charger–battery interaction always on. We add a small auxiliary system, a modulator, which couples only to the batteries. Repeated control is applied locally to the modulator, which reshapes the batteries’ effective dynamics, allowing energy transfer to be regulated remotely without directly manipulating the charger-battery primary system. When scaling to many batteries, the protocol preserves the collective charging advantage, with charging power growing as $N^{3/2}$ and charging time decreasing as $N^{-1/2}$. We further propose possible implementation using an NV center and surrounding nuclear spins, connecting the proposal to solid-state quantum platforms. In summary, our work turns indirect local operations into scalable control of quantum energy flow.► BibTeX data@article{Xie2026modulatorassisted, doi = {10.22331/q-2026-07-29-2178}, url = {https://doi.org/10.22331/q-2026-07-29-2178}, title = {Modulator-{A}ssisted {Z}eno {C}ontrol of {E}nergy {T}ransfer in {Q}uantum {B}atteries}, author = {Xie, Songbo and Sajjan, Manas and Ajoy, Ashok and Kais, Sabre}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2178}, month = jul, year = {2026} }► References [1] Francesco Campaioli, Stefano Gherardini, James Q Quach, Marco Polini, and Gian Marcello Andolina. ``Colloquium: quantum batteries''. Rev. Mod. Phys. 96, 031001 (2024). https://doi.org/10.1103/RevModPhys.96.031001 [2] Robert Alicki and Mark Fannes. ``Entanglement boost for extractable work from ensembles of quantum batteries''. Phys. Rev. E 87, 042123 (2013). https://doi.org/10.1103/PhysRevE.87.042123 [3] Nicolai Friis and Marcus Huber. ``Precision and work fluctuations in gaussian battery charging''. Quantum 2, 61 (2018). https://doi.org/10.22331/q-2018-04-23-61 [4] Alan C Santos, Barış Çakmak, Steve Campbell, and Nikolaj T Zinner. ``Stable adiabatic quantum batteries''. Phys. Rev. E 100, 032107 (2019). https://doi.org/10.1103/PhysRevE.100.032107 [5] Fu-Quan Dou, Yuan-Jin Wang, and Jian-An Sun. ``Highly efficient charging and discharging of three-level quantum batteries through shortcuts to adiabaticity''. Front. Phys. 17, 1–9 (2022). https://doi.org/10.1007/s11467-021-1130-5 [6] James Q Quach, Kirsty E McGhee, Lucia Ganzer, Dominic M Rouse, Brendon W Lovett, Erik M Gauger, Jonathan Keeling, Giulio Cerullo, David G Lidzey, and Tersilla Virgili. ``Superabsorption in an organic microcavity: Toward a quantum battery''. Sci. Adv. 8, eabk3160 (2022). https://doi.org/10.1126/sciadv.abk3160 [7] Chang-Kang Hu, Jiawei Qiu, Paulo JP Souza, Jiahao Yuan, Yuxuan Zhou, Libo Zhang, Ji Chu, Xianchuang Pan, Ling Hu, Jian Li, et al. ``Optimal charging of a superconducting quantum battery''. Quantum Science and Technology 7, 045018 (2022). https://doi.org/10.1088/2058-9565/ac8444 [8] I Maillette de Buy Wenniger, SE Thomas, M Maffei, SC Wein, M Pont, N Belabas, S Prasad, A Harouri, A Lemaı̂tre, I Sagnes, et al. ``Experimental analysis of energy transfers between a quantum emitter and light fields''. Phys. Rev. Lett. 131, 260401 (2023). https://doi.org/10.1103/PhysRevLett.131.260401 [9] Karen V Hovhannisyan, Martí Perarnau-Llobet, Marcus Huber, and Antonio Acín. ``Entanglement generation is not necessary for optimal work extraction''. Phys. Rev. Lett. 111, 240401 (2013). https://doi.org/10.1103/PhysRevLett.111.240401 [10] Felix C Binder, Sai Vinjanampathy, Kavan Modi, and John Goold. ``Quantacell: powerful charging of quantum batteries''. New J. Phys. 17, 075015 (2015). https://doi.org/10.1088/1367-2630/17/7/075015 [11] Francesco Campaioli, Felix A Pollock, Felix C Binder, Lucas Céleri, John Goold, Sai Vinjanampathy, and Kavan Modi. ``Enhancing the charging power of quantum batteries''. Phys. Rev. Lett. 118, 150601 (2017). https://doi.org/10.1103/PhysRevLett.118.150601 [12] Davide Rossini, Gian Marcello Andolina, Dario Rosa, Matteo Carrega, and Marco Polini. ``Quantum advantage in the charging process of sachdev-ye-kitaev batteries''. Phys. Rev. Lett. 125, 236402 (2020). https://doi.org/10.1103/PhysRevLett.125.236402 [13] Gian Marcello Andolina, Maximilian Keck, Andrea Mari, Vittorio Giovannetti, and Marco Polini. ``Quantum versus classical many-body batteries''. Phys. Rev. B 99, 205437 (2019). https://doi.org/10.1103/PhysRevB.99.205437 [14] Sergi Julià-Farré, Tymoteusz Salamon, Arnau Riera, Manabendra N Bera, and Maciej Lewenstein. ``Bounds on the capacity and power of quantum batteries''. Phys. Rev. Research 2, 023113 (2020). https://doi.org/10.1103/PhysRevResearch.2.023113 [15] Ju-Yeon Gyhm, Dominik Šafránek, and Dario Rosa. ``Quantum charging advantage cannot be extensive without global operations''. Phys. Rev. Lett. 128, 140501 (2022). https://doi.org/10.1103/PhysRevLett.128.140501 [16] Ju-Yeon Gyhm and Uwe R Fischer. ``Beneficial and detrimental entanglement for quantum battery charging''. AVS Quantum Science 6 (2024). https://doi.org/10.1116/5.0184903 [17] Gian Marcello Andolina, Vittoria Stanzione, Vittorio Giovannetti, and Marco Polini. ``Genuine quantum advantage in anharmonic bosonic quantum batteries''. Phys. Rev. Lett. 134, 240403 (2025). https://doi.org/10.1103/kzvn-dj7v [18] Antti O Niskanen, Yasunobu Nakamura, and Jaw-Shen Tsai. ``Tunable coupling scheme for flux qubits at the optimal point''. Phys. Rev. B 73, 094506 (2006). https://doi.org/10.1103/PhysRevB.73.094506 [19] AO Niskanen, Khalil Harrabi, F Yoshihara, Y Nakamura, S Lloyd, and Jaw Shen Tsai. ``Quantum coherent tunable coupling of superconducting qubits''. Science 316, 723–726 (2007). https://doi.org/10.1126/science.1141324 [20] Gavin K Brennen, Carlton M Caves, Poul S Jessen, and Ivan H Deutsch. ``Quantum logic gates in optical lattices''. Phys. Rev. Lett. 82, 1060 (1999). https://doi.org/10.1103/PhysRevLett.82.1060 [21] Johannes Zeiher, Rick Van Bijnen, Peter Schauß, Sebastian Hild, Jae-yoon Choi, Thomas Pohl, Immanuel Bloch, and Christian Gross. ``Many-body interferometry of a rydberg-dressed spin lattice''. Nat. Phys. 12, 1095–1099 (2016). https://doi.org/10.1038/nphys3835 [22] Dolev Bluvstein, Ahmed Omran, Harry Levine, Alexander Keesling, Giulia Semeghini, Sepehr Ebadi, Tout T Wang, Alexios A Michailidis, Nishad Maskara, Wen Wei Ho, et al. ``Controlling quantum many-body dynamics in driven rydberg atom arrays''. Science 371, 1355–1359 (2021). https://doi.org/10.1126/science.abg2530 [23] Anders Sørensen and Klaus Mølmer. ``Quantum computation with ions in thermal motion''. Phys. Rev. Lett. 82, 1971 (1999). https://doi.org/10.1103/PhysRevLett.82.1971 [24] Dietrich Leibfried, Brian DeMarco, Volker Meyer, David Lucas, Murray Barrett, Joe Britton, Wayne M Itano, B Jelenković, Chris Langer, Till Rosenband, et al. ``Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate''. Nature 422, 412–415 (2003). https://doi.org/10.1038/nature01492 [25] Gian Marcello Andolina, Donato Farina, Andrea Mari, Vittorio Pellegrini, Vittorio Giovannetti, and Marco Polini. ``Charger-mediated energy transfer in exactly solvable models for quantum batteries''. Phys. Rev. B 98, 205423 (2018). https://doi.org/10.1103/PhysRevB.98.205423 [26] Dario Ferraro, Michele Campisi, Gian Marcello Andolina, Vittorio Pellegrini, and Marco Polini. ``High-power collective charging of a solid-state quantum battery''. Phys. Rev. Lett. 120, 117702 (2018). https://doi.org/10.1103/PhysRevLett.120.117702 [27] Donato Farina, Gian Marcello Andolina, Andrea Mari, Marco Polini, and Vittorio Giovannetti. ``Charger-mediated energy transfer for quantum batteries: An open-system approach''. Phys. Rev. B 99, 035421 (2019). https://doi.org/10.1103/PhysRevB.99.035421 [28] Alba Crescente, Matteo Carrega, Maura Sassetti, and Dario Ferraro. ``Ultrafast charging in a two-photon dicke quantum battery''. Phys. Rev. B 102, 245407 (2020). https://doi.org/10.1103/PhysRevB.102.245407 [29] Anna Delmonte, Alba Crescente, Matteo Carrega, Dario Ferraro, and Maura Sassetti. ``Characterization of a two-photon quantum battery: Initial conditions, stability and work extraction''. Entropy 23, 612 (2021). https://doi.org/10.3390/e23050612 [30] Paolo Facchi and Saverino Pascazio. ``Quantum zeno dynamics: mathematical and physical aspects''. J. Phys. A Math. Theor. 41, 493001 (2008). https://doi.org/10.1088/1751-8113/41/49/493001 [31] Songbo Xie, Manas Sajjan, and Sabre Kais. ``Strong local passivity in unconventional scenarios: A new protocol for amplified quantum energy teleportation''. Entropy 27, 1147 (2025). https://doi.org/10.3390/e27111147 [32] Deepak Dhar, LK Grover, and SM Roy. ``Preserving quantum states using inverting pulses: a super-zeno effect''. Phys. Rev. Lett. 96, 100405 (2006). https://doi.org/10.1103/PhysRevLett.96.100405 [33] Harpreet Singh, Arvind, and Kavita Dorai. ``Experimental protection against evolution of states in a subspace via a super-zeno scheme on an nmr quantum information processor''. Phys. Rev. A 90, 052329 (2014). https://doi.org/10.1103/PhysRevA.90.052329 [34] Christopher C Gerry and Peter L Knight. ``Introductory quantum optics''. Cambridge university press. (2023). https://doi.org/10.1017/9781139151207 [35] Conor E Bradley, Joe Randall, Mohamed H Abobeih, Remon C Berrevoets, Maarten J Degen, Michiel A Bakker, Matthew Markham, Daniel J Twitchen, and Tim H Taminiau. ``A ten-qubit solid-state spin register with quantum memory up to one minute''. Phys. Rev. X 9, 031045 (2019). https://doi.org/10.1103/PhysRevX.9.031045 [36] Ashok Ajoy, Ulf Bissbort, Mikhail D Lukin, RonaldLee Walsworth, and Paola Cappellaro. ``Atomic-scale nuclear spin imaging using quantum-assisted sensors in diamond''. Phys. Rev. X 5, 011001 (2015). https://doi.org/10.1103/PhysRevX.5.011001 [37] A Dréau, J-R Maze, M Lesik, J-F Roch, and V Jacques. ``High-resolution spectroscopy of single nv defects coupled with nearby 13 c nuclear spins in diamond''. Phys. Rev. B 85, 134107 (2012). https://doi.org/10.1103/PhysRevB.85.134107 [38] V Jacques, P Neumann, J Beck, M Markham, D Twitchen, J Meijer, F Kaiser, G Balasubramanian, F Jelezko, and J Wrachtrup. ``Dynamic polarization of single nuclear spins by optical pumping of nitrogen-vacancy color centers in diamond at room temperature''. Phys. Rev. Lett. 102, 057403 (2009). https://doi.org/10.1103/PhysRevLett.102.057403 [39] Stefano Gherardini, Francesco Campaioli, Filippo Caruso, and Felix C Binder. ``Stabilizing open quantum batteries by sequential measurements''. Phys. Rev. Research 2, 013095 (2020). https://doi.org/10.1103/PhysRevResearch.2.013095 [40] Erwin L Hahn. ``Spin echoes''. Phys. 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A 109, 022210 (2024). https://doi.org/10.1103/PhysRevA.109.022210Cited byCould not fetch Crossref cited-by data during last attempt 2026-07-29 11:16:46: Could not fetch cited-by data for 10.22331/q-2026-07-29-2178 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-07-29 11:16:47: Cannot retrieve data from ADS due to rate limitations.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractEfficient operation of quantum batteries requires not only fast energy transfer but also the ability to halt the charging process to prevent reverse flow. Existing approaches typically rely on direct control of the charger-battery interaction, which can be experimentally demanding. Here we propose a modulator-assisted quantum battery protocol that enables indirect control of energy transfer while keeping the interaction always on. By applying repeated local unitary operations to an auxiliary modulator qubit, we exploit a Zeno-like mechanism to dynamically reshape the effective Hamiltonian and switch the charger-battery coupling on and off. We demonstrate this mechanism in a minimal three-body model and show that it remains effective beyond the ideal fast-control limit. We further extend the protocol to a collective many-body architecture, where it preserves the characteristic enhancement of charging power, scaling as $N^{3/2}$ with the number of battery units. We also discuss a possible implementation in an NV-${}^{13}$C spin platform. Our results establish modulator-assisted Zeno control as a scalable route to regulating energy transfer in quantum batteries.Featured image: Left side: A schematic representation of the modulator-assisted quantum battery, where the battery-charger coupling is always on. The effective coupling strength is modified through adding kicks to an external modulator, which only interacts locally with the battery. Right side: A schematic illustration of our modulator-assisted battery charging protocol when extended to $N$ batteries. Panel (a): Parallel-charging benchmark. An array of identical modulator-assisted Jaynes-Cummings quantum battery. Panel (b): Collective charging. A modulator-assisted Tavis-Cummings quantum battery.Popular summaryQuantum batteries can charge faster as they scale, because collective quantum effects enhance their charging power. But this quantum advantage comes with a fundamental challenge: quantum evolution is reversible. Once the battery is fully charged, the transfer must be stopped before the energy begins to flow back. Existing methods typically halt charging by directly tuning the battery, the charger, or the interaction between them. Such control requires direct access to the main energy-transfer components and becomes increasingly difficult in large or spatially separated systems. We introduce a new control strategy that leaves the physical charger–battery interaction always on. We add a small auxiliary system, a modulator, which couples only to the batteries. Repeated control is applied locally to the modulator, which reshapes the batteries’ effective dynamics, allowing energy transfer to be regulated remotely without directly manipulating the charger-battery primary system. When scaling to many batteries, the protocol preserves the collective charging advantage, with charging power growing as $N^{3/2}$ and charging time decreasing as $N^{-1/2}$. We further propose possible implementation using an NV center and surrounding nuclear spins, connecting the proposal to solid-state quantum platforms. In summary, our work turns indirect local operations into scalable control of quantum energy flow.► BibTeX data@article{Xie2026modulatorassisted, doi = {10.22331/q-2026-07-29-2178}, url = {https://doi.org/10.22331/q-2026-07-29-2178}, title = {Modulator-{A}ssisted {Z}eno {C}ontrol of {E}nergy {T}ransfer in {Q}uantum {B}atteries}, author = {Xie, Songbo and Sajjan, Manas and Ajoy, Ashok and Kais, Sabre}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2178}, month = jul, year = {2026} }► References [1] Francesco Campaioli, Stefano Gherardini, James Q Quach, Marco Polini, and Gian Marcello Andolina. ``Colloquium: quantum batteries''. Rev. Mod. Phys. 96, 031001 (2024). https://doi.org/10.1103/RevModPhys.96.031001 [2] Robert Alicki and Mark Fannes. ``Entanglement boost for extractable work from ensembles of quantum batteries''. Phys. Rev. E 87, 042123 (2013). https://doi.org/10.1103/PhysRevE.87.042123 [3] Nicolai Friis and Marcus Huber. ``Precision and work fluctuations in gaussian battery charging''. Quantum 2, 61 (2018). https://doi.org/10.22331/q-2018-04-23-61 [4] Alan C Santos, Barış Çakmak, Steve Campbell, and Nikolaj T Zinner. ``Stable adiabatic quantum batteries''. Phys. Rev. E 100, 032107 (2019). https://doi.org/10.1103/PhysRevE.100.032107 [5] Fu-Quan Dou, Yuan-Jin Wang, and Jian-An Sun. ``Highly efficient charging and discharging of three-level quantum batteries through shortcuts to adiabaticity''. Front. Phys. 17, 1–9 (2022). https://doi.org/10.1007/s11467-021-1130-5 [6] James Q Quach, Kirsty E McGhee, Lucia Ganzer, Dominic M Rouse, Brendon W Lovett, Erik M Gauger, Jonathan Keeling, Giulio Cerullo, David G Lidzey, and Tersilla Virgili. ``Superabsorption in an organic microcavity: Toward a quantum battery''. Sci. Adv. 8, eabk3160 (2022). https://doi.org/10.1126/sciadv.abk3160 [7] Chang-Kang Hu, Jiawei Qiu, Paulo JP Souza, Jiahao Yuan, Yuxuan Zhou, Libo Zhang, Ji Chu, Xianchuang Pan, Ling Hu, Jian Li, et al. ``Optimal charging of a superconducting quantum battery''. Quantum Science and Technology 7, 045018 (2022). https://doi.org/10.1088/2058-9565/ac8444 [8] I Maillette de Buy Wenniger, SE Thomas, M Maffei, SC Wein, M Pont, N Belabas, S Prasad, A Harouri, A Lemaı̂tre, I Sagnes, et al. ``Experimental analysis of energy transfers between a quantum emitter and light fields''. Phys. Rev. Lett. 131, 260401 (2023). https://doi.org/10.1103/PhysRevLett.131.260401 [9] Karen V Hovhannisyan, Martí Perarnau-Llobet, Marcus Huber, and Antonio Acín. ``Entanglement generation is not necessary for optimal work extraction''. Phys. Rev. Lett. 111, 240401 (2013). https://doi.org/10.1103/PhysRevLett.111.240401 [10] Felix C Binder, Sai Vinjanampathy, Kavan Modi, and John Goold. ``Quantacell: powerful charging of quantum batteries''. New J. Phys. 17, 075015 (2015). https://doi.org/10.1088/1367-2630/17/7/075015 [11] Francesco Campaioli, Felix A Pollock, Felix C Binder, Lucas Céleri, John Goold, Sai Vinjanampathy, and Kavan Modi. ``Enhancing the charging power of quantum batteries''. Phys. Rev. Lett. 118, 150601 (2017). https://doi.org/10.1103/PhysRevLett.118.150601 [12] Davide Rossini, Gian Marcello Andolina, Dario Rosa, Matteo Carrega, and Marco Polini. ``Quantum advantage in the charging process of sachdev-ye-kitaev batteries''. Phys. Rev. Lett. 125, 236402 (2020). https://doi.org/10.1103/PhysRevLett.125.236402 [13] Gian Marcello Andolina, Maximilian Keck, Andrea Mari, Vittorio Giovannetti, and Marco Polini. ``Quantum versus classical many-body batteries''. Phys. Rev. B 99, 205437 (2019). https://doi.org/10.1103/PhysRevB.99.205437 [14] Sergi Julià-Farré, Tymoteusz Salamon, Arnau Riera, Manabendra N Bera, and Maciej Lewenstein. ``Bounds on the capacity and power of quantum batteries''. Phys. Rev. Research 2, 023113 (2020). https://doi.org/10.1103/PhysRevResearch.2.023113 [15] Ju-Yeon Gyhm, Dominik Šafránek, and Dario Rosa. ``Quantum charging advantage cannot be extensive without global operations''. Phys. Rev. Lett. 128, 140501 (2022). https://doi.org/10.1103/PhysRevLett.128.140501 [16] Ju-Yeon Gyhm and Uwe R Fischer. ``Beneficial and detrimental entanglement for quantum battery charging''. AVS Quantum Science 6 (2024). https://doi.org/10.1116/5.0184903 [17] Gian Marcello Andolina, Vittoria Stanzione, Vittorio Giovannetti, and Marco Polini. ``Genuine quantum advantage in anharmonic bosonic quantum batteries''. Phys. Rev. Lett. 134, 240403 (2025). https://doi.org/10.1103/kzvn-dj7v [18] Antti O Niskanen, Yasunobu Nakamura, and Jaw-Shen Tsai. ``Tunable coupling scheme for flux qubits at the optimal point''. Phys. Rev. B 73, 094506 (2006). https://doi.org/10.1103/PhysRevB.73.094506 [19] AO Niskanen, Khalil Harrabi, F Yoshihara, Y Nakamura, S Lloyd, and Jaw Shen Tsai. ``Quantum coherent tunable coupling of superconducting qubits''. Science 316, 723–726 (2007). https://doi.org/10.1126/science.1141324 [20] Gavin K Brennen, Carlton M Caves, Poul S Jessen, and Ivan H Deutsch. ``Quantum logic gates in optical lattices''. Phys. Rev. Lett. 82, 1060 (1999). https://doi.org/10.1103/PhysRevLett.82.1060 [21] Johannes Zeiher, Rick Van Bijnen, Peter Schauß, Sebastian Hild, Jae-yoon Choi, Thomas Pohl, Immanuel Bloch, and Christian Gross. ``Many-body interferometry of a rydberg-dressed spin lattice''. Nat. Phys. 12, 1095–1099 (2016). https://doi.org/10.1038/nphys3835 [22] Dolev Bluvstein, Ahmed Omran, Harry Levine, Alexander Keesling, Giulia Semeghini, Sepehr Ebadi, Tout T Wang, Alexios A Michailidis, Nishad Maskara, Wen Wei Ho, et al. ``Controlling quantum many-body dynamics in driven rydberg atom arrays''. Science 371, 1355–1359 (2021). https://doi.org/10.1126/science.abg2530 [23] Anders Sørensen and Klaus Mølmer. ``Quantum computation with ions in thermal motion''. Phys. Rev. Lett. 82, 1971 (1999). https://doi.org/10.1103/PhysRevLett.82.1971 [24] Dietrich Leibfried, Brian DeMarco, Volker Meyer, David Lucas, Murray Barrett, Joe Britton, Wayne M Itano, B Jelenković, Chris Langer, Till Rosenband, et al. ``Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate''. Nature 422, 412–415 (2003). https://doi.org/10.1038/nature01492 [25] Gian Marcello Andolina, Donato Farina, Andrea Mari, Vittorio Pellegrini, Vittorio Giovannetti, and Marco Polini. ``Charger-mediated energy transfer in exactly solvable models for quantum batteries''. Phys. Rev. B 98, 205423 (2018). https://doi.org/10.1103/PhysRevB.98.205423 [26] Dario Ferraro, Michele Campisi, Gian Marcello Andolina, Vittorio Pellegrini, and Marco Polini. ``High-power collective charging of a solid-state quantum battery''. Phys. Rev. Lett. 120, 117702 (2018). https://doi.org/10.1103/PhysRevLett.120.117702 [27] Donato Farina, Gian Marcello Andolina, Andrea Mari, Marco Polini, and Vittorio Giovannetti. ``Charger-mediated energy transfer for quantum batteries: An open-system approach''. Phys. Rev. B 99, 035421 (2019). https://doi.org/10.1103/PhysRevB.99.035421 [28] Alba Crescente, Matteo Carrega, Maura Sassetti, and Dario Ferraro. ``Ultrafast charging in a two-photon dicke quantum battery''. Phys. Rev. B 102, 245407 (2020). https://doi.org/10.1103/PhysRevB.102.245407 [29] Anna Delmonte, Alba Crescente, Matteo Carrega, Dario Ferraro, and Maura Sassetti. ``Characterization of a two-photon quantum battery: Initial conditions, stability and work extraction''. Entropy 23, 612 (2021). https://doi.org/10.3390/e23050612 [30] Paolo Facchi and Saverino Pascazio. ``Quantum zeno dynamics: mathematical and physical aspects''. J. Phys. A Math. Theor. 41, 493001 (2008). https://doi.org/10.1088/1751-8113/41/49/493001 [31] Songbo Xie, Manas Sajjan, and Sabre Kais. ``Strong local passivity in unconventional scenarios: A new protocol for amplified quantum energy teleportation''. Entropy 27, 1147 (2025). https://doi.org/10.3390/e27111147 [32] Deepak Dhar, LK Grover, and SM Roy. ``Preserving quantum states using inverting pulses: a super-zeno effect''. Phys. Rev. Lett. 96, 100405 (2006). https://doi.org/10.1103/PhysRevLett.96.100405 [33] Harpreet Singh, Arvind, and Kavita Dorai. ``Experimental protection against evolution of states in a subspace via a super-zeno scheme on an nmr quantum information processor''. Phys. Rev. A 90, 052329 (2014). https://doi.org/10.1103/PhysRevA.90.052329 [34] Christopher C Gerry and Peter L Knight. ``Introductory quantum optics''. Cambridge university press. 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A 109, 022210 (2024). https://doi.org/10.1103/PhysRevA.109.022210Cited byCould not fetch Crossref cited-by data during last attempt 2026-07-29 11:16:46: Could not fetch cited-by data for 10.22331/q-2026-07-29-2178 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-07-29 11:16:47: Cannot retrieve data from ADS due to rate limitations.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
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