REVIEW 2 major objections 2 minor 59 references
Transverse interactions in Dicke quantum batteries can be controlled to induce spin squeezing and nonlinear torque that boost charging power and capacity.
Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →
T0 review · grok-4.3
2026-07-01 00:45 UTC pith:EBN6K3A3
load-bearing objection The paper claims transverse interactions can be controlled for spin squeezing and nonlinear torque to boost Dicke battery charging and beat ideal cases under dissipation, but the alignment step is the least secure part. the 2 major comments →
Spin-Squeezing-Enhanced Charging for Quantum Dicke Batteries
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
In the low-excitation limit, transverse interactions induce collective spin squeezing, causing critical mode softening and an exponential enhancement of effective coupling, which significantly boosts charging power. At higher excitations, these interactions act as a macroscopic nonlinear torque. By appropriately aligning this torque, we effectively lower phase-space dynamical barriers, guiding the system along optimal rapid-charging paths. Importantly, this cooperative enhancement remains highly robust under realistic dissipation, outperforming ideal, dissipationless Dicke QBs in specific regimes.
What carries the argument
Transverse interactions repurposed to generate collective spin squeezing (low excitation) and aligned macroscopic nonlinear torque (higher excitation) within the Dicke model.
Load-bearing premise
Transverse interactions can be controlled and aligned to produce the described spin squeezing and nonlinear torque effects without introducing competing detrimental processes.
What would settle it
Direct measurement showing whether charging power exhibits exponential growth with transverse coupling strength in the low-excitation regime, or whether a dissipative battery with aligned interactions exceeds the charging speed of an ideal dissipationless reference battery.
If this is right
- Charging power receives an exponential boost from the softened mode and enhanced coupling in the low-excitation regime.
- Alignment of the nonlinear torque steers the dynamics onto faster, lower-barrier charging trajectories.
- The performance advantage survives realistic dissipation and can surpass ideal non-dissipative Dicke batteries in targeted parameter ranges.
- The approach supplies a concrete blueprint for building dissipation-resistant, high-performance many-body quantum batteries.
Where Pith is reading between the lines
- The same interaction-repurposing strategy could be tested in other collective spin or cavity systems where transverse couplings are tunable.
- Experimental implementations would need precise control over the relative phase and strength of transverse terms to realize the claimed torque alignment.
- The identified optimal paths may intersect with existing quantum optimal-control methods for accelerating state transfer in open systems.
- Robustness against dissipation hints at possible operation in warm environments where perfect isolation is impractical.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper claims that transverse matter-matter interactions in Dicke quantum batteries, conventionally viewed as detrimental, can be controlled and repurposed as a synergistic resource. In the low-excitation regime, these interactions induce collective spin squeezing that causes critical mode softening and an exponential boost to the effective coupling, enhancing charging power. At higher excitations, the interactions manifest as a macroscopic nonlinear torque that, when appropriately aligned, lowers phase-space dynamical barriers to enable faster charging paths. The resulting cooperative enhancement is asserted to remain robust under realistic dissipation and to outperform ideal, dissipationless Dicke quantum batteries in specific regimes.
Significance. If the central claims are substantiated, the work offers a new design paradigm for many-body quantum batteries that turns intrinsic interactions into an asset rather than a liability, with particular value in the demonstrated robustness to dissipation. This could inform practical implementations of high-power, dissipation-resistant quantum energy storage devices.
major comments (2)
- [Model section (likely §2 or §3)] The load-bearing premise that transverse interactions can be tuned and aligned to produce spin squeezing and a synergistic nonlinear torque without introducing competing noise channels or shifting the system away from optimal paths is stated in the abstract but lacks an explicit protocol, bound, or derivation showing that the required control does not itself generate additional dissipation; this directly underpins the outperformance claim over ideal Dicke QBs.
- [Low-excitation analysis (likely §4)] The exponential enhancement of effective coupling via mode softening in the low-excitation limit is asserted but requires a concrete derivation or scaling relation (e.g., how the squeezing parameter enters the effective Hamiltonian or charging power) to confirm it follows from the transverse interaction term without additional assumptions.
minor comments (2)
- [Results and figures] Quantitative comparisons to the ideal dissipationless case should be presented with explicit parameter values and error bars in the relevant figures to delineate the 'specific regimes' of outperformance.
- [Throughout] Notation for the transverse interaction strength and the alignment angle of the nonlinear torque should be introduced consistently and defined at first use.
Simulated Author's Rebuttal
We thank the referee for the careful reading and constructive feedback. The comments highlight areas where additional detail will strengthen the manuscript. We address each major comment below and indicate the revisions made.
read point-by-point responses
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Referee: The load-bearing premise that transverse interactions can be tuned and aligned to produce spin squeezing and a synergistic nonlinear torque without introducing competing noise channels or shifting the system away from optimal paths is stated in the abstract but lacks an explicit protocol, bound, or derivation showing that the required control does not itself generate additional dissipation; this directly underpins the outperformance claim over ideal Dicke QBs.
Authors: We agree that an explicit protocol and bounds are needed to substantiate the tuning of transverse interactions. In the revised manuscript, we add a dedicated subsection to the model section that specifies the control protocol via external driving fields, derives bounds ensuring no additional dissipation channels are introduced beyond those already modeled, and shows that the alignment does not shift the system from the identified optimal paths. This directly supports the outperformance claim. revision: yes
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Referee: The exponential enhancement of effective coupling via mode softening in the low-excitation limit is asserted but requires a concrete derivation or scaling relation (e.g., how the squeezing parameter enters the effective Hamiltonian or charging power) to confirm it follows from the transverse interaction term without additional assumptions.
Authors: We appreciate this observation. The revised low-excitation analysis section now includes a step-by-step derivation starting from the transverse interaction term, showing how it generates the collective squeezing parameter, induces critical mode softening, and enters the effective Hamiltonian. We explicitly derive the exponential scaling of the effective coupling with the squeezing parameter and the resulting enhancement in charging power, confirming it follows directly without further assumptions. revision: yes
Circularity Check
No circularity: derivation remains self-contained from the Dicke model
full rationale
The provided abstract and description present a theoretical proposal that starts from the standard Dicke Hamiltonian, adds transverse interactions, and derives their effects on squeezing, mode softening, and torque alignment through standard many-body analysis. No equations, fitting procedures, or self-citations are shown that would reduce any claimed prediction or enhancement to an input by construction. The central claims rest on the model's dynamics rather than on renamed fits or load-bearing self-references, making the derivation independent of its own outputs.
Axiom & Free-Parameter Ledger
read the original abstract
High-power Dicke quantum batteries (QBs) typically exploit collective superradiance, whereas intrinsic matter-matter interactions are conventionally considered detrimental. Here, we propose a counterintuitive paradigm: these interactions can be controlled and repurposed as a synergistic resource to enhance charging power and capacity. In the low-excitation limit, transverse interactions induce collective spin squeezing, causing critical mode softening and an exponential enhancement of effective coupling, which significantly boosts charging power. At higher excitations, these interactions act as a macroscopic nonlinear torque. By appropriately aligning this torque, we effectively lower phase-space dynamical barriers, guiding the system along optimal rapid-charging paths. Importantly, this cooperative enhancement remains highly robust under realistic dissipation, outperforming ideal, dissipationless Dicke QBs in specific regimes. Our results provide a blueprint for exploiting matter interactions to design dissipation-resistant, high-performance many-body QBs.
Figures
Reference graph
Works this paper leans on
-
[1]
generates no spin squeezing in either regime and purely modifies the effective detuning ∆ z. Consequently, only 𝜔𝑎𝑡 𝐽𝑥/𝜔𝑎 0 10 −1 1 0 0.12 𝐸/𝜔𝑎 0 0.016𝐸/𝜔𝑎 0.09 0 𝐸/𝜔𝑎 𝜔𝑎𝑡 𝐽𝑦/𝜔𝑎 0 10 −1 1 𝜔𝑎𝑡 𝐽𝑧/𝜔𝑎 0 10 −1 1 (a) (b) (c) (d) (e) (f) Figure 2. HP-regime charging dynamics. (a,b,c) Stored energyE/ω a and (d,e,f) average powerP avg vs interaction strengthJ k/ω...
-
[2]
H. T. Quan, Quantum thermodynamic cycles and quantum heat engines, Phys. Rev. E79, 041129 (2009)
work page 2009
-
[3]
R. Alicki and M. Fannes, Entanglement boost for extractable work from ensembles of quantum batteries, Phys. Rev. E87, 042123 (2013). 6
work page 2013
-
[4]
Kosloff, Quantum thermodynamics: A dynamical viewpoint, Entropy15, 2100–2128 (2013)
R. Kosloff, Quantum thermodynamics: A dynamical viewpoint, Entropy15, 2100–2128 (2013)
work page 2013
- [5]
-
[6]
G. M. Andolina, M. Keck, A. Mari, M. Campisi, V. Giovannetti, and M. Polini, Extractable work, the role of correlations, and asymptotic freedom in quantum batteries, Phys. Rev. Lett.122, 047702 (2019)
work page 2019
-
[7]
G. Francica, F. C. Binder, G. Guarnieri, M. T. Mitchison, J. Goold, and F. Plastina, Quantum coherence and ergotropy, Phys. Rev. Lett.125, 180603 (2020)
work page 2020
-
[8]
G. Kurizki and A. G. Kofman,Thermodynamics and Control of Open Quantum Systems(Cambridge University Press, 2022)
work page 2022
-
[9]
F. Campaioli, S. Gherardini, J. Q. Quach, M. Polini, and G. M. Andolina, Colloquium: Quantum batteries, Rev. Mod. Phys.96, 031001 (2024)
work page 2024
-
[10]
K.-X. Yan, Y. Liu, Y. Xiao, J.-H. Lin, J. Song, Y.- H. Chen, F. Nori, and Y. Xia, Giant-atom quantum batteries: Lossless energy transfer via interference engineering, Phys. Rev. Lett.136, 180401 (2026)
work page 2026
-
[11]
F. Campaioli, F. A. Pollock, F. C. Binder, L. C´ eleri, J. Goold, S. Vinjanampathy, and K. Modi, Enhancing the charging power of quantum batteries, Phys. Rev. Lett. 118, 150601 (2017)
work page 2017
-
[12]
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)
work page 2018
-
[13]
J. Chen, L. Zhan, L. Shao, X. Zhang, Y. Zhang, and X. Wang, Charging quantum batteries with a general harmonic driving field, Ann. Phys.532(2020)
work page 2020
-
[14]
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. A103, 052220 (2021)
work page 2021
-
[15]
J. Dias, H. Wang, K. Nemoto, F. Nori, and W. J. Munro, Efficient charging of multiple open quantum batteries through dissipation and pumping, Phys. Rev. A113, 012617 (2026)
work page 2026
-
[16]
F. C. Binder, S. Vinjanampathy, K. Modi, and J. Goold, Quantacell: powerful charging of quantum batteries, New J. Phys.17, 075015 (2015)
work page 2015
-
[17]
S. Juli` a-Farr´ e, T. Salamon, A. Riera, M. N. Bera, and M. Lewenstein, Bounds on the capacity and power of quantum batteries, Phys. Rev. Res.2, 023113 (2020)
work page 2020
-
[18]
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)
work page 2020
-
[19]
S. Pokhrel and J. Gea-Banacloche, Large collective power enhancement in dissipative charging of a quantum battery, Phys. Rev. Lett.134, 130401 (2025)
work page 2025
-
[20]
R. H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev.93, 99 (1954)
work page 1954
-
[21]
M. Gross and S. Haroche, Superradiance: An essay on the theory of collective spontaneous emission, Phys. Rep. 93, 301–396 (1982)
work page 1982
-
[22]
L. Garziano, A. Settineri, O. Di Stefano, S. Savasta, and F. Nori, Gauge invariance of the Dicke and Hopfield models, Phys. Rev. A102, 023718 (2020)
work page 2020
- [23]
-
[24]
D.-L. Yang, F.-M. Yang, and F.-Q. Dou, Three-level Dicke quantum battery, Phys. Rev. B109, 235432 (2024)
work page 2024
-
[25]
A. Crescente, M. Carrega, M. Sassetti, and D. Ferraro, Ultrafast charging in a two-photon Dicke quantum battery, Phys. Rev. B102, 245407 (2020)
work page 2020
-
[26]
A. Delmonte, A. Crescente, M. Carrega, D. Ferraro, and M. Sassetti, Characterization of a two-photon quantum battery: Initial conditions, stability and work extraction, Entropy23, 612 (2021)
work page 2021
-
[27]
J. P. Mendon¸ ca, K. Jachymski, and Y. Wang, Role of matter interactions in superradiant phenomena, Phys. Rev. Lett.135, 133601 (2025)
work page 2025
-
[28]
S. J. Roof, K. J. Kemp, M. D. Havey, and I. M. Sokolov, Observation of single-photon superradiance and the cooperative Lamb shift in an extended sample of cold atoms, Phys. Rev. Lett.117, 073003 (2016)
work page 2016
-
[29]
B. M. Garraway, The Dicke model in quantum optics: Dicke model revisited, Phil. Trans. R. Soc. A369, 1137–1155 (2011)
work page 2011
- [30]
-
[31]
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, 10.1126/sciadv.abk3160 (2022)
- [32]
- [33]
-
[34]
M. Kitagawa and M. Ueda, Squeezed spin states, Phys. Rev. A47, 5138 (1993)
work page 1993
-
[35]
C. Luo, H. Zhang, A. Chu, C. Maruko, A. M. Rey, and J. K. Thompson, Hamiltonian engineering of collective XYZ spin models in an optical cavity, Nat. Phys.21, 916–923 (2025)
work page 2025
-
[36]
D. C. Mattis, Ferromagnetism and spin waves in the band theory, Phys. Rev.132, 2521 (1963)
work page 1963
- [37]
- [38]
-
[39]
J. Ma, X. G. Wang, C. P. Sun, and F. Nori, Quantum spin squeezing, Phys. Rep.509, 89–165 (2011)
work page 2011
-
[40]
M. O. Scully and M. S. Zubairy,Quantum Optics, 1st ed. (Cambridge University Press, 1997)
work page 1997
-
[41]
C. Emary and T. Brandes, Chaos and the quantum phase transition in the Dicke model, Phys. Rev. E67, 066203 (2003)
work page 2003
-
[42]
G. S. Agarwal,Quantum Optics(Cambridge University Press, 2012). 7 [42]https://link.aps.org/supplemental/XXXXXXX, see Supplemental Material for a detailed derivation and possible experimiental implementation
work page 2012
-
[43]
T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev.58, 1098 (1940)
work page 1940
-
[44]
X. Wang and B. C. Sanders, Relations between bosonic quadrature squeezing and atomic spin squeezing, Phys. Rev. A68, 033821 (2003)
work page 2003
-
[45]
W. Qin, A. Miranowicz, P.-B. Li, X.-Y. L¨ u, J. Q. You, and F. Nori, Exponentially enhanced light- matter interaction, cooperativities, and steady-state entanglement using parametric amplification, Phys. Rev. Lett.120, 093601 (2018)
work page 2018
-
[46]
W. Qin, A. F. Kockum, C. S. Mu˜ noz, A. Miranowicz, and F. Nori, Quantum amplification and simulation of strong and ultrastrong coupling of light and matter, Phys. Rep. 1078, 1–59 (2024)
work page 2024
-
[47]
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. B98, 205423 (2018)
work page 2018
- [48]
-
[49]
A. N. Omelyanchouk, S. N. Shevchenko, A. M. Zagoskin, E. Il’ichev, and F. Nori, Pseudo-Rabi oscillations in superconducting flux qubits in the classical regime, Phys. Rev. B78, 054512 (2008)
work page 2008
-
[50]
A. N. Omelyanchouk, S. Savel’ev, A. M. Zagoskin, E. Il’ichev, and F. Nori, Noise-induced quantum coherence and persistent Rabi oscillations in a Josephson flux qubit, Phys. Rev. B80, 212503 (2009)
work page 2009
-
[51]
L. Garziano, R. Stassi, V. Macr` ı, A. F. Kockum, S. Savasta, and F. Nori, Multiphoton quantum Rabi oscillations in ultrastrong cavity QED, Phys. Rev. A92, 063830 (2015)
work page 2015
-
[52]
Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, Shortcuts to adiabaticity for the quantum Rabi model: Efficient generation of giant entangled cat states via parametric amplification, Phys. Rev. Lett.126, 023602 (2021)
work page 2021
-
[53]
Y.-H. Chen, Z.-C. Shi, F. Nori, and Y. Xia, Error-tolerant amplification and simulation of the ultrastrong-coupling quantum Rabi model, Phys. Rev. Lett.133, 033603 (2024)
work page 2024
-
[54]
F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Atomic coherent states in quantum optics, Phys. Rev. A 6, 2211 (1972)
work page 1972
-
[55]
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. and Technol.7, 045018 (2022)
work page 2022
-
[56]
A. Camposeo, T. Virgili, F. Lombardi, G. Cerullo, D. Pisignano, and M. Polini, Quantum batteries: A materials science perspective, Adv. Mater.37(2025)
work page 2025
-
[57]
H. Carmichael,An Open Systems Approach to Quantum Optics: Lectures Presented at the Universit´ e Libre de Bruxelles October 28 to November 4, 1991(Springer Berlin Heidelberg, 1993)
work page 1991
-
[58]
D. F. Walls and G. J. Milburn,Quantum Optics (Springer Nature Switzerland, 2025)
work page 2025
-
[59]
J. C. Louw, J. N. Kriel, and M. Kastner, Thermalization of a Lipkin-Meshkov-Glick model coupled to a bosonic bath, Phys. Rev. A100, 022115 (2019)
work page 2019
discussion (0)
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