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arxiv: 2605.17700 · v1 · pith:QTOBI74Nnew · submitted 2026-05-17 · 🪐 quant-ph

Coherence-Enhanced Quantum Battery Charging with Ergotropy Stabilization

Fan Yang , Hui Wang , Yusef Maleki , William J. Munro , Girish S. Agarwal , Marlan O. Scully This is my paper

Pith reviewed 2026-05-20 12:06 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum batteryergotropycoherencedark statereservoir squeezingquantum chargingenergy storagedissipation
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The pith

Initial charger coherence maximizes and stabilizes steady-state ergotropy in quantum batteries via dark-state protection.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Quantum batteries aim to charge faster and store more usable energy than classical devices by drawing on quantum resources like coherence, yet environmental noise rapidly drains both the stored ergotropy and any protective coherence. This work introduces a dual-channel coherence approach that pairs internal coherence in the charger with external coherence from a squeezed reservoir, employing dark-state protection to shield the stored energy. In the practical regime where the charger and battery have similar sizes, the study demonstrates that these two coherence sources together boost the speed of energy transfer during charging. The central result is that the presence of initial coherence in the charger is what enables the highest and longest-lasting steady-state ergotropy. The advantages arise because the combined coherence sources generate local coherence inside the battery itself.

Core claim

The paper establishes that initial charger coherence is the fundamental resource for maximizing and stabilizing steady-state ergotropy through dark-state protection. In the resource-efficient regime of comparable charger and battery sizes, internal charger coherence and reservoir squeezing jointly enhance transient charging power, with the advantages driven by the buildup of local battery coherence that integrates both internal and external coherence sources.

What carries the argument

Dark-state protection that uses initial charger coherence to shield ergotropy from dissipation while integrating reservoir squeezing as an external coherence source.

Load-bearing premise

Dark-state protection combined with the interplay of internal charger coherence and reservoir squeezing can counteract environment-induced dissipation without creating new loss channels when charger and battery sizes are comparable.

What would settle it

Measure steady-state ergotropy in a quantum battery experiment with and without prepared initial charger coherence under reservoir squeezing; the prediction fails if ergotropy does not reach a higher, more stable value when initial coherence is supplied.

Figures

Figures reproduced from arXiv: 2605.17700 by Fan Yang, Girish S. Agarwal, Hui Wang, Marlan O. Scully, William J. Munro, Yusef Maleki.

Figure 1
Figure 1. Figure 1: Schematic of the model. A charger (NC spins) and a battery (NB spins) are coupled to a common reservoir. The charger is prepared in a product state |θ, ϕ⟩ ⊗NC 1/2 , and the battery is initialized in the fully down-polarized state | ↓⟩⊗NB . The two large spheres represent the collective-spin states of the charger and battery, and the red and green arrows inside them indicate the corresponding collective spi… view at source ↗
Figure 2
Figure 2. Figure 2: Steady-state battery performance in multi-spin [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Scaling of steady-state battery performance with [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Steady-state ergotropy components and subsystem [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Time evolution of the coherent ergotropy [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Scaling of maximum charging power per spin. (a): [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Time evolution of the battery ergotropy WB un￾der three reservoir protocols for two system sizes. Blue curves correspond to NB = NC = 4, and brown curves cor￾respond to NB = NC = 8. Solid lines denote the continuous￾squeezing protocol with r = 0.5 throughout, dashed lines denote the finite-time squeezing protocol in which the squeez￾ing is switched from r = 0.5 to r = 0 at γt = 0.5, and dotted lines denote… view at source ↗
read the original abstract

Quantum batteries utilize nonclassical resources to achieve charging speed and energy storage performances that surpass classical thermodynamic limits. However, the practical realization of quantum batteries is often constrained by the inevitable environment-induced dissipation of both stored ergotropy and coherence. To actively counteract these losses, we propose a dual-channel coherence framework that exploits dark-state protection to stabilize ergotropy. We conduct, for the first time, an investigation of the synergistic interplay between internal charger coherence and reservoir squeezing, the latter acting as a source of external coherence. In the resource-efficient regime where charger and battery sizes are comparable, our study shows that internal charger coherence and reservoir squeezing jointly enhance the transient charging power. Crucially, initial charger coherence is the fundamental resource for maximizing and stabilizing steady-state ergotropy through dark-state protection. Our analysis reveals that these advantages are driven by the buildup of local battery coherence, which emerges from the integration of both internal and external coherence sources. These results offer a robust pathway for high-power, stabilized energy storage in quantum architectures.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a dual-channel coherence framework for quantum batteries that exploits dark-state protection to stabilize ergotropy against environmental dissipation. It investigates the interplay between internal charger coherence and external coherence supplied by reservoir squeezing, focusing on the resource-efficient regime of comparable charger and battery sizes. The central claim is that initial charger coherence serves as the fundamental resource for maximizing and stabilizing steady-state ergotropy, with advantages arising from the resulting buildup of local battery coherence.

Significance. If the results hold, the work identifies a concrete mechanism for counteracting dissipation in quantum batteries using readily available coherence resources, which could improve both charging power and long-term energy storage stability in finite-size systems. The emphasis on the comparable-size regime addresses a practical constraint for scalable quantum devices.

major comments (2)
  1. [Model and Results sections] The central claim that dark-state protection plus internal coherence and reservoir squeezing stabilizes steady-state ergotropy without introducing new loss channels in the comparable-size regime (abstract and model section) requires explicit verification. The interaction term generating the dark state can still permit leakage once the charger and battery Hilbert-space dimensions become comparable; the manuscript should demonstrate that the steady-state ergotropy remains insensitive to small detunings and to the precise form of the squeezing operator, for example via analytic bounds or targeted numerical scans.
  2. [Results section] §3 (or equivalent results section): the reported enhancement of transient charging power and the buildup of local battery coherence must be shown to survive when the reservoir squeezing parameter and initial charger coherence strength are varied independently; if these quantities are the only free parameters, the advantage should be quantified relative to the case with zero initial coherence to confirm it is not an artifact of normalization.
minor comments (2)
  1. [Introduction] The abstract states that the study is conducted 'for the first time' on the synergistic interplay; a brief comparison paragraph in the introduction with the most closely related prior works on coherence-assisted charging would strengthen this positioning.
  2. [Model section] Notation for the dual-channel coherence framework and the definition of ergotropy in the open-system setting should be introduced with a single equation reference early in the model section to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address each major comment in detail below and will incorporate revisions to strengthen the verification of our claims.

read point-by-point responses

  1. Referee: [Model and Results sections] The central claim that dark-state protection plus internal coherence and reservoir squeezing stabilizes steady-state ergotropy without introducing new loss channels in the comparable-size regime (abstract and model section) requires explicit verification. The interaction term generating the dark state can still permit leakage once the charger and battery Hilbert-space dimensions become comparable; the manuscript should demonstrate that the steady-state ergotropy remains insensitive to small detunings and to the precise form of the squeezing operator, for example via analytic bounds or targeted numerical scans.

    Authors: We agree that explicit verification of robustness is necessary in the comparable-size regime. Our analysis indicates that the dark-state protection, combined with the buildup of local battery coherence, prevents leakage under the considered conditions, but we acknowledge that additional checks would strengthen the central claim. In the revised manuscript, we will add targeted numerical scans over small detunings and different forms of the squeezing operator, along with analytic bounds where possible, to confirm that steady-state ergotropy remains insensitive and no new loss channels are introduced. revision: yes

  2. Referee: [Results section] §3 (or equivalent results section): the reported enhancement of transient charging power and the buildup of local battery coherence must be shown to survive when the reservoir squeezing parameter and initial charger coherence strength are varied independently; if these quantities are the only free parameters, the advantage should be quantified relative to the case with zero initial coherence to confirm it is not an artifact of normalization.

    Authors: We will revise the results section to explicitly vary the reservoir squeezing parameter and initial charger coherence strength independently. We will also include direct comparisons to the zero initial coherence case, quantifying the relative enhancement in transient charging power and local battery coherence to demonstrate that the advantages are not normalization artifacts. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on standard open-system master equations

full rationale

The abstract and skeptic summary describe a model using dark-state protection, internal charger coherence, and reservoir squeezing to stabilize ergotropy in a quantum battery. No equations or self-citations are provided that reduce the central claims (e.g., steady-state ergotropy maximization) to fitted parameters or definitions by construction. The framework appears to solve a Lindblad master equation with coherence terms as inputs and ergotropy as an output observable, which is a standard non-circular procedure. Without explicit reduction of predictions to input normalizations or self-citation load-bearing, the derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on standard open quantum system modeling plus the introduction of a new dual-channel framework whose performance depends on tunable coherence parameters and the existence of protective dark states.

free parameters (2)
  • initial charger coherence strength
    The amount of coherence initially present in the charger, identified as the fundamental resource for stabilization.
  • reservoir squeezing parameter
    Controls the strength of external coherence supplied by the squeezed reservoir.
axioms (2)
  • standard math Dynamics of the charger-battery system are described by a quantum master equation that includes dissipation channels.
    The framework relies on standard Lindblad or similar open-system evolution to model environment-induced losses.
  • domain assumption Dark states exist and can protect ergotropy against selected decoherence processes.
    Dark-state protection is invoked as the mechanism that stabilizes steady-state ergotropy.
invented entities (1)
  • dual-channel coherence framework no independent evidence
    purpose: Combines internal charger coherence with external reservoir squeezing to achieve ergotropy stabilization.
    This is a proposed construct introduced in the paper to integrate the two coherence sources.

pith-pipeline@v0.9.0 · 5720 in / 1479 out tokens · 53062 ms · 2026-05-20T12:06:35.580551+00:00 · methodology

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Reference graph

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