pith. sign in

arxiv: 2604.17518 · v1 · submitted 2026-04-19 · 🪐 quant-ph

Thermal vapor quantum battery based on collective atomic spins

Jinyi Li , Juncheng Zheng , Xue Yang , Kainan Hu , Kanzheng Zhou , Junkai Zhuang , Hengyan Wang , Zhihao Ma
show 2 more authors
Mingxing Luo Wenqiang Zheng
This is my paper

Pith reviewed 2026-05-10 05:23 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum batteryatomic spin ensemblethermal vaporquantum coherenceroom temperatureunitary evolutionentropy relationsdephasing channel
0
0 comments X

The pith

A thermal vapor of rubidium atoms forms a room-temperature quantum battery whose capacity is measured directly from extremal energies reachable by unitary operations.

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

The paper shows that a collective spin ensemble of roughly 10^12 rubidium atoms in a thermal vapor cell can store energy as a quantum battery at room temperature, with coherence times longer than 110 ms. Capacity is defined and extracted operationally by measuring the maximum and minimum internal energies the ensemble can reach under unitary evolution, bypassing full state tomography. This method confirms that the total capacity splits into coherent and incoherent parts and that quantum coherence adds storage power even when level populations stay fixed. The work also maps the capacity quantitatively onto von Neumann, Tsallis, and linear entropies and demonstrates that a controlled magnetic-gradient dephasing channel reduces capacity in step with the loss of coherence.

Core claim

We realize a room-temperature quantum battery based on a collective atomic spin ensemble in a thermal alkali-metal vapor, containing approximately 10^12 87Rb atoms with coherence times exceeding 110 ms. We operationally determine the battery capacity by directly measuring the extremal internal energies accessible under unitary evolution. This tomography-free protocol agrees closely with the conventional state-based definition and verifies the decomposition of capacity into coherent and incoherent contributions. We further show that quantum coherence can substantially enhance the storage capability independently of level populations, and experimentally establish quantitative relations linking

What carries the argument

The tomography-free protocol that extracts battery capacity from the difference between the highest and lowest internal energies reachable by unitary evolution on the collective spin state.

If this is right

  • Capacity decomposes cleanly into coherent and incoherent contributions that can be tracked separately.
  • Quantum coherence increases extractable energy even when the atomic level populations are held constant.
  • Battery capacity maintains quantitative relations to von Neumann, Tsallis, and linear entropies that persist under controlled dephasing.
  • A magnetic-field gradient can be used as a tunable dephasing channel to reduce capacity monotonically with coherence loss.
  • Thermal atomic spin ensembles in vapor cells constitute a scalable platform for macroscopic quantum energy storage.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same vapor-cell platform already used for magnetometry and atomic clocks could host both sensing and energy-storage functions in one device.
  • Extending coherence times beyond 110 ms or increasing atom number would raise the absolute capacity while preserving the entropy relations.
  • The observed entropy-capacity links may apply to other collective spin systems, such as nitrogen-vacancy ensembles or trapped-ion crystals, if similar tomography-free protocols are implemented.

Load-bearing premise

Measuring extremal energies under unitary evolution fully captures the battery capacity and its coherent-incoherent split without systematic errors introduced by magnetic-gradient dephasing.

What would settle it

A side-by-side comparison in which the extremal energies measured by the unitary protocol deviate by more than experimental uncertainty from the energies computed from full state tomography would falsify the operational definition of capacity.

Figures

Figures reproduced from arXiv: 2604.17518 by Hengyan Wang, Jinyi Li, Juncheng Zheng, Junkai Zhuang, Kainan Hu, Kanzheng Zhou, Mingxing Luo, Wenqiang Zheng, Xue Yang, Zhihao Ma.

Figure 1
Figure 1. Figure 1: FIG. 1. Experimental platform for the thermal atomic-spin [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Microscopic charge–discharge cycle and experimental control sequence. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Experimental determination of quantum battery capacity and its entropic constraints. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Capacity degradation under controlled dephasing. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Experimental protocols for capacity measurements. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

Quantum batteries harness non-classical resources, such as quantum coherence and entanglement, to surpass the performance limits of classical energy-storage devices. Here we realize a room-temperature quantum battery based on a collective atomic spin ensemble in a thermal alkali-metal vapor, containing approximately $10^{12}$ $^{87}$Rb atoms with coherence times exceeding 110 ms. We operationally determine the battery capacity by directly measuring the extremal internal energies accessible under unitary evolution. This tomography-free protocol agrees closely with the conventional state-based definition and verifies the decomposition of capacity into coherent and incoherent contributions. We further show that quantum coherence can substantially enhance the storage capability independently of level populations, and experimentally establish quantitative relations linking battery capacity to von Neumann, Tsallis and linear entropies. By introducing a controlled dephasing channel with a magnetic-field gradient, we observe a monotonic reduction of capacity with coherence loss and track the corresponding evolution of the entropy-capacity relations. Our results identify thermal atomic spin ensembles as a scalable platform for quantum batteries and connect macroscopic quantum energy storage with operational quantum thermodynamics.

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 reports the experimental realization of a room-temperature quantum battery using a collective spin ensemble of ~10^12 87Rb atoms in thermal alkali vapor, with coherence times >110 ms. Battery capacity is determined operationally by directly measuring the extremal internal energies reachable under unitary evolution (tomography-free protocol), which is shown to agree closely with the conventional state-based definition. The work decomposes capacity into coherent and incoherent contributions, establishes quantitative links to von Neumann, Tsallis, and linear entropies, and demonstrates monotonic capacity reduction under controlled magnetic-gradient dephasing.

Significance. If the central claims hold, this is a significant experimental advance: it provides a scalable, room-temperature platform for quantum batteries based on macroscopic atomic ensembles, offers an operational verification of ergotropy without full tomography, and directly connects capacity to entropy measures while isolating coherence effects via controlled dephasing. The long coherence times and large atom number make the system promising for further quantum thermodynamics studies.

major comments (2)
  1. [Abstract and experimental methods] The central claim that the tomography-free extremal-energy protocol accurately captures the full battery capacity (and its coherent/incoherent decomposition) rests on the assumption that the implemented unitaries reach the global max/min eigenvalues of the effective Hamiltonian. The manuscript provides no quantitative verification (e.g., calibration data, pulse-sequence details, or bounds on residual magnetic inhomogeneity) that the RF/optical controls are complete enough to avoid systematic underestimation due to collective dephasing or finite bandwidth; this directly affects the reported close agreement with the state-based definition and the subsequent entropy relations.
  2. [Results on entropy relations and dephasing] The entropy-capacity relations and the monotonic reduction under controlled dephasing are presented as quantitative verifications, but without reported error bars, data-exclusion criteria, or statistical analysis of the capacity-entropy fits, it is unclear whether the observed relations are robust or could be affected by the same unitary incompleteness.
minor comments (2)
  1. [Introduction and theory] Clarify the precise definition of the operational capacity (extremal energies under unitary evolution) versus the state-based ergotropy in the main text, including any assumptions about the effective Hamiltonian.
  2. [Experimental setup] The coherence time of >110 ms is a key figure; provide the measurement protocol and any dependence on atom number or temperature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address each major comment point by point below, providing clarifications and indicating revisions made to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract and experimental methods] The central claim that the tomography-free extremal-energy protocol accurately captures the full battery capacity (and its coherent/incoherent decomposition) rests on the assumption that the implemented unitaries reach the global max/min eigenvalues of the effective Hamiltonian. The manuscript provides no quantitative verification (e.g., calibration data, pulse-sequence details, or bounds on residual magnetic inhomogeneity) that the RF/optical controls are complete enough to avoid systematic underestimation due to collective dephasing or finite bandwidth; this directly affects the reported close agreement with the state-based definition and the subsequent entropy relations.

    Authors: We acknowledge the value of explicit verification for the completeness of the applied unitaries. The original manuscript presented the close agreement (within experimental precision) between the tomography-free extremal-energy measurements and the state-based ergotropy calculation as supporting evidence for the protocol's validity, since the latter is derived from full state tomography. To address the concern directly, the revised manuscript includes additional details in the Methods section: RF pulse calibration data (Rabi frequencies and detuning bounds), the specific pulse sequence parameters used for the extremal energy projections, and quantitative bounds on residual magnetic inhomogeneity inferred from the measured coherence time exceeding 110 ms. These show that inhomogeneity-induced dephasing rates are low enough to support the assumption of near-global rotations for the collective spin ensemble. We agree that any residual incompleteness could in principle lead to underestimation, but note that such effects would impact both the tomography-free and state-based approaches in a correlated manner, preserving the reported agreement. revision: yes

  2. Referee: [Results on entropy relations and dephasing] The entropy-capacity relations and the monotonic reduction under controlled dephasing are presented as quantitative verifications, but without reported error bars, data-exclusion criteria, or statistical analysis of the capacity-entropy fits, it is unclear whether the observed relations are robust or could be affected by the same unitary incompleteness.

    Authors: We agree that the absence of explicit error bars and statistical details in the original presentation leaves the robustness of the entropy-capacity relations open to question. In the revised manuscript, we have added error bars to all data points in the relevant figures (derived from the standard deviation across 5–10 repeated experimental runs) and included a dedicated paragraph in the Results section describing the data analysis. This covers the data-exclusion criteria (based on a minimum signal-to-noise threshold for the absorption signals) and reports the results of linear regression fits to the capacity versus entropy data, including R-squared values and p-values confirming statistical significance. The monotonic reduction under controlled dephasing is now shown with these uncertainties, and the consistency of the relations across multiple dephasing strengths supports their robustness independent of minor unitary imperfections. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental measurements and relations are independent of inputs

full rationale

The paper's core results consist of direct experimental measurements of extremal internal energies under unitary evolution on a thermal Rb spin ensemble, with capacity decomposed into coherent/incoherent parts and related to entropies via controlled dephasing. These are operational protocols validated by agreement with state-based definitions, without any derivations, fitted parameters renamed as predictions, or self-citation chains that reduce claims to inputs by construction. The tomography-free approach and entropy-capacity relations are established through physical implementation and data, remaining self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum mechanics for unitary evolution and entropy definitions plus domain assumptions about collective spin coherence in thermal vapors; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (2)
  • standard math Standard quantum mechanics governs unitary evolution, internal energy, and von Neumann/Tsallis/linear entropy for the spin ensemble.
    Invoked for capacity definitions and entropy-capacity relations throughout the abstract.
  • domain assumption The thermal alkali vapor can be treated as a collective atomic spin system with coherence times exceeding 110 ms under the experimental conditions.
    Foundation for the room-temperature battery platform and dephasing control.

pith-pipeline@v0.9.0 · 5506 in / 1466 out tokens · 43132 ms · 2026-05-10T05:23:58.312255+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

51 extracted references · 1 canonical work pages

  1. [1]

    Campaioli, S

    F. Campaioli, S. Gherardini, J. Q. Quach, M. Polini, and G. M. Andolina, Colloquium: Quantum batteries, Rev. Mod. Phys.96, 031001 (2024)

    2024

  2. [2]

    Camposeo and others, Quantum batteries: a materials science perspective, Adv

    A. Camposeo and others, Quantum batteries: a materials science perspective, Adv. Mater.37, 2415073 (2025)

    2025

  3. [3]

    Lett.67, 565 (2004)

    A.E.Allahverdyan, R.Balian,andT.M.Nieuwenhuizen, Maximal work extraction from finite quantum systems, Europhys. Lett.67, 565 (2004)

    2004

  4. [4]

    Alicki and M

    R. Alicki and M. Fannes, Entanglement boost for ex- tractable work from ensembles of quantum batteries, Phys. Rev. E87, 042123 (2013)

    2013

  5. [5]

    Campaioli, F

    F. Campaioli, F. A. Pollock, F. C. Binder, and et al., En- hancing the charging power of quantum batteries, Phys. Rev. Lett.118, 150601 (2017)

    2017

  6. [6]

    H. L. Shi, S. Ding, Q. K. Wan, and et al., Entanglement, coherence, and extractable work in quantum batteries, Phys. Rev. Lett.129, 130602 (2022)

    2022

  7. [7]

    Perarnau-Llobet, K

    M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, N. Brunner, and A. Acín, Extractable work from correlations, Phys. Rev. X5, 041011 (2015)

    2015

  8. [8]

    G. M. Andolina, M. Keck, A. Mari, M. Campisi, V. Gio- vannetti, and M. Polini, Extractable work, the role of correlations, and asymptotic freedom in quantum bat- teries, Phys. Rev. Lett.122, 047702 (2019)

    2019

  9. [9]

    F. H. Kamin, F. T. Tabesh, S. Salimi, and A. C. Santos, Entanglement, coherence, and charging process of quan- tum batteries, Phys. Rev. E102, 7 (2020)

    2020

  10. [10]

    R. P. A. Simon, J. Anders, and K. V. Hovhannisyan, Correlations enable lossless ergotropy transport, Phys. Rev. Lett.134, 010408 (2025)

    2025

  11. [11]

    Ferraro, M

    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)

    2018

  12. [12]

    T. P. Le, J. Levinsen, K. Modi, M. M. Parish, and F. A. Pollock, Spin-chain model of a many-body quantum bat- tery, Phys. Rev. A97, 022106 (2018). 10

    2018

  13. [13]

    Rossini, G

    D. Rossini, G. M. Andolina, D. Rosa, M. Carrega, and M. Polini, Quantum advantage in the charging process of sachdev-ye-kitaevbatteries,Phys.Rev.Lett.125,236402 (2020)

    2020

  14. [14]

    L.P.García-Pintos, A.Hamma,andA.DelCampo,Fluc- tuations in extractable work bound the charging power of quantum batteries, Phys. Rev. Lett.125, 040601 (2020)

    2020

  15. [15]

    Ahmadi, P

    B. Ahmadi, P. Mazurek, P. Horodecki, and S. Barzanjeh, Nonreciprocal quantum batteries, Phys. Rev. Lett.132, 210402 (2024)

    2024

  16. [16]

    A. G. Catalano, S. M. Giampaolo, O. Morsch, V. Giovan- netti, and F. Franchini, Frustrating quantum batteries, PRX Quantum5, 030319 (2024)

    2024

  17. [17]

    Z.-G. Lu, G. Tian, X.-Y. Lü, and C. Shang, Topological quantum batteries, Phys. Rev. Lett.134, 180401 (2025)

    2025

  18. [18]

    Acín, Entanglement generation is not necessary for optimal work extraction, Phys

    K.V.Hovhannisyan, M.Perarnau-Llobet, M.Huber,and A. Acín, Entanglement generation is not necessary for optimal work extraction, Phys. Rev. Lett.111, 240401 (2013)

    2013

  19. [19]

    Skrzypczyk, A

    P. Skrzypczyk, A. J. Short, and S. Popescu, Work extrac- tion and thermodynamics for individual quantum sys- tems, Nat. Comm.5, 4185 (2014)

    2014

  20. [20]

    J. G. Richens and L. Masanes, Work extraction from quantum systems with bounded fluctuations in work, Nat. Comm.7, 13511 (2016)

    2016

  21. [21]

    Tirone, M

    S. Tirone, M. Salvatore, and V. Giovannetti, Work ex- traction processes from noisy quantum batteries: The role of nonlocal resources, Phys. Rev. Lett.131, 060402 (2023)

    2023

  22. [22]

    Salvia, G

    R. Salvia, G. De Palma, and V. Giovannetti, Optimal local work extraction from bipartite quantum systems in the presence of hamiltonian couplings, Phys. Rev. A107, 012405 (2023)

    2023

  23. [23]

    F. C. Binder, S. Vinjanampathy, K. Modi, and J. Goold, Quantacell: powerfulchargingofquantumbatteries,New J. Phys.17, 075015 (2015)

    2015

  24. [24]

    Song, H.-B

    W.-L. Song, H.-B. Liu, B. Zhou, W.-L. Yang, and J.-H. An,Remotecharginganddegradationsuppressionforthe quantum battery, Phys. Rev. Lett.132, 090401 (2024)

    2024

  25. [25]

    G. M. Andolina, V. Stanzione, V. Giovannetti, and M. Polini, Genuine quantum advantage in anharmonic bosonic quantum batteries, Phys. Rev. Lett.134, 240430 (2025)

    2025

  26. [26]

    Julià-Farré, T

    S. Julià-Farré, 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)

    2020

  27. [27]

    Francica, F

    G. Francica, F. C. Binder, G. Guarnieri, M. T. Mitchi- son, J. Goold, and F. Plastina, Quantum coherence and ergotropy, Phys. Rev. Lett.125, 180603 (2020)

    2020

  28. [28]

    T.Zhang, H.Yang, S.M.Fei,andetal.,Local-projective- measurement-enhanced quantum battery capacity, Phys. Rev. A109, 042424 (2024)

    2024

  29. [29]

    Perarnau-Llobet and F

    M. Perarnau-Llobet and F. Binder, Quantum thermody- namics for quantum technologies, Nat. Rev. Phys.2, 545 (2020)

    2020

  30. [30]

    Horodecki and J

    M. Horodecki and J. Oppenheim, Fundamental limita- tions for quantum and nanoscale thermodynamics, Nat. Comm.4, 2059 (2013)

    2059

  31. [31]

    Alicki and M

    R. Alicki and M. Fannes, Quantum thermodynamics, Phys. Rep.680, 1 (2019)

    2019

  32. [32]

    Ganardi, T

    R. Ganardi, T. V. Kondra, N. H. Ng, and A. Streltsov, Second law of entanglement manipulation with an entan- glement battery, Phys. Rev. Lett.135, 010202 (2025)

    2025

  33. [33]

    Yu, Optimal charging of a superconducting quan- tum battery, Quantum Sci

    C.K.Hu, J.Qiu, P.J.Souza, J.Yuan, Y.Zhou, L.Zhang, and D. Yu, Optimal charging of a superconducting quan- tum battery, Quantum Sci. Tech.7, 045018 (2022)

    2022

  34. [34]

    Zhang, P

    J. Zhang, P. Wang, W. Chen, and et al., Single-ion infor- mation engine for charging quantum battery, Phys. Rev. Lett.135, 140403 (2025)

    2025

  35. [35]

    Maillette de Buy Wenniger, S

    I. Maillette de Buy Wenniger, S. E. Thomas, M. Maf- fei, S. C. Wein, M. Pont, and P. Senellart, Experimental analysis of energy transfers between a quantum emitter and light fields, Phys. Rev. Lett.131, 260401 (2023)

    2023

  36. [36]

    Z. Niu, Y. Wu, Y. Wang, X. Rong, and J. Du, Exper- imental investigation of coherent ergotropy in a single spin system, Phys. Rev. Lett.133, 180401 (2024)

    2024

  37. [37]

    Joshi and T

    J. Joshi and T. S. Mahesh, Experimental investigation of a quantum battery using star-topology nmr spin systems, Phys. Rev. A106, 042601 (2022)

    2022

  38. [38]

    H.-L. Shi, L. Gan, K. Zhang, X.-H. Wang, and W.-L. Yang, Quantum charging advantage from multipartite entanglement, arXiv:2503.02667 (2025)

    work page arXiv 2025

  39. [39]

    Zheng, H

    W. Zheng, H. Wang, R. Schmieg, A. Oesterle, and E. S. Polzik, Entanglement-enhanced magnetic induction to- mography, Phys. Rev. Lett.130, 203602 (2023)

    2023

  40. [40]

    H. Bao, J. Duan, S. Jin, X. Lu, P. Li, W. Qu, M. Wang, I. Novikova, E. E. Mikhailov, K.-F. Zhao,et al., Spin squeezing of10 11 atoms by prediction and retrodiction measurements, Nature581, 159 (2020)

    2020

  41. [41]

    J. Kong, R. Jiménez-Martínez, C. Troullinou, V. G. Lucivero, G. Tóth, and M. W. Mitchell, Measurement- induced, spatially-extended entanglement in a hot, strongly-interacting atomic system, Nat. Comm.11, 2415 (2020)

    2020

  42. [42]

    Novikov, J

    V. Novikov, J. Jia, T. B. Brasil, A. Grimaldi, M. Bo- coum, M. Balabas, J. H. Müller, E. Zeuthen, and E. S. Polzik, Hybrid quantum network for sensing in the acous- tic frequency range, Nature , 1 (2025)

    2025

  43. [43]

    Krauter, C

    H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, Entangle- ment generated by dissipation and steady state entangle- ment of two macroscopic objects, Phys. Rev. Lett.107, 080503 (2011)

    2011

  44. [44]

    X. Yang, Y. H. Yang, M. Alimuddin, R. Salvia, S. M. Fei, L. M. Zhao, and M. X. Luo, Battery capacity of energy- storing quantum systems, Phys. Rev. Lett.131, 030402 (2023)

    2023

  45. [45]

    An, J.-N

    S. An, J.-N. Zhang, M. Um, D. Lv, Y. Lu, J. Zhang, Z.- Q. Yin, H. Quan, and K. Kim, Experimental test of the quantum jarzynski equality with a trapped-ion system, Nat. Phys.11, 193 (2015)

    2015

  46. [46]

    T. B. Batalhão, A. M. Souza, L. Mazzola, R. Auccaise, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, Experi- mental reconstruction of work distribution and study of fluctuation relations in a closed quantum system, Phys. Rev. Lett.113, 140601 (2014)

    2014

  47. [47]

    Horodecki, P

    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009)

    2009

  48. [48]

    P.StrasbergandA.Winter,Firstandsecondlawofquan- tum thermodynamics: A consistent derivation based on a microscopic definition of entropy, PRX Quantum2, 030202 (2021)

    2021

  49. [49]

    Baumgratz, M

    T. Baumgratz, M. Cramer, and M. B. Plenio, Quantify- ing coherence, Phys. Rev. Lett.113, 140401 (2014)

    2014

  50. [50]

    Tsallis, Possible generalization of boltzmann-gibbs statistics, J

    C. Tsallis, Possible generalization of boltzmann-gibbs statistics, J. Stat. Phys.52, 479 (1988). 11

    1988

  51. [51]

    Appelt, A

    S. Appelt, A. B.-A. Baranga, C. Erickson, M. Romalis, A. Young, and W. Happer, Theory of spin-exchange op- tical pumping of 3 he and 129 xe, Phys. Rev. A58, 1412 (1998)

    1998