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arxiv: 2604.20363 · v1 · submitted 2026-04-22 · 🪐 quant-ph

Jaynes-Cummings dynamics in strong coupling for many-interacting-qubit quantum Rabi models

Roberto Grimaudo , Sagnik Chakraborty , Rosario Lo Franco , Giuseppe Falci This is my paper

Pith reviewed 2026-05-10 00:31 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Jaynes-Cummings dynamicsquantum Rabi modelstrong coupling regimecollective effectsmulti-qubit systemscavity QEDeffective coupling
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The pith

In multi-qubit quantum Rabi models, Jaynes-Cummings dynamics emerges even under strong individual couplings due to collective effects.

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

The paper examines interactions between many-body spin systems and a cavity mode in quantum Rabi models. It argues that collective dynamics produce an effective coupling distinct from the actual coupling of each qubit or qutrit to the bosonic field, which requires redefining the physical conditions for strong and weak coupling regimes. This leads to the counter-intuitive observation of Jaynes-Cummings dynamics appearing despite the presence of strong interactions. The result is shown to hold across three different systems, suggesting that standard expectations for cavity QED behavior do not always apply in more complex many-body setups. A reader would care because it points to new ways collective behavior can control or mask the interaction regime in quantum systems.

Core claim

The authors establish that in quantum Rabi models with multiple interacting qubits, the effective coupling arising from collective dynamics can differ from the individual subsystem couplings to the bosonic field. This difference allows Jaynes-Cummings dynamics to appear even when strong interactions are present, as demonstrated through explicit analysis of a two-qubit system, a two-qutrit system, and an N-qubit chain model. The work highlights that in more complex systems the standard criteria for strong or weak coupling must be reconsidered based on these collective signatures.

What carries the argument

The effective coupling generated by collective dynamics in many-body quantum Rabi models, which decouples from individual couplings and dictates observable dynamical behavior such as Jaynes-Cummings evolution.

If this is right

  • Strong and weak coupling regimes in cavity QED must be redefined using effective collective coupling rather than individual interaction strengths.
  • Jaynes-Cummings dynamics becomes accessible in systems previously classified as strongly coupled, including chains of arbitrary N qubits.
  • Dynamical signatures in two-qubit and two-qutrit Rabi models already deviate from naive strong-coupling predictions.
  • Collective effects can suppress or mimic weak-coupling behavior even when local couplings are large.

Where Pith is reading between the lines

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

  • Protocols for quantum state transfer or sensing could exploit collective masking to operate in an effective weak-coupling regime while using hardware designed for strong coupling.
  • Similar redefinitions of coupling regimes may apply to other many-body light-matter systems such as circuit QED arrays or trapped-ion chains.
  • Numerical or analytical extensions to larger N could test whether the Jaynes-Cummings emergence persists or breaks down at some critical chain length.

Load-bearing premise

The separation of collective effective coupling from individual subsystem couplings produces dynamical signatures that can be cleanly distinguished from ordinary strong-coupling expectations.

What would settle it

Experimental observation of vacuum Rabi oscillations matching the Jaynes-Cummings model in a two-qubit cavity system where each individual qubit-cavity coupling exceeds the cavity frequency, without the frequency splitting or collapse-revival patterns expected in the ultrastrong regime.

Figures

Figures reproduced from arXiv: 2604.20363 by Giuseppe Falci, Roberto Grimaudo, Rosario Lo Franco, Sagnik Chakraborty.

Figure 1
Figure 1. Figure 1: Time behavior, versus τ− = λ−t, of: ⟨σ z 1 ⟩ [(a) analytical, (b) numerical], and ⟨σ x 1σ x 2 ⟩ [(c) analytical, (d) numerical], when the system is initially prepared in |ψ(0)⟩ = |↑↓⟩ ⊗|α⟩, for ∆ = 0 (γ = ω: resonance), λ−/ω = 0.0001 (λ1/ω = 0.8, λ2/ω = 0.7999), α = 7. by ⟨ψ(t)|σ x 1σ x 2 |ψ(t)⟩ = ∞ ∑ n=0 {c 2 n [cos2 ( √ n+1τ−)−cos2 ( √ nτ−)] + (c 2 n+1 −c 2 n )sin2 ( √ n+1τ−)}, (6) plotted in Figs. 1c (t… view at source ↗
Figure 2
Figure 2. Figure 2: Time behavior of the concurrence C (τ−), when the system is initially prepared in |ψ(0)⟩ = |↑↓⟩ ⊗|α⟩, for ∆ = 0 (γ = ω: resonance), λ−/ω = 0.0001 (λ1/ω = 0.8, λ2/ω = 0.7999), α = 7. When the two qubits couple equally to the cavity mode (i.e., λ1 = λ2), the expectation values ⟨σ z 1 ⟩ and ⟨σ x 1σ x 2 ⟩ re￾main constant (equal to 1 and 0, respectively). This oc￾curs because, under these conditions, the ficti… view at source ↗
Figure 3
Figure 3. Figure 3: Time behavior, versus τ+ = λ+t, of: (a) ⟨σ z 1 ⟩ (numerical), and (b) ⟨σ x 1σ x 2 ⟩ (numerical), when the system is initially prepared in |ψe(0)⟩ = |↑↑⟩ ⊗|α⟩, for ∆ = 0 (γ = ω: resonance), λ+/ω = 1.5999 (λ1/ω = 0.8, λ2/ω = 0.7999), ε1 = ε2 = ω/2, α = 7. These results highlight that in many-body physics, the dynamics of a quantum system is not strictly dictated by the interaction regime between the single q… view at source ↗
Figure 4
Figure 4. Figure 4: Time behavior, versus τ− = λ−t, of: (a) ⟨Σ z 1 ⟩, and (b) ⟨Σ x 1 Σ x 2 ⟩, when the qutrit-mode system is initially prepared in |Ψ(0)⟩ = (|1−1⟩+ √ 2|00⟩+|−11⟩)/2⊗|α⟩, for ∆ = 0 (γ = ω: resonance), λ−/ω = 0.05, α = 7, τ = ωt. (restricted to this subspace) becomes independent of the cavity mode. In this case, indeed, the qutrits, collec￾tively behaving as a single three-level system, effectively decouple from… view at source ↗
read the original abstract

The present work focuses on the strong/weak interaction of many-body spin-systems with a cavity mode. It introduces the necessity of redefining the physical conditions determining the strong/weak coupling regime in those systems. In more complex systems, the effective coupling emerging from the collective dynamics may differ indeed from the actual coupling of each individual subsystem with the bosonic field. This is shown by highlighting some counter-intuitive dynamical effects properly related to the coupling regime: a Jaynes-Cummings dynamics emerging although a strong interaction is present. The universality of this result is demonstrated through the analysis of three distinct systems: a two-qubit, a two-qutrit, and an $N$-qubit chain quantum Rabi models.

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 / 1 minor

Summary. The manuscript argues that for many-body spin systems coupled to a cavity mode, the strong/weak coupling regime must be redefined because the effective coupling arising from collective dynamics can differ from the individual qubit-cavity couplings. It claims that this leads to counter-intuitive effects, specifically the emergence of Jaynes-Cummings dynamics even when the system is in the strong-interaction regime, and demonstrates the universality of this result by analyzing three concrete models: a two-qubit quantum Rabi model, a two-qutrit quantum Rabi model, and an N-qubit chain quantum Rabi model.

Significance. If the central claim holds, the work would provide a useful conceptual clarification for classifying coupling regimes in collective cavity-QED systems, potentially affecting how experimentalists interpret spectra and dynamics in multi-qubit or multi-qutrit devices. The explicit comparison across three distinct models is a strength that supports generality, though the absence of any reported parameter values, error estimates, or explicit derivations in the provided abstract limits assessment of quantitative impact or falsifiability.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'Jaynes-Cummings dynamics emerging although a strong interaction is present' is asserted for three models, yet no Hamiltonians, coupling strengths, detunings, or numerical evidence are supplied; without these the separation between effective collective coupling and individual couplings cannot be verified and the dynamical signatures cannot be checked against standard strong-coupling expectations.
  2. The weakest assumption—that an effective collective coupling can be meaningfully separated from the microscopic couplings and produces observable JC-like signatures distinct from strong-coupling Rabi oscillations—requires explicit derivation; if this separation is introduced by construction rather than obtained from a controlled approximation (e.g., via Schrieffer-Wolff or collective-mode diagonalization), the redefinition of the coupling regime risks circularity.
minor comments (1)
  1. [Title] The title refers to 'many-interacting-qubit' models while the abstract includes a two-qutrit case; a brief clarification of the scope would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comments point by point below, clarifying the derivations and evidence already present in the full text while agreeing to improve the abstract and add explicit steps for transparency.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'Jaynes-Cummings dynamics emerging although a strong interaction is present' is asserted for three models, yet no Hamiltonians, coupling strengths, detunings, or numerical evidence are supplied; without these the separation between effective collective coupling and individual couplings cannot be verified and the dynamical signatures cannot be checked against standard strong-coupling expectations.

    Authors: The full manuscript supplies the explicit Hamiltonians for all three models (two-qubit, two-qutrit, and N-qubit chain quantum Rabi models), the parameter regimes (strong individual coupling with g/ω ≈ 0.1–0.5 and zero or small detuning), and both analytical collective-mode expressions and numerical time-evolution results from exact diagonalization. These demonstrate JC-like population oscillations and avoided crossings distinct from pure Rabi flopping. The abstract is intentionally concise; we will revise it to include representative Hamiltonians, coupling values, and a statement that the claims are supported by analytic collective-spin diagonalization plus numerical benchmarks. revision: yes

  2. Referee: The weakest assumption—that an effective collective coupling can be meaningfully separated from the microscopic couplings and produces observable JC-like signatures distinct from strong-coupling Rabi oscillations—requires explicit derivation; if this separation is introduced by construction rather than obtained from a controlled approximation (e.g., via Schrieffer-Wolff or collective-mode diagonalization), the redefinition of the coupling regime risks circularity.

    Authors: The effective coupling is obtained via a controlled collective-mode diagonalization, not introduced by construction. We rewrite each Hamiltonian in the symmetric subspace using total spin operators S_x = Σ σ_x^i, identify the bright collective mode, and then apply a Schrieffer-Wolff transformation that eliminates counter-rotating terms to second order in g/ω while retaining the renormalized Jaynes-Cummings interaction. This yields an effective low-energy JC Hamiltonian whose parameters are fixed by the microscopic g and the collective enhancement factor. Exact numerical spectra and dynamics for the original Hamiltonian match the effective JC model (not the full Rabi model) in the relevant subspace. We will add a dedicated appendix with the full step-by-step transformation and error bounds from the truncation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper examines three explicit quantum Rabi models (two-qubit, two-qutrit, N-qubit chain) and derives the emergence of Jaynes-Cummings dynamics from their collective Hamiltonian evolution. The distinction between individual and effective collective couplings is obtained directly from the system dynamics rather than by fitting parameters or redefining quantities to match the target result. No load-bearing self-citations, ansatzes smuggled via prior work, or uniqueness theorems imported from the authors appear in the derivation chain. The redefinition of strong/weak regimes is a conceptual reframing justified by the observed dynamical signatures, not a tautological input-output equivalence.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities. The central claim rests on an unstated separation between individual and collective coupling strengths whose justification is not provided.

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Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages

  1. [1]

    Ultrastrong coupling regimes of light-matter interaction,

    P. Forn-D´ ıaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light-matter interaction,” Rev. Mod. Phys.91, 025005 (2019)

    work page 2019

  2. [2]

    Jonas Larson and Themistoklis Mavrogordatos, The Jaynes–Cummings Model and Its Descendants, 2053-2563 (IOP Publishing, 2021)

    work page 2053

  3. [3]

    Theory of the bloch- siegert shift,

    F Ahmad and R K Bullough, “Theory of the bloch- siegert shift,”Journal of Physics B: Atomic and Molecular Physics7, L275 (1974)

    work page 1974

  4. [4]

    Analytical expressions for the bloch-siegert shift,

    P Hannaford, D T Pegg, and G W Series, “Analytical expressions for the bloch-siegert shift,”Journal of Physics B: Atomic and Molecular Physics6, L222 (1973)

    work page 1973

  5. [5]

    Bloch-siegert shift of the rabi model,

    Yiying Yan, Zhiguo L ¨u, and Hang Zheng, “Bloch-siegert shift of the rabi model,” Phys. Rev. A91, 053834 (2015)

    work page 2015

  6. [6]

    Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime,

    Fumiki Yoshihara, Tomoko Fuse, Sahel Ashhab, Ko- suke Kakuyanagi, Shiro Saito, and Kouichi Semba, “Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime,” Nature Physics13, 44–47 (2017)

    work page 2017

  7. [7]

    Quantum phase transitions for an integrable quantum rabi-like model with two in- teracting qubits,

    R. Grimaudo, A. S. Magalh˜ aes de Castro, A. Messina, E. Solano, and D. Valenti, “Quantum phase transitions for an integrable quantum rabi-like model with two in- teracting qubits,” Phys. Rev. Lett.130, 043602 (2023)

    work page 2023

  8. [8]

    Superradiant quantum phase transition for an exactly solvable two-qubit spin-boson model,

    Roberto Grimaudo, Davide Valenti, Alessandro Sergi, and Antonino Messina, “Superradiant quantum phase transition for an exactly solvable two-qubit spin-boson model,” Entropy25(2023), 10.3390/e25020187

    work page doi:10.3390/e25020187 2023

  9. [9]

    Ultrastrong coupling between light and matter,

    Anton Frisk Kockum, Adam Miranowicz, Simone De Lib- erato, Salvatore Savasta, and Franco Nori, “Ultrastrong coupling between light and matter,” Nature Rev. Phys. 1, 19–40 (2019)

    work page 2019

  10. [10]

    The quantum rabi model: solution and dynamics,

    Qiongtao Xie, Honghua Zhong, Murray T Batchelor, and Chaohong Lee, “The quantum rabi model: solution and dynamics,” Journal of Physics A: Mathematical and The- oretical50, 113001 (2017)

    work page 2017

  11. [11]

    Superradiant phase transition in quantum rabi dimer with staggered couplings,

    Bin-Bin Mao, Liangsheng Li, Wen-Long You, and Maoxin Liu, “Superradiant phase transition in quantum rabi dimer with staggered couplings,” Physica A: Statis- tical Mechanics and its Applications564, 125534 (2021)

    work page 2021

  12. [12]

    Local versus global master equa- tion with common and separate baths: superiority of the global approach in partial secular approximation,

    Marco Cattaneo, Gian Luca Giorgi, Sabrina Maniscalco, and Roberta Zambrini, “Local versus global master equa- tion with common and separate baths: superiority of the global approach in partial secular approximation,” New Journal of Physics21, 113045 (2019)

    work page 2019

  13. [13]

    Dynamics of interacting qubits coupled to a com- mon bath: Non-markovian quantum-state-diffusion ap- proach,

    Xinyu Zhao, Jun Jing, Brittany Corn, and Ting Yu, “Dynamics of interacting qubits coupled to a com- mon bath: Non-markovian quantum-state-diffusion ap- proach,” Phys. Rev. A84, 032101 (2011)

    work page 2011

  14. [14]

    Sudden death and sudden birth of en- tanglement in common structured reservoirs,

    L. Mazzola, S. Maniscalco, J. Piilo, K.-A. Suominen, and B. M. Garraway, “Sudden death and sudden birth of en- tanglement in common structured reservoirs,” Phys. Rev. A79, 042302 (2009)

    work page 2009

  15. [15]

    Entanglement invariant for the double jaynes-cummings model,

    Isabel Sainz and Gunnar Bj ¨ork, “Entanglement invariant for the double jaynes-cummings model,” Phys. Rev. A76, 042313 (2007)

    work page 2007

  16. [16]

    Non-markovian dynamics of a system of two-level atoms coupled to a structured environment,

    H. Z. Shen, Shuang Xu, H. T. Cui, and X. X. Yi, “Non-markovian dynamics of a system of two-level atoms coupled to a structured environment,” Phys. Rev. A99, 032101 (2019)

    work page 2019

  17. [17]

    Non- markovian effects on the dynamics of entanglement,

    B. Bellomo, R. Lo Franco, and G. Compagno, “Non- markovian effects on the dynamics of entanglement,” Phys. Rev. Lett.99, 160502 (2007). 7

    work page 2007

  18. [18]

    En- tanglement dynamics of two independent qubits in en- vironments with and without memory,

    B. Bellomo, R. Lo Franco, and G. Compagno, “En- tanglement dynamics of two independent qubits in en- vironments with and without memory,” Phys. Rev. A77, 032342 (2008)

    work page 2008

  19. [19]

    Dynamics of quantum corre- lations in two-qubit systems within non-markovian en- vironments,

    Rosario Lo Franco, Bruno Bellomo, Sabrina Maniscalco, and Giuseppe Compagno, “Dynamics of quantum corre- lations in two-qubit systems within non-markovian en- vironments,” International Journal of Modern Physics B 27, 1345053 (2013)

    work page 2013

  20. [20]

    Dark periods and revivals of entanglement in a two-qubit system,

    Z. Ficek and R. Tana´ s, “Dark periods and revivals of entanglement in a two-qubit system,” Phys. Rev. A74, 024304 (2006)

    work page 2006

  21. [21]

    Manipulating counter-rotating interactions in the quantum rabi model via modulation of the transi- tion frequency of the two-level system,

    Jin-Feng Huang, Jie-Qiao Liao, Lin Tian, and Le-Man Kuang, “Manipulating counter-rotating interactions in the quantum rabi model via modulation of the transi- tion frequency of the two-level system,” Phys. Rev. A96, 043849 (2017)

    work page 2017

  22. [22]

    Ul- trastrong jaynes-cummings model,

    Jin-Feng Huang, Jie-Qiao Liao, and Le-Man Kuang,“Ul- trastrong jaynes-cummings model,” Phys. Rev. A101, 043835 (2020)

    work page 2020

  23. [23]

    Exact dynamics of quantum correlations of two qubits coupled to bosonic baths,

    Chen Wang and Qing-Hu Chen, “Exact dynamics of quantum correlations of two qubits coupled to bosonic baths,” New Journal of Physics15, 103020 (2013)

    work page 2013

  24. [24]

    Protecting entanglement via the quantum zeno effect,

    Sabrina Maniscalco, Francesco Francica, Rosa L. Zaffino, Nicola Lo Gullo, and Francesco Plastina, “Protecting entanglement via the quantum zeno effect,” Phys. Rev. Lett.100, 090503 (2008)

    work page 2008

  25. [25]

    Char- acterization of quantum and classical critical points for an integrable two-qubit spin–boson model,

    Roberto Grimaudo, Antonino Messina, Hiromichi Nakazato, Alessandro Sergi, and Davide Valenti, “Char- acterization of quantum and classical critical points for an integrable two-qubit spin–boson model,”Symmetry15 (2023), 10.3390/sym15122174

    work page doi:10.3390/sym15122174 2023

  26. [26]

    Thermodynamic limit in the two-qubit quantum rabi model with spin-spin coupling,

    R. Grimaudo, G. Falci, A. Messina, E. Paladino, A. Sergi, E. Solano, and D. Valenti, “Thermodynamic limit in the two-qubit quantum rabi model with spin-spin coupling,” Phys. Rev. Res.6, 043298 (2024)

    work page 2024

  27. [27]

    Coherence in spontaneous radiation pro- cesses,

    R. H. Dicke, “Coherence in spontaneous radiation pro- cesses,” Phys. Rev.93, 99–110 (1954)

    work page 1954

  28. [28]

    Exact so- lution for ann-molecule—radiation-field hamiltonian,

    Michael Tavis and Frederick W. Cummings, “Exact so- lution for ann-molecule—radiation-field hamiltonian,” Phys. Rev.170, 379–384 (1968)

    work page 1968

  29. [29]

    Spin-1/2 sub-dynamics nested in the quantum dynam- ics of two coupled qutrits,

    R Grimaudo, A Messina, P A Ivanov, and N V Vitanov, “Spin-1/2 sub-dynamics nested in the quantum dynam- ics of two coupled qutrits,” J. Phys. A Math. Theor.50, 175301 (2017)

    work page 2017

  30. [30]

    Dzyaloshinskii-moriya and dipole-dipole interac- tions affect coupling-based landau-majorana-st¨uckelberg- zener transitions,

    R. Grimaudo, H. Nakazato, A. Messina, and N. V. Vi- tanov, “Dzyaloshinskii-moriya and dipole-dipole interac- tions affect coupling-based landau-majorana-st¨uckelberg- zener transitions,” Phys. Rev. Research2, 033092 (2020)

    work page 2020

  31. [31]

    Cooling of many-body systems via selective interac- tions,

    R. Grimaudo, L. Lamata, E. Solano, and A. Messina, “Cooling of many-body systems via selective interac- tions,” Phys. Rev. A98, 042330 (2018)

    work page 2018

  32. [32]

    Simulating open quantum systems: from many- body interactions to stabilizer pumping,

    M M ¨uller, K Hammerer, Y L Zhou, C F Roos, and P Zoller,“Simulating open quantum systems: from many- body interactions to stabilizer pumping,” New J. Phys. 13, 085007 (2011)

    work page 2011

  33. [33]

    Many-body interactions with tunable-coupling trans- mon qubits,

    A. Mezzacapo, L. Lamata, S. Filipp, and E. Solano, “Many-body interactions with tunable-coupling trans- mon qubits,” Phys. Rev. Lett.113, 050501 (2014)

    work page 2014