Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

The paper claims a polaron-style displacement followed by a small photon-number truncation yields compact Hamiltonians that remain accurate from weak to deep-strong light-matter coupling.

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 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 22:07 UTC pith:NEMGLRE7

load-bearing objection Polaron-truncation method that shines for spectra, overclaims for ground-state observables. the 3 major comments →

arxiv 2511.11903 v2 pith:NEMGLRE7 submitted 2025-11-14 quant-ph cond-mat.mes-hall

Compact cavity-dressed Hamiltonian framework at arbitrarily strong light-matter coupling

Jakub Garwo{\l}a , Dvira Segal This is my paper
classification quant-ph cond-mat.mes-hall PACS 42.50.Pq
keywords cavity-dressed Hamiltonianultrastrong couplingdeep strong couplingquantum Rabi modelDicke-Heisenberg modelpolaron transformationnon-perturbative mappingstrong light-matter coupling
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper claims that strongly coupled light-matter systems can be described by a compact, closed-form Hamiltonian obtained by applying an entangling (polaron) displacement to the photons and then keeping only the lowest M photon-number sectors. It shows for the quantum Rabi model that this cavity-dressed Hamiltonian with M=4 reproduces the first six eigenenergies across weak, ultrastrong, and deep-strong coupling, whereas a bare Fock-truncated Hamiltonian with N=10 diverges. For the Dicke-Heisenberg spin chain, low-degree CDHs reproduce magnetization phase diagrams, entanglement entropy, and structure factors with a small fraction of the Hilbert-space dimension used in brute-force simulations. The method is claimed to be systematically convergent and to extend to multimode and leaky cavities, providing analytical forms that reveal the mechanisms of cavity-mediated interactions.

Core claim

On its own terms, the paper's central claim is that the unitary transformation U_P = exp[Σ (λ_n/Ω_n) S_n(a_n† − a_n)] dresses the matter operators with photon displacements, and that truncating the transformed Hamiltonian to M photon-number sectors yields a series of cavity-dressed Hamiltonians that converge to the exact spectrum and equilibrium observables at arbitrarily strong coupling. The evidence is construction plus numerical benchmarking: closed-form M=1,2,3,4 CDHs for the Rabi model, a closed-form M=3 CDH for the Dicke-Heisenberg model, and the demonstration that resonant and ultrastrong regimes, where bare truncation fails badly, are captured with small M. The paper does not claim a

What carries the argument

The central object is the cavity-dressed Hamiltonian (CDH): after the polaron displacement U_P is applied, the transformed Hamiltonian is decomposed into blocks labeled by photon occupation numbers, and all but the lowest M sectors are discarded. The key identities are closed-form matrix elements of rotated operators in the number-state basis, obtained either by momentum-space integrals over Hermite polynomials or by spectral decomposition of the coupling operator into displacement operators. These give analytical expressions for every block, so the CDH is a finite-dimensional, systematically improvable effective Hamiltonian rather than a numerically constructed one.

Load-bearing premise

The load-bearing premise is that truncating the dressed Hamiltonian to the M lowest photon sectors converges to the exact limit for every strongly coupled system and every observable of interest; this is asserted and shown numerically for two models, but not proven, and the paper's own supplementary material documents non-monotonic convergence that forces M_P=20 for ground-state observables.

What would settle it

Compute the exact ground-state photon number ⟨a†a⟩ for the single-mode Rabi model at resonance (Ω=2Δ) and λ/Δ=3, where the paper's M=4 CDH is accurate for the first six energies; if the CDH prediction with M_P=20 does not approach the exact value as M grows from 1 to 6, the claim that the CDH framework captures strongly coupled light-matter systems at arbitrary coupling would be refuted for cavity observables. Alternatively, a simple two-mode model with noncommuting coupling operators at strong coupling would test the general multimode claim: if increasing M fails to reduce the ground-state en

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Rabi-model spectra in the resonant ultrastrong regime can be computed with M=4 dressed levels where N=10 bare levels diverge, cutting the Hilbert-space dimension needed for comparable accuracy.
  • Thermal and ground-state observables such as magnetization converge with increasing M; ground-state calculations may require a larger rotation space M_P (up to 20) even when M=4 suffices for energies.
  • For the Dicke-Heisenberg chain, M=1 already captures the ferromagnetic-paramagnetic crossover and M=3 reproduces structure factors, so phase diagrams can be mapped with a small effective dimension.
  • The mapping exposes the physics: an effective spin splitting suppressed by exp(−2λ²/Ω²), a cavity-mediated all-to-all spin coupling in the x direction, and renormalization and mixing of Heisenberg couplings with closed-form dressing functions.
  • The same construction applies to multimode cavities with noncommuting coupling operators and to leaky cavities, extending the method beyond the benchmarked single-mode models.

Where Pith is reading between the lines

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

  • The strongest untested implication is that convergence extends to arbitrary observables; the paper itself computes no cavity observables, and ground-state photon statistics are the natural stress test. If CDH fails there, the 'arbitrarily strong coupling' claim should be read as limited to matter observables and spectra.
  • Because the dressed Hamiltonian is an effective spin model with all-to-all interactions, the same closed forms could be fed into tensor-network or mean-field treatments of longer chains and higher dimensions; the paper's L=8 numerics suggest the advantage grows with L.
  • The non-monotonic convergence reported for difficult parameters hints that a rigorous error bound in terms of M, λ/Ω, and the operator norm of S_n would be needed to turn the recipe into a method with guaranteed accuracy; without it, users must benchmark each new model.
  • For open systems, combining the leaky-cavity CDH with standard dissipative evolution of the dressed Hamiltonian may give a practical route to ultrastrong-coupling dynamics, which the paper lists as future work.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript presents a cavity-dressed Hamiltonian (CDH) framework for strongly coupled light-matter systems. The method applies a multimode polaron transformation and then truncates the transformed Hamiltonian to the M lowest Fock states, yielding closed-form effective Hamiltonians for matter observables and spectra. The approach is applied to the quantum Rabi model, where closed-form M=2 and M=4 CDHs are given, and to a Dicke-Heisenberg spin chain, where M=1 and M=3 CDHs reproduce phase diagrams and structure factors. The central claim is that the finite-M CDHs form a systematically convergent series that outperforms conventional bare-truncation approaches from weak through deep-strong coupling.

Significance. If the convergence claim can be substantiated, the CDH framework is a useful non-perturbative tool for ultrastrong-coupling cavity QED: it is analytically transparent, computationally cheap, and benchmarked against the exact Braak solution and brute-force diagonalization. The closed-form expressions and the explicit comparison with bare truncation are valuable. However, the manuscript's advertised scope—'systematically convergent' and 'arbitrarily strong coupling'—is broader than what the numerical benchmarks and the supplementary material actually establish, particularly for ground-state observables.

major comments (3)
  1. [SI Sec. I C; Fig. 5] The abstract and Introduction claim that the CDH series is 'systematically convergent' for spectra and ground-state/thermal observables. The supplementary material itself states that for ground-state observables in 'difficult' parameter ranges (low temperature, resonance) convergence in M is non-monotonic and one must use M_P=20 for the operator rotation—the same dimension required for bare convergence. This directly contradicts the advertised compactness and systematic improvability for observables, since accuracy is not controlled by M alone. Please either restrict the central claim to spectral properties, or provide a rigorous convergence criterion/protocol for choosing M_P, or state the observable-convergence claim as a conjecture with explicit numerical support.
  2. [Eq. (2), Eq. (34), SI Sec. I C] The CDH mapping is a unitary transformation, but the computational scheme uses a Hamiltonian truncated to M levels while the rotated operator in the expectation value is truncated separately at M_P levels. There is no proof or error bound that the sequence of such hybrid truncations converges to the exact limit for arbitrary couplings and observables. The benchmarks cover two models. The title 'arbitrarily strong light-matter coupling' and the statement of exactness in the deep-strong limit require either a proof for a defined class of Hamiltonians/observables or a clear qualification that these are empirical convergence properties, not established general theorems.
  3. [Fig. 3 caption; SI Sec. I C] The main-text ground-state phase diagrams in Fig. 3 are computed with M_P=M, as stated in the caption, while SI Sec. I C reports that at resonance ground-state observables require M_P=20 to obtain physical behavior in the deep-strong limit. This raises a concrete concern about whether the Dicke-Heisenberg phase diagrams, which extend to strong coupling, are quantitatively reliable in the deep-strong region. Please clarify whether Fig. 3 was produced with M_P=M or M_P=20, and discuss the sensitivity of the reported phase boundaries to M_P.
minor comments (4)
  1. [Eq. (6)] The notation E_{±,±′} is not defined precisely; the expression has two nested square roots, so the reader has to infer how the four sign combinations are assigned. Please spell this out or label the states explicitly.
  2. [Abstract/Introduction] The phrase 'arbitrarily strong light-matter coupling' is stronger than the quantitative benchmarks: Fig. 2 covers λ/Δ up to 5 for spectra, and the deep-strong limit is only discussed qualitatively. Please qualify the scope in the abstract or cite the specific benchmark ranges.
  3. [SI title] There is a typo in the supplementary title: 'Dicke-Hiesenberg' should be 'Dicke-Heisenberg'.
  4. [Main text, paragraph after Eq. (9)] The main text says 'For ground state observables, M_P > M was required to achieve convergence' but does not reconcile this with the earlier assertion that the method is systematically convergent for observables. This sentence should be expanded or moved to qualify the claim.

Circularity Check

0 steps flagged

No significant circularity: CDH is a derived unitary truncation benchmarked externally; self-citations are not load-bearing.

full rationale

The central derivation is a unitary polaron transformation whose block matrix elements are computed by explicit momentum integrals or spectral decomposition (SI Eqs. 18, 26-28; main-text Eq. 3). The CDH is then defined by truncating to M Fock states; no parameter is fitted to the target data. Spectral benchmarks are compared with Braak's independent analytical solution (Ref. 63) and with converged bare truncations (Fig. 2); Dicke-Heisenberg phase diagrams are compared with brute-force N=20 calculations (Fig. 3). The dressing functions f_M,g_M,h,v,w in SI Eq. (40) are closed-form expressions derived from displacement-operator matrix elements, not adjusted to reproduce observables. The self-references (Refs. 54, 55, 65) refer either to prior independent formalisms or to the accompanying supplemental material included in this submission, which contains the full derivation; none defines the target result in terms of itself. The SI caveat that ground-state observables require M_P > M, with non-monotonic M-convergence in difficult parameter ranges (SI Sec. I C; Figs. 4-5), is a convergence/validation limitation rather than a circularity: M_P is a separate operator-rotation truncation and is not a fitted parameter tuned to match reported exact results. Thus no load-bearing step reduces by construction to its own inputs; the minor score reflects only non-load-bearing self-citations.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

The central derivation is a unitary polaron transform plus Fock-block truncation. No fitted physical parameters or invented entities are introduced; the only hand-set numerical controls are the truncation orders M and M_P, whose adequacy is established empirically rather than by a theorem.

free parameters (2)
  • Cavity truncation order M = M = 1..4 for Rabi; M = 1, 3 for Dicke-Heisenberg
    Number of polaron-frame Fock levels kept in H_cdh(M). Central spectral and observable results depend on this manually chosen cutoff, and no a priori error bound is provided.
  • Operator rotation dimension M_P = M_P = M (thermal states); M_P = 20 (ground-state observables at resonance/deep-strong)
    Dimension used to rotate observables by U_P before truncating to M; required to exceed M for ground-state magnetization, chosen by monitoring monotonic convergence and the lambda->infinity limit rather than by a systematic rule.
axioms (5)
  • standard math The polaron/entangling transformation U_P is unitary and exactly preserves the spectrum.
    Uses U_P = exp(Sum_n lambda_n/Omega_n S_n (a^dag - a)); for self-adjoint S_n this is a standard unitary (Stone's theorem). Invoked in Eq. (2) and throughout.
  • ad hoc to paper M-level truncation of the polaron-frame Hamiltonian yields a systematically convergent sequence to the exact limit.
    Asserted in the abstract/Introduction as 'systematically convergent' and 'converge to the exact limit', but no proof or error bound is given; supported only by numerical benchmarks for two models.
  • domain assumption Equilibrium observables can be computed as Tr[e^{-beta H_cdh(M)} O_cdh]/Z with the canonical mean-force state.
    Exact for an isolated system before truncation; for leaky cavities/baths it relies on the mean-force Hamiltonian approximation (Refs. 82-83), which is not benchmarked here.
  • standard math The momentum representation and Hermite/displacement matrix-element identities used to evaluate blocks are valid.
    SI Sec. I A, Eqs. (17), (26)-(28); standard integral identities for harmonic-oscillator states.
  • domain assumption Coupling operators S_n are such that the unitary and block matrix elements are well defined (self-adjoint; bounded in the examples).
    Examples use Pauli operators; the method is advertised for general molecular/material Hamiltonians, where S_n may be unbounded, but no such case is analyzed.

pith-pipeline@v1.3.0-alltime-deepseek · 23476 in / 17863 out tokens · 169221 ms · 2026-08-03T22:07:45.507207+00:00 · methodology

0 comments
read the original abstract

We present a non-perturbative Hamiltonian mapping method for quantum systems strongly coupled to a quantized field mode (cavity), yielding compact closed-form representations of hybrid light-matter systems. The mapping method builds on an entangling transformation of photonic and atomic degrees of freedom. By truncating the resulting cavity-dressed Hamiltonian (CDH) to successively larger excitation sectors, we construct a series of compact models that converge to the exact limit, outpacing conventional approaches even in the challenging resonant and ultrastrong light-matter regime. The mapping principle also applies to multimode cavities coupled to matter through noncommuting operators and to leaky cavities. We benchmark the CDH framework on the quantum Rabi model, demonstrating accurate spectral predictions in both weak and strong coupling regimes, together with converging ground-state and thermal observables. We study the Dicke-Heisenberg lattice model and determine its phase diagram under resonant and strong light-matter coupling, achieving significant computational savings over brute-force simulations and identifying cavity-mediated spin correlations both analytically and numerically. The closed-form and compactness of the CDH provide both physical insight and enhanced computational efficiency, facilitating studies of strongly coupled hybrid light-matter systems.

Figures

Figures reproduced from arXiv: 2511.11903 by Dvira Segal, Jakub Garwo{\l}a.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) The quantum Rabi model with a spin coupled to a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a)-(c) Eigenenergies of the quantum Rabi model against the coupling strength [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Ground state phase diagrams of the Dicke-XX Heisenberg model (a) in the bare representation with [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Average magnetization, [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Average ground state magnetization, [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Phase diagrams of the Dicke-XX Heisenberg model using the average magnetization [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Structure factors of the XX Dicke-Heisenberg chain with respect to the scaled coupling strength [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Cuts of the phase diagram of the Dicke-XX Heisenberg model along the horizontal lines, where [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Phase diagrams of the Dicke-XXX Heisenberg model. (a)-(b) The order parameter is the magnetization [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Average magnetization [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗

discussion (0)

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

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Variational non-gaussian approach to interacting spin-boson models

    quant-ph 2026-07 conditional novelty 6.0

    A hybrid non-Gaussian variational and DMRG solver gives accurate Dicke and Dicke-Ising ground states without explicit photon truncation and with smaller MPS bond dimension.

Reference graph

Works this paper leans on

86 extracted references · 41 canonical work pages · cited by 1 Pith paper

  1. [1]

    Forn-D\' az , author L

    author author P. Forn-D\' az , author L. Lamata , author E. Rico , author J. Kono , \ and\ author E. Solano ,\ title title Ultrastrong coupling regimes of light-matter interaction , \ 10.1103/RevModPhys.91.025005 journal journal Rev. Mod. Phys. \ volume 91 ,\ pages 025005 ( year 2019 ) NoStop

    doi:10.1103/revmodphys.91.025005 2019

  2. [2]

    Schlawin , author D

    author author F. Schlawin , author D. M. \ Kennes , \ and\ author M. A. \ Sentef ,\ title title Cavity quantum materials , \ 10.1063/5.0083825 journal journal Applied Physics Reviews \ volume 9 ,\ pages 011312 ( year 2022 ) ,\ note special Collection: Quantum Materials and 2D Superlattices NoStop

    doi:10.1063/5.0083825 2022

  3. [3]

    Frisk Kockum , author A

    author author A. Frisk Kockum , author A. Miranowicz , author S. De Liberato , author S. Savasta , \ and\ author F. Nori ,\ title title Ultrastrong coupling between light and matter , \ 10.1038/s42254-018-0006-2 journal journal Nature Reviews Physics \ volume 1 ,\ pages 19--40 ( year 2019 ) NoStop

    doi:10.1038/s42254-018-0006-2 2019

  4. [4]

    author author T. W. \ Ebbesen , author A. Rubio , \ and\ author G. D. \ Scholes ,\ title title Introduction: Polaritonic chemistry , \ @noop journal journal Chemical Reviews \ volume 123 ,\ pages 12037--12038 ( year 2023 ) NoStop

    2023

  5. [5]

    \ Li , author Bingyu \ Cui , author Joseph E

    author author Tao E. \ Li , author Bingyu \ Cui , author Joseph E. \ Subotnik , \ and\ author Abraham \ Nitzan ,\ title title Molecular polaritonics: Chemical dynamics under strong light–matter coupling , \ https://doi.org/10.1146/annurev-physchem-090519-042621 journal journal Annual Review of Physical Chemistry \ volume 73 ,\ pages 43--71 ( year 2022 ) NoStop

    doi:10.1146/annurev-physchem-090519-042621 2022

  6. [6]

    Mandal , author M

    author author A. Mandal , author M. A. \ Taylor , author B. M. \ Weight , author E. R. \ Koessler , author X. Li , \ and\ author P. Huo ,\ title title Theoretical advances in polaritonic chemistry and molecular cavity quantum electrodynamics , \ 10.1021/acs.chemrev.2c00855 journal journal Chem. Rev. \ volume 123 ,\ pages 9786 ( year 2023 ) NoStop

    doi:10.1021/acs.chemrev.2c00855 2023

  7. [7]

    Sandik , author J

    author author G. Sandik , author J. Feist , author F. J. \ Garc \'i a-Vidal , \ and\ author T. Schwartz ,\ title title Cavity-enhanced energy transport in molecular systems , \ 10.1038/s41563-024-02038-1 journal journal Nature Materials \ volume 24 ,\ pages 344--355 ( year 2025 ) NoStop

    work page doi:10.1038/s41563-024-02038-1 2025

  8. [8]

    Shalabney , author J

    author author A. Shalabney , author J. George , author J. Hutchison , author G. Pupillo , author C. Genet , \ and\ author T. W. \ Ebbesen ,\ title title Coherent coupling of molecular resonators with a microcavity mode , \ 10.1038/ncomms6981 journal journal Nature Communications \ volume 6 ,\ pages 5981 ( year 2015 ) NoStop

    work page doi:10.1038/ncomms6981 2015

  9. [9]

    George , author A

    author author J. George , author A. Shalabney , author J. A. \ Hutchison , author C. Genet , \ and\ author T. W. \ Ebbesen ,\ title title Liquid-phase vibrational strong coupling , \ 10.1021/acs.jpclett.5b00204 journal journal The Journal of Physical Chemistry Letters \ volume 6 ,\ pages 1027--1031 ( year 2015 ) NoStop

    doi:10.1021/acs.jpclett.5b00204 2015

  10. [10]

    author author R. M. A. \ Vergauwe , author J. George , author T. Chervy , author J. A. \ Hutchison , author A. Shalabney , author V. Y. \ Torbeev , \ and\ author T. W. \ Ebbesen ,\ title title Quantum strong coupling with protein vibrational modes , \ 10.1021/acs.jpclett.6b01943 journal journal The Journal of Physical Chemistry Letters \ volume 7 ,\ pages...

    work page doi:10.1021/acs.jpclett.6b01943 2016

  11. [11]

    \ Varma , author Joseph \ Moran , author Thibault \ Chervy , author Xiaolan \ Zhong , author Elo \"i se \ Devaux , author Cyriaque \ Genet , author James A

    author author Anoop \ Thomas , author Jino \ George , author Atef \ Shalabney , author Marian \ Dryzhakov , author Sreejith J. \ Varma , author Joseph \ Moran , author Thibault \ Chervy , author Xiaolan \ Zhong , author Elo \"i se \ Devaux , author Cyriaque \ Genet , author James A. \ Hutchison , \ and\ author Thomas W. \ Ebbesen ,\ title title Ground-sta...

    doi:10.1002/anie.201605504 2016

  12. [12]

    \ Mart \'i nez-Mart \'i nez , author Meng \ Du , author Raphael F

    author author Luis A. \ Mart \'i nez-Mart \'i nez , author Meng \ Du , author Raphael F. \ Ribeiro , author Stéphane \ K \'e na-Cohen , \ and\ author Joel \ Yuen-Zhou ,\ title title Polariton-assisted singlet fission in acene aggregates , \ 10.1021/acs.jpclett.8b00455 journal journal The Journal of Physical Chemistry Letters \ volume 9 ,\ pages 1951--1957...

    work page doi:10.1021/acs.jpclett.8b00455 1951

  13. [13]

    Thomas , author L

    author author A. Thomas , author L. Lethuillier-Karl , author K. Nagarajan , author R. M. A. \ Vergauwe , author J. George , author T. Chervy , author A. Shalabney , author E. Devaux , author C. Genet , author J. Moran , \ and\ author T. W. \ Ebbesen ,\ title title Tilting a ground-state reactivity landscape by vibrational strong coupling , \ 10.1126/scie...

    doi:10.1126/science.aau7742 2019

  14. [14]

    author author Ran \ Damari , author Omri \ Weinberg , author Daniel \ Krotkov , author Natalia \ Demina , author Katherine \ Akulov , author Adina \ Golombek , author Tal \ Schwartz , \ and\ author Sharly \ Fleischer ,\ title title Strong coupling of collective intermolecular vibrations in organic materials at terahertz frequencies , \ 10.1038/s41467-019-...

    work page doi:10.1038/s41467-019-11266-5 2019

  15. [15]

    author author Kenji \ Hirai , author Hiroto \ Ishikawa , author Thibault \ Chervy , author James A. \ Hutchison , \ and\ author Hiroshi \ Uji-i ,\ title title Selective crystallization via vibrational strong coupling , \ 10.1039/D1SC03706D journal journal Chemical Science \ volume 12 ,\ pages 11986--11994 ( year 2021 ) ,\ note edge Article NoStop

    work page doi:10.1039/d1sc03706d 2021

  16. [16]

    Patrahau , author M

    author author B. Patrahau , author M. Piejko , author R. J. \ Mayer , author C. Antheaume , author T. Sangchai , author G. Ragazzon , author A. Jayachandran , author E. Devaux , author C. Genet , author J. Moran , \ and\ author T. W. \ Ebbesen ,\ title title Direct observation of polaritonic chemistry by nuclear magnetic resonance spectroscopy , \ 10.1002...

    doi:10.1002/anie.202401368 2024

  17. [17]

    author author Xiao-Yun \ Li , author Arkajit \ Mandal , \ and\ author Pengfei \ Huo ,\ title title Cavity frequency-dependent theory for vibrational polariton chemistry , \ 10.1038/s41467-021-21524-9 journal journal Nature Communications \ volume 12 ,\ pages 1315 ( year 2021 ) NoStop

    work page doi:10.1038/s41467-021-21524-9 2021

  18. [18]

    author author Pei-Yun \ Yang \ and\ author Jianshu \ Cao ,\ title title Quantum effects in chemical reactions under polaritonic vibrational strong coupling , \ 10.1021/acs.jpclett.1c02151 journal journal The Journal of Physical Chemistry Letters \ volume 12 ,\ pages 9531--9538 ( year 2021 ) NoStop

    work page doi:10.1021/acs.jpclett.1c02151 2021

  19. [19]

    \ Lindoy , author Arkajit \ Mandal , \ and\ author David R

    author author Lachlan P. \ Lindoy , author Arkajit \ Mandal , \ and\ author David R. \ Reichman ,\ title title Quantum dynamical effects of vibrational strong coupling in chemical reactivity , \ @noop journal journal Nature Comm. \ volume 14 ,\ pages 2733 ( year 2023 ) NoStop

    2023

  20. [20]

    \ Zhang , \ and\ author Joel M

    author author Qi Yu , author Dong H. \ Zhang , \ and\ author Joel M. \ Bowman ,\ title title Theoretical and quantum mechanical deconstruction of vibrational energy transfer pathways modified by collective vibrational strong coupling , \ 10.1038/s41467-025-XXXX-X journal journal Nature Communications \ volume 16 ,\ pages 6760 ( year 2025 ) NoStop

    work page doi:10.1038/s41467-025-xxxx-x 2025

  21. [21]

    author author J. A. \ Hutchison , author T. Schwartz , author C. Genet , author E. Devaux , \ and\ author T. W. \ Ebbesen ,\ title title Modifying chemical landscapes by coupling to vacuum fields , \ 10.1002/anie.201107033 journal journal Angewandte Chemie International Edition \ volume 51 ,\ pages 1592--1596 ( year 2012 ) NoStop

    doi:10.1002/anie.201107033 2012

  22. [22]

    George , author James A

    author author Emanuele \ Orgiu , author J. George , author James A. \ Hutchison , author E. Devaux , author Jean-François \ Dayen , author Bernard \ Doudin , author F. Stellacci , author Cyriaque \ Genet , author J. Schachenmayer , author Claudiu \ Genes , author Guido \ Pupillo , author Paolo \ Samor \`i , \ and\ author T. W. \ Ebbesen ,\ title title Con...

    doi:10.1038/nmat4392 2015

  23. [23]

    author author Georgi Gary \ Rozenman , author Katherine \ Akulov , author Adina \ Golombek , \ and\ author Tal \ Schwartz ,\ title title Long-range transport of organic exciton-polaritons revealed by ultrafast microscopy , \ 10.1021/acsphotonics.7b01332 journal journal ACS Photonics \ volume 5 ,\ pages 105--110 ( year 2018 ) NoStop

    doi:10.1021/acsphotonics.7b01332 2018

  24. [24]

    Munkhbat , author M

    author author B. Munkhbat , author M. Wers \"a ll , author D. G. \ Baranov , author T. J. \ Antosiewicz , \ and\ author T. Shegai ,\ title title Suppression of photo-oxidation of organic chromophores by strong coupling to plasmonic nanoantennas , \ 10.1126/sciadv.aas9552 journal journal Science Advances \ volume 4 ,\ pages eaas9552 ( year 2018 ) NoStop

    work page doi:10.1126/sciadv.aas9552 2018

  25. [25]

    author author Kati \ Stranius , author Manuel \ Hertzog , \ and\ author Karl \ Börjesson ,\ title title Selective manipulation of electronically excited states through strong light–matter interactions , \ 10.1038/s41467-018-04736-1 journal journal Nature Communications \ volume 9 ,\ pages 2273 ( year 2018 ) NoStop

    doi:10.1038/s41467-018-04736-1 2018

  26. [26]

    Eizner , author L

    author author E. Eizner , author L. A. \ Mart \'i nez-Mart \'i nez , author J. Yuen-Zhou , \ and\ author S. K \'e na-Cohen ,\ title title Inverting singlet and triplet excited states using strong light--matter coupling , \ 10.1126/sciadv.aax4482 journal journal Science Advances \ volume 5 ,\ pages eaax4482 ( year 2019 ) NoStop

    doi:10.1126/sciadv.aax4482 2019

  27. [27]

    \ Blach , author Victoria A

    author author Daria D. \ Blach , author Victoria A. \ Lumsargis , author Daniel E. \ Clark , author Chern \ Chuang , author Kang \ Wang , author Letian \ Dou , author Richard D. \ Schaller , author Jianshu \ Cao , author Christina W. \ Li , \ and\ author Libai \ Huang ,\ title title Superradiance and exciton delocalization in perovskite quantum dot superl...

    work page doi:10.1021/acs.nanolett.2c02706 2022

  28. [28]

    author author Fabijan \ Pavosevic , author Robert L. \ Smith , \ and\ author Angel \ Rubio ,\ title title Computational study on the catalytic control of endo/exo diels-alder reactions by cavity quantum vacuum fluctuations , \ https://doi.org/10.1038/s41467-023-38474-w journal journal Nature Comm. \ volume 14 ,\ pages 2766 ( year 2023 ) NoStop

    doi:10.1038/s41467-023-38474-w 2023

  29. [29]

    author author Anael \ Ben-Asher , author Thomas \ Schnappinger , author Markus \ Kowalewski , \ and\ author Johannes \ Feist ,\ title title Enhanced photoisomerization with hybrid metallodielectric cavities based on mode interference , \ 10.1063/5.0252988 journal journal J. Chem. Phys. \ volume 162 ,\ pages 094308 ( year 2025 ) NoStop

    work page doi:10.1063/5.0252988 2025

  30. [30]

    \ Arnardottir , author Piper \ Fowler-Wright , author Christos \ Tserkezis , author Brendon W

    author author Kristin B. \ Arnardottir , author Piper \ Fowler-Wright , author Christos \ Tserkezis , author Brendon W. \ Lovett , \ and\ author Jonathan \ Keeling ,\ title title Non-markovian effects in long-range polariton-mediated energy transfer , \ https://doi.org/10.1063/5.0245977 journal journal The Journal of Chemical Physics \ volume 163 ,\ pages...

    work page doi:10.1063/5.0245977 2025

  31. [31]

    Wallraff , author D

    author author A. Wallraff , author D. I. \ Schuster , author A. Blais , author L. Frunzio , author R.-S. \ Huang , author J. Majer , author S. Kumar , author S. M. \ Girvin , \ and\ author R. J. \ Schoelkopf ,\ title title Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics , \ 10.1038/nature02851 journal jo...

    doi:10.1038/nature02851 2004

  32. [32]

    \ Sundaresan , author Yanbing \ Liu , author Darius \ Sadri , author L\'aszl\'o J

    author author Neereja M. \ Sundaresan , author Yanbing \ Liu , author Darius \ Sadri , author L\'aszl\'o J. \ Sz o o cs , author Devin L. \ Underwood , author Moein \ Malekakhlagh , author Hakan E. \ T\"ureci , \ and\ author Andrew A. \ Houck ,\ title title Beyond strong coupling in a multimode cavity , \ 10.1103/PhysRevX.5.021035 journal journal Phys. Re...

    work page doi:10.1103/physrevx.5.021035 2015

  33. [33]

    Forn-D \'i az , author J

    author author P. Forn-D \'i az , author J. J. \ Garc \'i a-Ripoll , author B. Peropadre , author J.-L. \ Orgiazzi , author M. A. \ Yurtalan , author R. Belyansky , author C. M. \ Wilson , \ and\ author A. Lupascu ,\ title title Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime , \ 10.1038/nphys3...

    doi:10.1038/nphys3905 2017

  34. [34]

    author author Dingshun \ Lv , author Shuoming \ An , author Zhenyu \ Liu , author Jing-Ning \ Zhang , author Julen S. \ Pedernales , author Lucas \ Lamata , author Enrique \ Solano , \ and\ author Kihwan \ Kim ,\ title title Quantum simulation of the quantum rabi model in a trapped ion , \ 10.1103/PhysRevX.8.021027 journal journal Phys. Rev. X \ volume 8 ...

    doi:10.1103/physrevx.8.021027 2018

  35. [35]

    author author Roman \ Kuzmin , author Nitish \ Mehta , author Nicholas \ Grabon , author Raymond \ Mencia , \ and\ author Vladimir E. \ Manucharyan ,\ title title Superstrong coupling in circuit quantum electrodynamics , \ 10.1038/s41534-019-0132-x journal journal npj Quantum Information \ volume 5 ,\ pages 20 ( year 2019 ) NoStop

    work page doi:10.1038/s41534-019-0132-x 2019

  36. [36]

    Janzen , author X

    author author N. Janzen , author X. Dai , author S. Ren , author J. Shi , \ and\ author A. Lupascu ,\ title title Tunable coupler for mediating interactions between a two-level system and a waveguide from a decoupled state to the ultrastrong coupling regime , \ 10.1103/PhysRevResearch.5.033155 journal journal Phys. Rev. Res. \ volume 5 ,\ pages 033155 ( y...

    work page doi:10.1103/physrevresearch.5.033155 2023

  37. [37]

    author author J. A. \ Campos-Gonzalez-Angulo , author R. F. \ Ribeiro , \ and\ author J. Yuen-Zhou ,\ title title Resonant catalysis of thermally activated chemical reactions with vibrational polaritons , \ 10.1038/s41467-019-12636-1 journal journal Nature Communications \ volume 10 ,\ pages 4685 ( year 2019 ) NoStop

    doi:10.1038/s41467-019-12636-1 2019

  38. [38]

    author author Nicholas \ Anto-Sztrikacs , author Ahsan \ Nazir , \ and\ author Dvira \ Segal ,\ title title Effective-hamiltonian theory of open quantum systems at strong coupling , \ 10.1103/PRXQuantum.4.020307 journal journal PRX Quantum \ volume 4 ,\ pages 020307 ( year 2023 ) NoStop

    work page doi:10.1103/prxquantum.4.020307 2023

  39. [39]

    \ Fiechter , author Johan E

    author author Marit R. \ Fiechter , author Johan E. \ Runeson , author Joseph E. \ Lawrence , \ and\ author Jeremy O. \ Richardson ,\ title title How quantum is the resonance behavior in vibrational polariton chemistry? \ 10.1021/acs.jpclett.3c01154 journal journal The Journal of Physical Chemistry Letters \ volume 14 ,\ pages 8261--8267 ( year 2023 ) NoStop

    work page doi:10.1021/acs.jpclett.3c01154 2023

  40. [40]

    \ Mueller , author Yu Okamura , author Bruno G

    author author Niclas S. \ Mueller , author Yu Okamura , author Bruno G. M. \ Vieira , author Sabrina \ Juergensen , author Holger \ Lange , author Eduardo B. \ Barros , author Florian \ Schulz , \ and\ author Stephanie \ Reich ,\ title title Deep strong light–matter coupling in plasmonic nanoparticle crystals , \ 10.1038/s41586-020-2508-1 journal journal ...

    doi:10.1038/s41586-020-2508-1 2020

  41. [41]

    author author Giacomo \ Jarc , author Shahla Yasmin \ Mathengattil , author Angela \ Montanaro , author Francesca \ Giusti , author Enrico Maria \ Rigoni , author Rudi \ Sergo , author Francesca \ Fassioli , author Stephan \ Winnerl , author Simone \ Dal Zilio , author Dragan \ Mihailovic , author Peter \ Prelovšek , author Martin \ Eckstein , \ and\ auth...

    doi:10.1038/s41586-023-06633-0 2023

  42. [42]

    O ztop , \ and\ author H. E. \ T \

    author author M. Schir \'o , author M. Bordyuh , author B. \"O ztop , \ and\ author H. E. \ T \"u reci ,\ title title Phase transition of light in cavity qed lattices , \ 10.1103/PhysRevLett.109.053601 journal journal Phys. Rev. Lett. \ volume 109 ,\ pages 053601 ( year 2012 ) NoStop

    work page doi:10.1103/physrevlett.109.053601 2012

  43. [43]

    author author Emil \ Vinas Bostrom , author Adithya \ Sriram , author Martin \ Claassen , \ and\ author Angel \ Rubio ,\ title title Controlling the magnetic state of the proximate quantum spin liquid -rucl3 with an optical cavity , \ https://doi.org/10.1038/s41524-023-01158-6 journal journal npj Comp. Mat. \ volume 9 ( year 2023 ),\ https://doi.org/10.10...

    doi:10.1038/s41524-023-01158-6 2023

  44. [44]

    author author Alexandre \ Le Boit \'e ,\ title title Theoretical methods for ultrastrong light-matter interactions , \ 10.1002/qute.201900140 journal journal Advanced Quantum Technologies \ volume 3 ,\ pages 1900140 ( year 2020 ) NoStop

    work page doi:10.1002/qute.201900140 2020

  45. [45]

    author author E. K. \ Twyeffort Irish ,\ title title Generalized rotating-wave approximation for arbitrarily large coupling , \ 10.1103/PhysRevLett.99.173601 journal journal Phys. Rev. Lett. \ volume 99 ,\ pages 173601 ( year 2007 ) NoStop

    work page doi:10.1103/physrevlett.99.173601 2007

  46. [46]

    author author Daniele \ De Bernardis ,\ title title Relaxation breakdown and resonant tunneling in ultrastrong-coupling cavity qed , \ 10.1103/PhysRevA.108.043717 journal journal Phys. Rev. A \ volume 108 ,\ pages 043717 ( year 2023 ) NoStop

    work page doi:10.1103/physreva.108.043717 2023

  47. [47]

    author author Alexander \ Semenov \ and\ author Abraham \ Nitzan ,\ title title Electron transfer in confined electromagnetic fields , \ 10.1063/1.5095940 journal journal The Journal of Chemical Physics \ volume 150 ,\ pages 174122 ( year 2019 ) NoStop

    doi:10.1063/1.5095940 2019

  48. [48]

    author author M. A. C. \ Saller , author Y. Lai , \ and\ author E. Geva ,\ title title An accurate linearized semiclassical approach for calculating cavity-modified charge transfer rate constants , \ @noop journal journal Journal of Physical Chemistry Letters \ volume 13 ,\ pages 2330--2337 ( year 2022 ) NoStop

    2022

  49. [49]

    author author M. A. C. \ Saller , author Y. Lai , \ and\ author E. Geva ,\ title title Cavity-modified fermi's golden rule rate constants: Beyond the single mode approximation , \ https://doi.org/10.1063/5.0172265 journal journal Journal of Chemical Physics \ volume 159 ,\ pages 151105 ( year 2023 ) NoStop

    work page doi:10.1063/5.0172265 2023

  50. [50]

    author author Wenxiang \ Ying \ and\ author Abraham \ Nitzan ,\ title title Electron transfer in confined electromagnetic fields: a unified fermi's golden rule rate theory and extension to lossy cavities , \ @noop journal journal arXiv:2511.04017 \ ( year 2025 ) ,\ http://arxiv.org/abs/2511.04017 arXiv:2511.04017 NoStop

    Pith/arXiv arXiv 2025

  51. [51]

    \ Love , author Alán \ Aspuru-Guzik , \ and\ author Jeremy L

    author author Alberto \ Peruzzo , author Jarrod \ McClean , author Peter \ Shadbolt , author Man-Hong \ Yung , author Xiao-Qi \ Zhou , author Peter J. \ Love , author Alán \ Aspuru-Guzik , \ and\ author Jeremy L. \ O’Brien ,\ title title A variational eigenvalue solver on a photonic quantum processor , \ 10.1038/ncomms5213 journal journal Nature Communica...

    doi:10.1038/ncomms5213 2014

  52. [52]

    author author Agustin \ Di Paolo , author Panagiotis Kl. \ Barkoutsos , author Ivano \ Tavernelli , \ and\ author Alexandre \ Blais ,\ title title Variational quantum simulation of ultrastrong light-matter coupling , \ 10.1103/PhysRevResearch.2.033364 journal journal Phys. Rev. Res. \ volume 2 ,\ pages 033364 ( year 2020 ) NoStop

    work page doi:10.1103/physrevresearch.2.033364 2020

  53. [53]

    author author Zhi-Hao \ Cui , author Arkajyoti \ Mandal , \ and\ author David R. \ Reichman ,\ title title Variational lang--firsov approach plus m ller--plesset perturbation theory with applications to Ab Initio polaritonic chemistry , \ 10.1021/acs.jctc.3c01011 journal journal Journal of Chemical Theory and Computation \ volume 20 ,\ pages 1143--1156 ( ...

    work page doi:10.1021/acs.jctc.3c01011 2024

  54. [54]

    author author Jakub \ Garwo a \ and\ author Dvira \ Segal ,\ title title Open quantum systems with noncommuting coupling operators: An analytic approach , \ @noop journal journal Physical Review B \ volume 110 ,\ pages 174304 ( year 2024 ) NoStop

    2024

  55. [55]

    author author Jitian \ Chen , author Jakub \ Garwo a , \ and\ author Dvira \ Segal ,\ title title Suppression of decoherence dynamics by a dissipative bath at strong coupling , \ 10.1103/3d9c-4x2q journal journal Phys. Rev. A \ volume 112 ,\ pages 022209 ( year 2025 ) NoStop

    work page doi:10.1103/3d9c-4x2q 2025

  56. [56]

    \ Garc\' a-Vidal , author Antonio I

    author author Ivan \ Medina , author Francisco J. \ Garc\' a-Vidal , author Antonio I. \ Fern\'andez-Dom\' nguez , \ and\ author Johannes \ Feist ,\ title title Few-mode field quantization of arbitrary electromagnetic spectral densities , \ 10.1103/PhysRevLett.126.093601 journal journal Phys. Rev. Lett. \ volume 126 ,\ pages 093601 ( year 2021 ) NoStop

    doi:10.1103/physrevlett.126.093601 2021

  57. [57]

    author author Maksim \ Lednev , author Francisco J. \ Garc\' a-Vidal , \ and\ author Johannes \ Feist ,\ title title Lindblad master equation capable of describing hybrid quantum systems in the ultrastrong coupling regime , \ 10.1103/PhysRevLett.132.106902 journal journal Phys. Rev. Lett. \ volume 132 ,\ pages 106902 ( year 2024 ) NoStop

    work page doi:10.1103/physrevlett.132.106902 2024

  58. [58]

    author author Yuto \ Ashida , author Ata c c \ I \. I mamo g g lu , \ and\ author Eugene \ Demler ,\ title title Cavity quantum electrodynamics at arbitrary light-matter coupling strengths , \ 10.1103/PhysRevLett.126.153603 journal journal Phys. Rev. Lett. \ volume 126 ,\ pages 153603 ( year 2021 ) NoStop

    doi:10.1103/physrevlett.126.153603 2021

  59. [59]

    author author Matthias \ Bauer \ and\ author Andreas \ Dreuw ,\ title title Perturbation theoretical approaches to strong light--matter coupling in ground and excited electronic states for the description of molecular polaritons , \ 10.1063/5.0142403 journal journal The Journal of Chemical Physics \ volume 158 ,\ pages 124128 ( year 2023 ) NoStop

    work page doi:10.1063/5.0142403 2023

  60. [60]

    author author Yassir \ El Moutaoukal , author Rosario R. \ Riso , author Matteo \ Castagnola , author Enrico \ Ronca , \ and\ author Henrik \ Koch ,\ title title Strong coupling m ller--plesset perturbation theory , \ 10.1021/acs.jctc.4c01160 journal journal Journal of Chemical Theory and Computation \ volume 21 ,\ pages 3981--3992 ( year 2025 ) NoStop

    work page doi:10.1021/acs.jctc.4c01160 2025

  61. [61]

    \ Jaynes \ and\ author F.W

    author author E.T. \ Jaynes \ and\ author F.W. \ Cummings ,\ title title Comparison of quantum and semiclassical radiation theories with application to the beam maser , \ 10.1109/PROC.1963.1664 journal journal Proceedings of the IEEE \ volume 51 ,\ pages 89--109 ( year 1963 ) NoStop

    arXiv 1963

  62. [62]

    author author E. K. \ Twyeffort Irish , author J. Gea-Banacloche , author I. Martin , \ and\ author K. C. \ Schwab ,\ title title Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator , \ 10.1103/PhysRevB.72.195410 journal journal Phys. Rev. B \ volume 72 ,\ pages 195410 ( year 2005 ) NoStop

    doi:10.1103/physrevb.72.195410 2005

  63. [63]

    Braak ,\ title title Integrability of the rabi model , \ 10.1103/PhysRevLett.107.100401 journal journal Phys

    author author D. Braak ,\ title title Integrability of the rabi model , \ 10.1103/PhysRevLett.107.100401 journal journal Phys. Rev. Lett. \ volume 107 ,\ pages 100401 ( year 2011 ) NoStop

    doi:10.1103/physrevlett.107.100401 2011

  64. [64]

    author author Qiongtao \ Xie , author Honghua \ Zhong , author Murray T. \ Batchelor , \ and\ author Chaohong \ Lee ,\ title title The quantum rabi model: solution and dynamics , \ 10.1088/1751-8121/aa5a65 journal journal Journal of Physics A: Mathematical and Theoretical \ volume 50 ,\ pages 113001 ( year 2017 ) NoStop

    doi:10.1088/1751-8121/aa5a65 2017

  65. [65]

    author author Jakub \ Garwo a \ and\ author Dvira \ Segal ,\ title title Supplemental material , \ @noop \ ( year 2025 ) NoStop

    2025

  66. [66]

    author author I. I. \ Rabi ,\ title title On the process of space quantization , \ 10.1103/PhysRev.49.324 journal journal Phys. Rev. \ volume 49 ,\ pages 324--328 ( year 1936 ) NoStop

    doi:10.1103/physrev.49.324 1936

  67. [67]

    author author R. H. \ Dicke ,\ title title Coherence in spontaneous radiation processes , \ 10.1103/PhysRev.93.99 journal journal Phys. Rev. \ volume 93 ,\ pages 99--110 ( year 1954 ) NoStop

    doi:10.1103/physrev.93.99 1954

  68. [68]

    Heisenberg ,\ title title Zur theorie des ferromagnetismus , \ 10.1007/BF01328601 journal journal Zeitschrift für Physik \ volume 49 ,\ pages 619--636 ( year 1928 ) NoStop

    author author W. Heisenberg ,\ title title Zur theorie des ferromagnetismus , \ 10.1007/BF01328601 journal journal Zeitschrift für Physik \ volume 49 ,\ pages 619--636 ( year 1928 ) NoStop

    doi:10.1007/bf01328601 1928

  69. [69]

    author author Jo\ ao Pedro \ Mendon c c a , author Krzysztof \ Jachymski , \ and\ author Yao \ Wang ,\ title title Role of matter interactions in superradiant phenomena , \ 10.1103/z8gv-7yyk journal journal Phys. Rev. Lett. \ volume 135 ,\ pages 133601 ( year 2025 ) NoStop

    work page doi:10.1103/z8gv-7yyk 2025

  70. [70]

    author author Yuanwei \ Zhang , author Lixian \ Yu , author J.-Q. \ Liang , author Gang \ Chen , author Suotang \ Jia , \ and\ author Franco \ Nori ,\ title title Quantum phases in circuit qed with a superconducting qubit array , \ 10.1038/srep04083 journal journal Scientific Reports \ volume 4 ,\ pages 4083 ( year 2014 ) NoStop

    doi:10.1038/srep04083 2014

  71. [71]

    role of matter interactions in superradiant phenomena

    author author Max \ Hörmann , author Anja \ Langheld , author Jonas \ Leibig , author Andreas \ Schellenberger , \ and\ author Kai Phillip \ Schmidt ,\ title title Comment on "role of matter interactions in superradiant phenomena" , \ @noop journal journal arXiv:2511.08452 \ ( year 2025 ) NoStop

    arXiv 2025

  72. [72]

    Grimaudo , author N

    author author R. Grimaudo , author N. V. \ Vitanov , \ and\ author A. Messina ,\ title title Landau-majorana-st "uckelberg-zener dynamics driven by coupling for two interacting qutrit systems , \ 10.1103/PhysRevB.99.214406 journal journal Physical Review B \ volume 99 ,\ pages 214406 ( a ) ,\ note publisher: American Physical Society NoStop

    work page doi:10.1103/physrevb.99.214406

  73. [73]

    author author R Grimaudo , author A Messina , author P A \ Ivanov , \ and\ author N V \ Vitanov ,\ title title Spin-1/2 sub-dynamics nested in the quantum dynamics of two coupled qutrits , \ 10.1088/1751-8121/aa5fb6 journal journal Journal of Physics A: Mathematical and Theoretical \ volume 50 ,\ pages 175301 ( b ) ,\ note publisher: IOP Publishing NoStop

    work page doi:10.1088/1751-8121/aa5fb6

  74. [74]

    author author Raphael \ Holzinger \ and\ author Claudiu \ Genes ,\ title title A compact analytical solution of the dicke superradiance master equation via residue calculus , \ doi:10.1515/zna-2025-0179 journal journal Zeitschrift für Naturforschung A \ volume 80 ,\ pages 673--679 ( year 2025 ) NoStop

    work page doi:10.1515/zna-2025-0179 2025

  75. [75]

    Alaeian , \ and\ author F

    author author Wenqi \ Tong , author H. Alaeian , \ and\ author F. Robicheaux ,\ title title Phase transitions in open dicke model: a degenerate perturbation theory approach , \ @noop journal journal arXiv:2505.12696 \ ( year 2025 ) ,\ http://arxiv.org/abs/2505.12696 2505.12696 NoStop

    arXiv 2025

  76. [76]

    author author Peter \ Kirton \ and\ author Jonathan \ Keeling ,\ title title Suppressing and restoring the dicke superradiance transition by dephasing and decay , \ 10.1103/PhysRevLett.118.123602 journal journal Phys. Rev. Lett. \ volume 118 ,\ pages 123602 ( year 2017 ) NoStop

    doi:10.1103/physrevlett.118.123602 2017

  77. [77]

    author author Yuguo \ Su , author Zhijie \ Sun , author Yiying \ Yan , author Hengyan \ Wang , author Junyan \ Luo , author Tiantian \ Ying , author Hongbin \ Liang , \ and\ author Yi-Xiao \ Huang ,\ title title Dynamical multipartite entanglement in a generalized tavis-cummings model with xy spin interaction , \ 10.1103/PhysRevA.111.052415 journal journa...

    work page doi:10.1103/physreva.111.052415 2025

  78. [78]

    author author Fu-Quan \ Dou , author Hang \ Zhou , \ and\ author Jian-An \ Sun ,\ title title Cavity heisenberg-spin-chain quantum battery , \ 10.1103/PhysRevA.106.032212 journal journal Phys. Rev. A \ volume 106 ,\ pages 032212 ( year 2022 ) NoStop

    work page doi:10.1103/physreva.106.032212 2022

  79. [79]

    author author Jochen \ Braumüller , author Michael \ Marthaler , author Andre \ Schneider , author Alexander \ Stehli , author Hannes \ Rotzinger , author Martin \ Weides , \ and\ author Alexey V. \ Ustinov ,\ title title Analog quantum simulation of the rabi model in the ultra-strong coupling regime , \ 10.1038/s41467-017-00894-w journal journal Nature C...

    work page doi:10.1038/s41467-017-00894-w 2017

  80. [80]

    author author E. K. \ Twyeffort Irish \ and\ author A. D. \ Armour ,\ title title Defining the semiclassical limit of the quantum rabi hamiltonian , \ 10.1103/PhysRevLett.129.183603 journal journal Phys. Rev. Lett. \ volume 129 ,\ pages 183603 ( year 2022 ) NoStop

    work page doi:10.1103/physrevlett.129.183603 2022

Showing first 80 references.