Pith. sign in

REVIEW 2 major objections 4 minor 55 references

Two-atom Dicke model with atom-atom interaction

T0 review · 2 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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

Pith's one-line read This paper shows that a flip-flop interaction between two atoms in a cavity can completely remove the superradiance threshold and change its critical scaling.

desk verdict The closed-system analysis is solid and the J=2δ zero-threshold result is genuinely new; but the dissipative phase boundary for J>2δ with spin relaxation rests on a flawed linearization and needs to be rederived. read the letter →

arxiv 2608.12625 v1 pith:AWUQK3HL submitted 2026-08-12 quant-ph

Lin Jiao , Han Pu This is my paper · ORCID
classification quant-ph
keywords Dickemodelsuperradiantphasetransitionatom-atominteractionzero-thresholdsuperradiancecriticalexponentdissipativequantumRabicavityQED
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks what a direct interaction between emitters does to superradiance and answers it with the simplest model that still allows exact analytics: two interacting atoms coupled to a single cavity mode in the classical oscillator limit. It shows that the superradiant threshold $\tilde g_c$ depends non-monotonically on the flip-flop interaction strength $J$ and vanishes exactly at $J=2\delta$, where the two lowest spin states become degenerate. At that point, any nonzero atom-photon coupling produces photons, and the photon number grows as $\tilde g^2$ rather than linearly, placing the transition in a different universality class. The zero threshold and the quadratic onset persist under both photon loss and local spin relaxation, and near the degeneracy the dissipative dynamics shows a metastable two-stage relaxation. The result identifies atom-atom interaction, not just light-matter coupling, as a control knob for superradiant criticality in a system realizable with two qubits in circuit QED or a trapped ion.

What carries the argument

The central object is the triplet manifold $|t_-\rangle$, $|t_0\rangle$, $|t_+\rangle$ of the two-atom spin Hamiltonian, with the singlet inert because $\Sigma_x|s\rangle=0$. In the classical oscillator limit $\omega\ll\delta$, the photon operators are replaced by a c-number $\alpha$, producing an effective transverse field $\lambda=2g\alpha$ on the spins; the ground state follows from the mean-field energy functional $E(\alpha)=\omega\alpha^2+\epsilon_0(\lambda)$. The argument turns on the degeneracy between $|t_-\rangle$ and $|t_0\rangle$ at $J=2\delta$: nondegenerate perturbation theory fails there, and projecting onto the degenerate subspace gives $\epsilon_0(\lambda)=-2\delta-\sqrt{2}|\lambda|$, a linear cusp that makes $\alpha=0$ unstable for any $g>0$. That cusp is what produces the quadratic photon-number onset. For the open system, the load-bearing reduction is the spin-projected effective Liouvillian, which maps the dissipative problem onto a damped Rabi model with detuning $\Delta=2\delta-J$, so all threshold calculations reduce to linear stability of that effective model.

What would settle it

A direct experimental check: fix the two-atom interaction at $J=2\delta$ in a simulator with $\omega\ll\delta$ (for example, two superconducting qubits coupled to a resonator) and measure the mean photon number as $g$ is swept from zero upward. The paper predicts $n\propto\tilde g^2$ for every nonzero $g$; a linear onset $n\propto(\tilde g-\tilde g_c)$ with a finite $\tilde g_c>0$, or an absence of photons below a threshold, would contradict the central claim. A numerical check beyond the $\omega\ll\delta$ limit would also settle it: if exact diagonalization at comparable $\omega$ and $\delta$ shows a finite threshold at $J=2\delta$, the zero-threshold and $\gamma=2$ results are artifacts of the classical-oscillator limit.

Watch

Extended reading notes

Core claim

Within the triplet sector of two coupled spins, the cavity couples only through $\Sigma_x$, and the spin ground state changes from $|t_-\rangle$ to $|t_0\rangle$ at $J=2\delta$. Perturbation theory in the effective transverse field $\lambda=2g\alpha$ yields the closed-form critical coupling $\tilde g_c^2=(2-J/\delta)/8$ for $J<2\delta$ and $\tilde g_c^2=(J/\delta-4\delta/J)/16$ for $J>2\delta$, with $\tilde g_c=0$ at the degeneracy. At degeneracy the mean-field energy acquires a linear cusp in $\alpha$, so the origin is unstable for every $g>0$; minimizing gives $n\propto\tilde g^2$, i.e. the exponent $\gamma=2$, whereas away from degeneracy $\gamma=1$. Cavity decay only rescales the threshold by the factor $1+(\kappa/2\omega)^2$, and with local spin relaxation the system reduces to an effective Rabi model with detuning $\Delta=2\delta-J$, whose threshold still vanishes at $\Delta=0$ while the photon number at degeneracy obeys $n_{\rm ss}=2(1+\gamma_\downarrow/\kappa)g^2/((\kappa+\gamma_\downarrow)^2/4+\omega^2)$. The normal phase on the $J>2\delta$ side is nearly maximally entangled, and crossing from it into the superradiant phase decreases rather than increases atomic excitation.

Load-bearing premise

The sharp phase boundary and the zero threshold assume the photon frequency $\omega$ is much smaller than the atomic transition frequency $\delta$, so the photon field can be replaced by a classical amplitude; if this separation of scales fails, the claimed threshold suppression and quadratic onset are not guaranteed.

Editorial extensions

If this is right

  • At $J=2\delta$, the cavity is populated for every nonzero $g$; a measurement of $n(\tilde g)$ should show $n\propto\tilde g^2$ ($\gamma=2$), and this holds under cavity photon loss and under local spin relaxation.
  • The phase boundary $\tilde g_c(J/\delta)$ is non-monotonic and has a cusp at zero at $J/\delta=2$; detuning the interaction either side restores the conventional linear onset $\gamma=1$, so the degeneracy is the control parameter that changes the universality class.
  • In the presence of photon loss alone, the steady state near degeneracy has all three triplet states almost equally populated, and relaxation from $|t_-,0\rangle$ proceeds through a metastable plateau on the cavity-loss time scale before the slow Liouvillian relaxation sets in.
  • With local spin relaxation, the two-atom problem becomes an effective damped Rabi model with interaction-tunable detuning $\Delta=2\delta-J$; at $\Delta=0$ the threshold remains zero and the $|t_0\rangle$ population rises toward $1/2$, so dissipation combined with interaction increases atom-atom entanglement relative to the equal-population triplet steady state.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Extension not in the paper: the mechanism looks generic — any interaction that degenerates two low-energy atomic states connected by the cavity-coupling operator should produce a zero-threshold soft mode, so similar threshold cusps should appear in multi-atom and multimode Dicke generalizations.
  • Extension not in the paper: the predicted crossover from $\gamma=1$ to $\gamma=2$ as $J/\delta$ approaches 2 from either side is directly measurable by fitting $n(\tilde g)$ at several fixed interaction strengths; this would test the universality-class change without needing exact degeneracy.
  • Extension not in the paper: the effective Rabi detuning $\Delta=2\delta-J$ means the interaction can be used as a knob to reach effective strong coupling at small bare $g$, with practical implications for ultrastrong-coupling experiments.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper analyzes a two-atom Dicke model with flip-flop interatomic interaction in the classical oscillator limit. It derives analytic expressions for the closed-system superradiance boundary, finding that the critical coupling vanishes at the interaction-induced degeneracy point J=2δ and that the photon-number onset becomes quadratic there. The paper extends the analysis to open systems with photon loss and local spin relaxation, deriving phase boundaries, showing that the zero threshold survives, and studying metastable dynamics and population distributions.

Significance. If correct, the results establish atom-atom interaction as a qualitative tuning knob for superradiant criticality, including the complete suppression of the threshold and a change of the photon-number onset exponent. The strength of the paper is its analytic tractability: the phase boundaries and exponents are derived from the Hamiltonian without fitted parameters and are confirmed by exact diagonalization. The open-system analysis, including the metastable manifold and the reduced two-level model, is well executed. The paper should be of interest to the quantum-optics and circuit-QED communities.

major comments (2)
  1. [Main text Eq. (9) and SM Sec. III.B, Eq. (S74)] The Δ<0 branch of Eq. (9) vanishes in the limit γ↓→0, whereas the pure-photon-loss phase boundary (SM Eq. S37) is finite for J/δ>2. This discontinuity arises because the reduced model is derived by projecting out the |t+⟩ and singlet states, which is justified only for finite spin relaxation; the γ↓→0 limit lies outside the reduced model's validity. The authors should state this validity condition and, ideally, verify the Δ<0 branch against full-Liouvillian numerics for finite γ↓.
  2. [Main text near Eq. (3) and Conclusion] The claim that the transition at J=2δ belongs to a 'different universality class' is based solely on the photon-number exponent γ=2 measured at a single fine-tuned point in a two-atom model. Since no other critical exponents are computed and the limit is the classical-oscillator limit, the term 'universality class' is stronger than the evidence supports; please replace it with 'critical exponent' or provide additional scaling information.
minor comments (4)
  1. [Main text Eq. (3)] The definition of the critical exponent uses n(g̃)∝(g̃−g̃_c)^γ; near a zero-threshold point (g̃_c=0) the standard scaling form with a multiplicative factor is not given, which could confuse the γ=2 result. Consider stating the scaling more explicitly.
  2. [Fig. 1(b)] The labels NP1 and NP2 are explained in the text but do not appear in the figure; adding the labels directly to the figure would improve readability.
  3. [SM Sec. II.C] The rate-equation derivation of the triplet populations assumes the cavity is in the vacuum state; this is a valid leading-order choice but the reader should be reminded that it neglects the classical displacement of the cavity in the superradiant phase.
  4. [Main text around Eq. (6)] After introducing the flip-flop interaction, the singlet state is mentioned as a dark state and then ignored. In the presence of spin relaxation the singlet is no longer dark; a short comment on its role in the reduced model would help the reader.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: all phase boundaries and exponents are derived from the Hamiltonian and reduced Liouvillian; the only self-citation is contextual and non-load-bearing.

full rationale

The paper's central claims are derived rather than fitted. The closed-system boundary Eq. (2) follows from perturbation theory around |t−⟩ and |t0⟩ (SM Eqs. S4–S9), the zero threshold at J=2δ from the degenerate-subspace Landau energy (SM Eqs. S10–S12), and the exponents γ=2 and γ=1 from the Puiseux and ordinary expansions of Eqs. (S13)–(S21). None of these steps imports a fitted parameter or an externally asserted result. The photon-loss boundary Eq. (5) is obtained from the zero-frequency feedback condition (SM Eqs. S26–S37), and the spin-relaxation boundary from the projected reduced Liouvillian (SM Eqs. S58–S74), with the degenerate-point photon number following exactly from the closed system (9)–(11) and Eq. (11). Numerical exact diagonalization and full-Liouvillian results are used only as checks. The only self-citation with author overlap, Ref. [34], appears in a contextual list of extended Dicke/Ising models [27–34] and is not used as an input to any derivation; Ref. [25] is likewise a platform citation. The text itself flags a limitation of the rate-equation population estimate near the degenerate point ("the analytic result shows discrepancies at lower g"), but that concerns an auxiliary approximation and is not a circular step. The classical-oscillator assumption ω≪δ delimits the Landau construction but is not derived from the conclusion. The skeptical sign-error concern about Eq. (S74) is a technical-correctness issue, not a circularity. Accordingly there is no circular step; score 1 only acknowledges the minor non-load-bearing self-citation.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard quantum optics assumptions: the classical oscillator limit, Markovian dissipation, and for the spin-relaxation case a two-state projection. These are stated explicitly in the paper and are standard for the Dicke/Rabi context; no parameters are fitted to data.

assumptions (4)
  • domain assumption Classical oscillator limit ω << δ justifies mean-field treatment of the cavity field as a c-number α.
    Used in SM Sec. I to derive the Landau energy E(α)=ωα^2+ε_0(λ); without this limit the sharp phase transition and critical exponents in a two-atom model are not defined.
  • domain assumption Markovian Lindblad master equations describe photon loss and local spin relaxation.
    Used in Eqs. (4) and (6); this standard quantum-optics assumption is stated but not derived.
  • domain assumption For the spin-relaxation case, the steady state is dominated by the {|t_->, |t_0>} subspace, justifying the reduced two-level model.
    Used in SM Sec. III to project onto the reduced Rabi model; validated numerically for the chosen parameters but is an approximation.
  • standard math The singlet state is a dark state for the flip-flop Hamiltonian and can be ignored in the closed and pure-photon-loss cases.
    Exact decoupling follows from Σ_x|s>=0 in Eq. (1); used throughout the main text and SM.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Two-atom Dicke model with atom-atom interaction." pith.science (2026). https://pith.science/paper/AWUQK3HL

@misc{pith2026260812625,
  author       = {Pith},
  title        = {Pith review of: Two-atom Dicke model with atom-atom interaction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AWUQK3HL}},
  note         = {Machine review of arXiv:2608.12625}
}
read the original abstract

Interactions among emitters provide a powerful means of controlling collective light--matter phenomena, yet their role in superradiant criticality has not been thoroughly investigated. Here we construct a minimal model that can yield analytical insights --- a Dicke model with two interacting atoms coupled to a single mode cavity --- to study such interaction effects. We show that interaction changes the phase boundary, and may even completely suppress the atom-photon coupling threshold for superradiance and change the universality class of the phase transition. We further study the dissipative phase transition and quantum dynamics in the presence of dissipation channels such as photon loss and spin relaxation. Our results demonstrate important roles played by the atom-atom interaction and how it can be engineered to control atom-photon coupling.

Figures

Figures reproduced from arXiv: 2608.12625 by the authors.

Figure 1
Figure 1. (d), while they are nearly maximally entangled in NP2. In the superradiance phase (SP), the atom-atom entanglement is intermediate between the two normal phases. In curious detail, in conventional superradiance systems, when crossing the phase boundary from NP to SP, the atomic excited state population increases. This is still the case crossing the boundary between NP1 and SP. However, going from NP2 to SP, the oppo… view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. (f) the trace distance DMM between the initial states (|t+, 0⟩ and |t−, 0⟩) and the MM at the given J/δ. One can see that in the entire parameter regime, |t+, 0⟩ has a very small DMM, meaning that it has a signifi￾cant weight in the MM. Hence, starting from |t+, 0⟩, one expects a slow relaxation on the time scale ∆−1 L . By con￾trast, near the degenerate point J/δ = 2, |t−, 0⟩ has a large DMM, indicating that it has… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

55 extracted references · 22 canonical work pages

  1. [1]

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

    1954

  2. [2]

    Hepp and E

    K. Hepp and E. H. Lieb, On the superradiant phase tran- sition for molecules in a quantized radiation field: The Dicke maser model, Ann. Phys. (N.Y.)76, 360 (1973)

    1973

  3. [3]

    Y. K. Wang and F. T. Hioe, Phase transition in the Dicke model of superradiance, Phys. Rev. A7, 831 (1973)

    1973

  4. [6]

    Dimer, B

    F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED sys- tem, Phys. Rev. A75, 013804 (2007)

    2007

  5. [7]

    E. G. D. Torre, S. Diehl, M. D. Lukin, S. Sachdev, and P. Strack, Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities, Phys. Rev. A87, 023831 (2013)

    2013

  6. [8]

    Hwang, P

    M.-J. Hwang, P. Rabl, and M. B. Plenio, Dissipative phase transition in the open quantum Rabi model, Phys. Rev. A97, 013825 (2018)

    2018

  7. [9]

    Baumann, C

    K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Dicke quantum phase transition with a superfluid gas in an optical cavity, Nature464, 1301 (2010)

    2010

  8. [10]

    Klinder, H

    J. Klinder, H. Keßler, M. R. Bakhtiari, M. Thorwart, and A. Hemmerich, Observation of a Superradiant Mott Insulator in the Dicke-Hubbard Model, Phys. Rev. Lett. 115, 230403 (2015)

    work page 2015

Show all 55 references
  1. [11]

    Zhiqiang, C

    Z. Zhiqiang, C. H. Lee, R. Kumar, K. J. Arnold, S. J. Masson, A. S. Parkins, and M. D. Barrett, Nonequilib- rium phase transition in a spin-1 Dicke model, Optica4, 424 (2017)

    2017

  2. [12]

    V. D. Vaidya, Y. Guo, R. M. Kroeze, K. E. Ballan- tine, A. J. Koll´ ar, J. Keeling, and B. L. Lev, Tunable- Range, Photon-Mediated Atomic Interactions in Multi- mode Cavity QED, Phys. Rev. X8, 011002 (2018)

    2018

  3. [13]

    Zhang, Y

    X. Zhang, Y. Chen, Z. Wu, J. Wang, J. Fan, S. Deng, and H. Wu, Observation of a superradiant quantum phase transition in an intracavity degenerate Fermi gas, Science 373, 1359 (2021)

    2021

  4. [14]

    J. A. Muniz, D. Barberena, R. J. Lewis-Swan, D. J. Young, J. R. K. Cline, A. M. Rey, and J. K. Thompson, Exploring dynamical phase transitions with cold atoms in an optical cavity, Nature580, 602 (2020)

    2020

  5. [15]

    Ferri, R

    F. Ferri, R. Rosa-Medina, F. Finger, N. Dogra, M. Sori- ente, O. Zilberberg, T. Donner, and T. Esslinger, Emerg- ing dissipative phases in a superradiant quantum gas with tunable decay, Phys. Rev. X11, 041046 (2021)

    2021

  6. [16]

    Zwettler, F

    T. Zwettler, F. Marijanovic, T. B¨ uhler, S. Chattopad- hyay, G. Del Pace, L. Skolc, V. Helson, S. Uchino, E. Demler, and J.-P. Brantut, Cavity-mediated charge and pair-density waves in a unitary Fermi gas, Nat. Com- mun.17, 496 (2026)

    2026

  7. [17]

    Safavi-Naini, R

    A. Safavi-Naini, R. J. Lewis-Swan, J. G. Bohnet, M. G¨ arttner, K. A. Gilmore, J. E. Jordan, J. Cohn, J. K. Freericks, A. M. Rey, and J. J. Bollinger, Verification of a many-ion simulator of the Dicke model through slow quenches across a phase transition, Phys. Rev. Lett.121, ...

    2018

  8. [18]

    Cai, Z.-D

    M.-L. Cai, Z.-D. Liu, W.-D. Zhao, Y.-K. Wu, Q.-X. Mei, Y. Jiang, L. He, X. Zhang, Z.-C. Zhou, and L.-M. Duan, 6 Observation of a quantum phase transition in the quan- tum Rabi model with a single trapped ion, Nat. Commun. 12, 1126 (2021)

    2021

  9. [19]

    D. Lv, S. An, Z. Liu, J.-N. Zhang, J. S. Pedernales, L. Lamata, E. Solano, and K. Kim, Quantum simula- tion of the quantum Rabi model in a trapped ion, Phys. Rev. X8, 021027 (2018)

    2018

  10. [20]

    Braum¨ uller, M

    J. Braum¨ uller, M. Marthaler, A. Schneider, A. Stehli, H. Rotzinger, M. Weides, and A. V. Ustinov, Analog quantum simulation of the Rabi model in the ultra-strong coupling regime, Nat. Commun.8, 779 (2017)

    2017

  11. [21]

    X. Chen, Z. Wu, M. Jiang, X.-Y. L¨ u, X. Peng, and J. Du, Experimental quantum simulation of superradiant phase transition beyond no-go theorem via antisqueezing, Nat. Commun.12, 6281 (2021)

    2021

  12. [22]

    Zheng, W

    R.-H. Zheng, W. Ning, Y.-H. Chen, J.-H. L¨ u, L.-T. Shen, K. Xu, Y.-R. Zhang, D. Xu, H. Li, Y. Xia, F. Wu, Z.- B. Yang, A. Miranowicz, N. Lambert, D. Zheng, H. Fan, F. Nori, and S.-B. Zheng, Observation of a superradiant phase transition with emergent cat states, Phys. Rev. Le...

    2023

  13. [23]

    R. Sett, F. Hassani, D. Phan, S. Barzanjeh, A. Vukics, and J. M. Fink, Emergent macroscopic bistability in- duced by a single superconducting qubit, PRX Quantum 5, 010327 (2024)

    2024

  14. [24]

    X. Li, M. Bamba, N. Yuan, Q. Zhang, Y. Zhao, M. Xiang, K. Xu, Z. Jin, W. Ren, G. Ma, S. Cao, D. Turchinovich, and J. Kono, Observation of Dicke cooperativity in mag- netic interactions, Science361, 794 (2018)

    2018

  15. [25]

    Marquez Peraca, X

    N. Marquez Peraca, X. Li, J. M. Moya, K. Hayashida, D. Kim, X. Ma, K. J. Neubauer, D. Fallas Padilla, C.-L. Huang, P. Dai, A. H. Nevidomskyy, H. Pu, E. Morosan, S. Cao, M. Bamba, and J. Kono, Quantum simulation of an extended Dicke model with a magnetic solid, Com- mun. Mater....

    2024

  16. [26]

    D. Kim, S. Dasgupta, X. Ma, J.-M. Park, H.-T. Wei, X. Li, L. Luo, J. Doumani, W. Yang, D. Cheng, R. H. J. Kim, H. O. Everitt, S. Kimura, H. Nojiri, J. Wang, S. Cao, M. Bamba, K. R. A. Hazzard, and J. Kono, Observation of the magnonic Dicke superradiant phase transition, Sci. A...

    2025

  17. [27]

    Gopalakrishnan, B

    S. Gopalakrishnan, B. L. Lev, and P. M. Goldbart, Frustration and glassiness in spin models with cavity- mediated interactions, Phys. Rev. Lett.107, 277201 (2011)

    2011

  18. [28]

    Strack and S

    P. Strack and S. Sachdev, Dicke quantum spin glass of atoms and photons, Phys. Rev. Lett.107, 277202 (2011)

    2011

  19. [29]

    Jaako, Z.-L

    T. Jaako, Z.-L. Xiang, J. J. Garcia-Ripoll, and P. Rabl, Ultrastrong-coupling phenomena beyond the Dicke model, Phys. Rev. A94, 033850 (2016)

    2016

  20. [30]

    Cortese, L

    E. Cortese, L. Garziano, and S. De Liberato, Polariton spectrum of the Dicke-Ising model, Phys. Rev. A96, 053861 (2017)

    2017

  21. [31]

    J. Rohn, M. H¨ ormann, C. Genes, and K. P. Schmidt, Ising model in a light-induced quantized transverse field, Phys. Rev. Research2, 023131 (2020)

    2020

  22. [32]

    J. P. Mendon¸ ca, K. Jachymski, and Y. Wang, Role of Matter Interactions in Superradiant Phenomena, Phys. Rev. Lett.135, 133601 (2025)

    2025

  23. [33]

    S. Sur, Y. Wang, M. Mahankali, S. Paschen, and Q. Si, Amplified response of cavity-coupled quantum-critical systems, Nat. Commun.17, 4404 (2026)

    2026

  24. [34]

    Z. Rao, X. Lin, X. Luo, G. Guo, H. Pu, and M. Gong, Unilateral criticality and phase transition in the cavity- Ising model (2025), arXiv:2509.04391 [quant-ph]

    2025 arXiv

  25. [35]

    Landig, L

    R. Landig, L. Hruby, N. Dogra, M. Landini, R. Mottl, T. Donner, and T. Esslinger, Quantum phases from com- peting short- and long-range interactions in an optical lattice, Nature532, 476 (2016)

    2016

  26. [36]

    Helson, T

    V. Helson, T. Zwettler, F. Mivehvar, E. Colella, K. Roux, H. Konishi, H. Ritsch, and J.-P. Brantut, Density-wave ordering in a unitary Fermi gas with photon-mediated interactions, Nature618, 716 (2023)

    2023

  27. [37]

    Landini, N

    M. Landini, N. Dogra, K. Kroeger, L. Hruby, T. Don- ner, and T. Esslinger, Formation of a Spin Texture in a Quantum Gas Coupled to a Cavity, Phys. Rev. Lett. 120, 223602 (2018)

    2018

  28. [38]

    E. J. Davis, G. Bentsen, L. Homeier, T. Li, and M. H. Schleier-Smith, Photon-Mediated Spin-Exchange Dynamics of Spin-1 Atoms, Phys. Rev. Lett.122, 010405 (2019)

    2019

  29. [39]

    Finger, R

    F. Finger, R. Rosa-Medina, N. Reiter, P. Christodoulou, T. Donner, and T. Esslinger, Spin- and momentum- correlated atom pairs mediated by photon exchange and seeded by vacuum fluctuations, Phys. Rev. Lett.132, 093402 (2024)

    2024

  30. [40]

    Zwettler, G

    T. Zwettler, G. Del Pace, F. Marijanovic, S. Chattopad- hyay, T. B¨ uhler, C.-M. Halati, L. Skolc, L. Tolle, V. Hel- son, G. Bolognini, A. Fabre, S. Uchino, T. Giamarchi, E. Demler, and J. P. Brantut, Nonequilibrium dynam- ics of long-range interacting fermions, Phys. Rev. X15...

    2025

  31. [41]

    Blais, A

    A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys.93, 025005 (2021)

    2021

  32. [42]

    Pita-Vidal, J

    M. Pita-Vidal, J. J. Wesdorp, L. J. Splitthoff, A. Barg- erbos, Y. Liu, L. P. Kouwenhoven, and C. K. Andersen, Strong tunable coupling between two distant supercon- ducting spin qubits, Nat. Phys.20, 1158 (2024)

    2024

  33. [43]

    Foss-Feig, G

    M. Foss-Feig, G. Pagano, A. C. Potter, and N. Y. Yao, Progress in trapped-ion quantum simulation, Annu. Rev. Condens. Matter Phys.16, 145 (2025)

    2025

  34. [44]

    See Supplemental Material for derivations of the closed- system critical boundaries and photon-number scal- ing, the dissipative phase boundaries under photon loss and local spin relaxation, the triplet-sector steady- state uniqueness and population distribution, the spin- pro...

  35. [45]

    W. K. Wootters, Entanglement of formation of an ar- bitrary state of two qubits, Phys. Rev. Lett.80, 2245 (1998)

    1998

  36. [46]

    Minganti, A

    F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Spec- tral theory of liouvillians for dissipative phase transitions, Phys. Rev. A98, 042118 (2018)

    2018

  37. [47]

    Macieszczak, M

    K. Macieszczak, M. Gut ¸˘ a, I. Lesanovsky, and J. P. Garra- han, Towards a theory of metastability in open quantum dynamics, Phys. Rev. Lett.116, 240404 (2016)

    2016

  38. [48]

    J. T. Barreiro, M. M¨ uller, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Hennrich, C. F. Roos, P. Zoller, and R. Blatt, An open-system quantum simulator with trapped ions, Nature470, 486 (2011)

    2011

  39. [50]

    Baumgartner, H

    B. Baumgartner, H. Narnhofer, and W. Thirring, Analy- sis of quantum semigroups with gks–lindblad generators. i. simple generators, J. Phys. A: Math. Theor.41, 065201 (2008). 7

    2008

  40. [51]

    Jurcevic, B

    P. Jurcevic, B. P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, and C. F. Roos, Quasiparticle engineering and entanglement propagation in a quantum many-body sys- tem, Nature511, 202 (2014)

    2014

  41. [52]

    Schlawin, D

    F. Schlawin, D. M. Kennes, and M. A. Sentef, Cavity quantum materials, Appl. Phys. Rev.9, 011312 (2022)

    2022

  42. [53]

    Forn-D´ ıaz, L

    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)

    2019

  43. [54]

    Two-atom Dicke model with atom-atom interaction

    A. Baydin, H. Zhu, M. Bamba, K. R. A. Hazzard, and J. Kono, Perspective on the quantum vacuum in matter, Opt. Mater. Express15, 1833 (2025). Supplemental Material for “Two-atom Dicke model with atom-atom interaction” Lin Jiao 1,∗ and Han Pu 1,† 1Department of Physics and Astro...

    2025

  44. [55]

    Emary and T

    C. Emary and T. Brandes, Quantum chaos triggered by precursors of a quantum phase transition: The Dicke model, Phys. Rev. Lett.90, 044101 (2003)

    2003

  45. [56]

    Hwang, R

    M.-J. Hwang, R. Puebla, and M. B. Plenio, Quantum Phase Transition and Universal Dynamics in the Rabi Model, Phys. Rev. Lett.115, 180404 (2015)

    2015

  46. [57]

    D. E. Evans, Irreducible quantum dynamical semigroups, Commun. Math. Phys.54, 293 (1977)

    1977

  47. [58]

    Baumgartner, H

    B. Baumgartner, H. Narnhofer, and W. Thirring, Analysis of quantum semigroups with gks–lindblad generators. i. simple generators, J. Phys. A: Math. Theor.41, 065201 (2008)

    2008

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.