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Approaching Carnot Efficiency at Finite Power in an Experimentally Feasible Quantum Heat Engine

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Pith's one-line read Quantum heat engine hits Carnot efficiency without losing power

desk verdict Concrete circuit-QED proposal for Carnot-at-finite-power; analytical framework is sound but numerical verification stops well short of the asymptotic regime read the letter →

arxiv 2607.08713 v1 pith:RKPFNJLV submitted 2026-07-09 quant-ph cond-mat.stat-mech

Shogo Toma , Atsushi Noguchi , Ken Funo , Hiroyasu Tajima This is my paper · ORCID
classification quant-phcond-mat.stat-mech
keywords heatcarnotefficiencyenginefinitepowerapproachasymptotic
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

A fundamental tension in thermodynamics is that the most efficient heat engine — the Carnot cycle — produces zero power, because it must run infinitely slowly. For classical engines governed by local Markovian dynamics, a proven trade-off (the Shiraishi–Saito–Tasaki bound) forbids even an asymptotic approach to Carnot efficiency at finite power: the bound ties power to a quantity called activity, which scales only linearly with system size, making Carnot efficiency and finite power mathematically incompatible. This paper proposes a superconducting-circuit heat engine that breaks through that barrier by exploiting a quantum dissipative mechanism called the coupler-assisted swap (CAS), in which a driven qubit mediates the exchange of c photons between two cavity modes. The CAS process generates an effective jump operator L_c = (a†_1)^c (a_2)^c whose activity scales as O(N^c) rather than O(N), where N is the total photon number serving as the effective system size. For CAS-2 (c=2), the activity scales as O(N²), which the trade-off bound permits to coexist with efficiency approaching Carnot as η = η_C − O(1/N) at power P = O(N). The authors construct an explicit two-stroke engine cycle, derive the scaling analytically from an effective master equation, and verify it numerically by integrating the full microscopic master equation for N = 2 through 15 using experimentally realistic superconducting-circuit parameters. The numerical data confirm both the O(N) power scaling and the O(1/N) efficiency gap. The key insight is that the CAS architecture natively realizes the collective enhancement previously studied only in abstract symmetric many-qubit models: the fixed-N two-mode bosonic Hilbert space maps onto the symmetric subspace of N spin-1/2 particles (the Dicke ladder), where multi-photon transitions acquire superradiant matrix elements scaling as N^c, but without requiring N physical qubits or engineered nonlocal dissipators.

What carries the argument

The central object is the CAS-c jump operator L_c = (a†_1)^c (a_2)^c, which exchanges c photons between two cavity modes via a driven qubit. In the Schwinger-boson representation, the fixed-total-photon-number two-mode space maps onto the fully symmetric Dicke ladder of N spin-1/2 particles, and L_c maps to (S_-)^c, a c-body collective lowering operator. The activity A(t), defined as the sum of squared energy transfers weighted by jump rates, scales as O(N^c) near thermal equilibrium because the collective matrix elements of (S_±)^c within the symmetric subspace grow as N^c. The Shiraishi–Saito–Tasaki bound P ≤ β_L η(η_C − η) Ā then permits η_C − η = O(N^{1−c}) at P = O(N) whenever c ≥ 2. A

What would settle it

Direct numerical integration of the full microscopic master equation (before the Schrieffer–Wolff and Born–Markov reductions) for increasing N would falsify the scaling if the power ceases to grow linearly or the efficiency gap ceases to shrink as 1/N, indicating that non-resonant processes or photon loss outside the hierarchical window degrade performance before the asymptotic regime is reached. Experimental realization in a superconducting-circuit device would falsify the claim if the measured efficiency and power fail to follow the predicted scalings within the stated parameter regime.

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Extended reading notes

Core claim

The coupler-assisted swap mechanism in a superconducting-circuit architecture — two cavity modes coupled through a driven qubit and a Purcell filter — natively produces an effective collective jump operator whose activity scales superlinearly (as O(N^c) for the CAS-c process), enabling an engine that approaches Carnot efficiency as η_C − O(1/N) while maintaining finite power O(N), thereby circumventing the power-efficiency trade-off that is provably inescapable for classical Markovian engines. This is the first concrete, experimentally implementable platform to realize the collective-enhancement route to Carnot efficiency at finite power.

Load-bearing premise

The claimed scaling holds only within a hierarchical parameter window where photon loss is negligible relative to the CAS process and the Markov approximation underlying the effective description remains valid. The middle term in this hierarchy grows as N^{c/2}, so the available window narrows as the system scales up. The numerical verification reaches only N = 15, leaving open whether the hierarchy survives for the large N needed to make the efficiency gap meaningfully small

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Editorial analysis

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

Referee Report

2 major / 6 minor

Summary. This Letter proposes a superconducting-circuit quantum heat engine that exploits a coupler-assisted swap (CAS) mechanism to emulate collective dissipation, thereby enhancing the thermodynamic activity beyond the linear scaling that constrains classical Markovian engines. The authors show analytically that for the CAS-2 process, the activity scales as $O(N^2)$ with the conserved total photon number $N$, permitting $eta = eta_C - O(1/N)$ at finite power $P = O(N)$ within the effective GKSL description. They verify the predicted scalings by direct numerical integration of the full master equation [Eq. (4)] for $N = 2, ldots, 15$ using experimentally realistic circuit-QED parameters. The work bridges abstract finite-time thermodynamic bounds and a concrete experimental platform, which is a valuable contribution.

Significance. The paper addresses a well-known open question: whether the quantum advantage in evading the power-efficiency trade-off (predicted in Refs. [7,8]) can be realized in an experimentally implementable system. The proposal to use the CAS mechanism in superconducting circuits to simulate collective jump operators without requiring $N$ physical qubits or engineered nonlocal dissipators is a genuinely creative solution. The analytical derivation from the full master equation through Schrieffer-Wolff and Nakajima-Zwanzig projections is detailed and internally consistent, with clearly stated approximations. The numerical verification against the full master equation (not just the effective description) for small $N$ adds credibility. The connection to Dicke superradiance via the Schwinger-boson mapping (End Matter) provides useful physical insight. The falsifiable prediction of specific scaling laws ($P propto N$, $eta_C - eta propto 1/N$) in a concrete parameter regime is a strength.

major comments (2)
  1. The hierarchical regime [Eq. (9)] is load-bearing for the central claim, since the effective CAS description [Eq. (8)] and hence the scaling $eta = eta_C - O(1/N)$, $P = O(N)$ are guaranteed only within this window. The middle term of the left inequality scales as $N^{c/2} = N$ for $c=2$, while the upper bound $g_f^2/kappa$ is $N$-independent (since $g_f, kappa, g_{1,2}, Omega, omega_{1,2}$ are held fixed per the protocol description). The paper does not explicitly verify that the optimized parameters used in Fig. 3 satisfy Eq. (9) at each $N$, nor does it estimate the maximum $N$ for which the hierarchy survives with the footnote-40 parameters. A rough estimate using those parameters suggests the right inequality breaks down around $N sim 250$, which is well beyond $N=15$ but still finite. The authors should (i) explicitly check and report whether the parameters of Fig. 3 satisfy Eq. (9
  2. Supplemental Material Sec. V and Figs. S1(a,b) reveal that at $N=15$, the full dynamics exhibits slow drift between superselection sectors, requiring a post-hoc projection onto the initial sector to obtain a closed thermodynamic cycle. While the projected dynamics is shown to be thermodynamically consistent [Figs. S1(c,d)], the physical engine would experience this inter-sector leakage. The paper should discuss the physical origin of this drift, its timescale relative to the engine cycle, and whether it constitutes a fundamental limitation or a numerical artifact of the truncation. If the drift reflects a real physical process (e.g., higher-order non-resonant terms that break the photon-number conservation), it could undermine the scaling claim at large $N$ and should be addressed. The current text mentions it only in a footnote [35] and the SM, without assessing its impact on the asympt
minor comments (6)
  1. The temperature difference $T_H - T_L = 1$ mK (footnote 40) is extremely small relative to the qubit frequencies ($omega_q/2pi sim 5$ GHz, corresponding to $sim 240$ mK). While this is necessary to approach Carnot efficiency, it would help to comment on whether such fine temperature control is experimentally realistic, or whether this is an idealization that limits the practical relevance of the parameter regime.
  2. In Eq. (16), the activity $A(t)$ involves $omega_q(t)^2$ in the prefactor. Since $omega_q$ is $N$-dependent (tuned as the engine scales), the claim that $A = O(N^c)$ near the steady state should specify that this $N$-dependence of $omega_q$ does not alter the scaling, or the $O(N^c)$ should be stated more precisely.
  3. The statement below Eq. (7) that dispersive terms proportional to $a_i^dagger a_i sigma_z$ cancel by choosing $g_1$ and $g_2$ appropriately is important for the effective description. It would help to state the specific condition on $g_1/g_2$ or cross-reference the SM derivation (Eq. S26) where $chi_1 = chi_2$ is imposed.
  4. Fig. 3 caption states that all parameters are 'optimized to maximize the performance of the full master equation.' It would improve reproducibility to state the optimization method and whether the optimized parameters remain within the hierarchical window [Eq. (9)] for each $N$.
  5. The efficiency $eta$ is stated as fixed by the choice of $omega_{qnu}$ [Eq. (14)], which makes it exact by construction rather than a result of the dynamics. While this is legitimate (the heat ratio is determined by the photon transfer which is symmetric), it would be worth clarifying that the $O(1/N)$ correction arises from the relation $beta_L omega_{qL} - beta_H omega_{qH} = O(1/N)$, not from Eq. (14) itself, to avoid confusion about whether the efficiency formula is accurate at finite $N$.
  6. In the End Matter, the mapping to the Dicke ladder via Schwinger bosons is a nice insight. The statement that $(S^pm)^c$ are '$c$-body nonlocal operators whose direct implementation as dissipators is generally infeasible' could cite specific prior work that has attempted or discussed such implementations, to strengthen the claim that CAS provides a genuine advantage over what is already stated.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; self-citations to Refs. [7,8] provide theoretical motivation but the key derivation steps are independently re-derived and numerically verified.

full rationale

The paper's central claim—η = η_C − O(1/N) at finite power P = O(N)—rests on a derivation chain that is substantially self-contained. (1) The SST trade-off bound [Eq. (1)] comes from Refs. [5,6] (Shiraishi, Saito, Tasaki—external authors). (2) The quantum extension showing that enhanced activity can evade this bound is from Refs. [7,8] (Tajima, Funo—co-authors), but the present paper does not treat this as a black box: it explicitly re-derives the O(N^c) activity scaling via the Schwinger-boson/Dicke-ladder mapping [Eqs. (19)–(20)] and reviews the bound derivation in Supp. Mat. Sec. I [Eqs. (S5)–(S7)]. (3) The efficiency η ≈ 1 − ω_{qL}/ω_{qH} [Eq. (14)] is derived from the CAS heat-current definitions [Eqs. (10)–(13)], not fitted. The approach to Carnot is by parameter choice (tuning ω_{qL}), which is standard engine design, not circularity—the non-trivial claim is that finite power survives this tuning, which requires the O(N²) activity scaling. (4) The power scaling P = O(N) [Eq. (18)] follows from the derived relaxation rate Γ_ν = 2N²(γ_{2→1} + 3γ_{1→2}) and is independently verified by numerical integration of the full master equation [Eq. (4)] for N = 2,…,15 (Fig. 3), not the effective description. (5) Heat and work definitions are cross-checked against the underlying unitary dynamics [Supp. Mat. Sec. III, Eqs. (S74)–(S88)]. The self-citations to [7,8] are motivational/framework-setting rather than load-bearing: the specific CAS architecture, its effective description, the scaling analysis, and the numerical verification are all carried out in this paper. No step reduces to its inputs by construction.

Assumptions & free parameters 4 free parameters · 4 assumptions · 1 invented entities

The axiom ledger is moderate. The free parameters δ and ε are fixed constants, not fitted. The N-dependent parameter optimization is a form of fitting but is applied consistently to both full and effective models. The key axioms (Markov approximation, negligible decoherence, bosonic fluctuation relation) are standard domain assumptions whose validity is discussed but not rigorously bounded for the parameter regime used.

free parameters (4)
  • δ = 0.3
    Cycle parameter controlling oscillation amplitude of ⟨n₂⟩ between n₂⁻ and n₂⁺ [Eq. (17)], chosen N-independent and fixed.
  • ε = 0.001
    Controls the gap between hot and cold steady states via ⟨n₂⟩ss,L = ⟨n₂⟩ss,H − ε/N. Fixed constant, not fitted to data.
  • N-dependent ω_qL, ω_dν, τ_ν = optimized per N
    Stated as 'optimized to maximize performance of the full master equation' [Fig. 3 caption]. These are tuned per data point, which is a form of fitting.
  • Cavity/qubit/filter parameters = ω₁/2π=3 GHz, ω₂/2π=3.8 GHz, etc.
    Fixed physical parameters chosen within state-of-the-art ranges [40]. Not free in the theoretical sense but represent a specific design choice.
assumptions (4)
  • domain assumption Markovian bath assumption for the Purcell filter environment
    The filter cavity is assumed coupled to a Markovian bath [Eq. (4)], and the Born-Markov approximation is used to eliminate the qubit+filter [Supp. Mat. II.E]. Validity requires τ_s⁻¹ ≪ γ_P.
  • domain assumption Negligible intrinsic relaxation and dephasing of cavities and qubit
    Stated below Eq. (5): 'we neglect the intrinsic relaxation and dephasing... assuming the engine cycle is completed on a timescale much shorter than the corresponding coherence times.' This is load-bearing for the effective description.
  • domain assumption Bosonic fluctuation relation ⟨n₂²⟩ ≈ 2⟨n₂⟩ + 2⟨n₂⟩² near Gibbs steady state
    Used in Supp. Mat. IV to close the rate equation and derive exponential relaxation. Exact at Gibbs state, approximate nearby; the quality of this approximation for finite N is not bounded.
  • standard math Schrieffer-Wolff expansion converges in the dispersive regime
    The perturbative expansion in g_{1,2}/Δω and Ω/Δω [Eq. (5)] is assumed controlled. Higher-order terms are dropped at O(λ⁴) or O(λ⁶).
invented entities (1)
  • CAS-c effective jump operator L_c = (a₁†)^c (a₂)^c independent evidence
    purpose: Emulates collective (S₋)^c jump in the Dicke ladder using two cavity modes, enabling O(N^c) activity scaling without N physical qubits.
    The CAS mechanism has been experimentally demonstrated in circuit-QED [Refs. 18-22]. The mapping to Dicke superradiance is shown in the End Matter. The jump operator is derived, not postulated.

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Pith. "Pith review of Approaching Carnot Efficiency at Finite Power in an Experimentally Feasible Quantum Heat Engine." pith.science (2026). https://pith.science/paper/RKPFNJLV

@misc{pith2026260708713,
  author       = {Pith},
  title        = {Pith review of: Approaching Carnot Efficiency at Finite Power in an Experimentally Feasible Quantum Heat Engine},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RKPFNJLV}},
  note         = {Machine review of arXiv:2607.08713}
}
read the original abstract

Whether a heat engine can approach Carnot efficiency while maintaining finite power is a fundamental question in finite-time thermodynamics. For classical Markovian heat engines with local interactions, the power-efficiency trade-off forbids an asymptotic approach to Carnot efficiency at finite power. In quantum systems, by contrast, degeneracy, symmetry, and collective jumps have been theoretically predicted to enable such an asymptotic attainment by enhancing activity. It has remained open, however, whether this mechanism can be realized in an experimentally implementable heat engine. In this Letter, we propose a superconducting-circuit heat engine that emulates the collective enhancement, thereby enabling an asymptotic approach to Carnot efficiency at finite power. This result demonstrates that, in an implementable model, such an enhanced dissipative mechanism circumvents the power-efficiency trade-off of classical Markovian engines. Our work connects abstract bounds in finite-time thermodynamics to a concrete circuit-QED platform and suggests a route toward quantum-device design based on collectively enhanced dissipative processes.

Figures

Figures reproduced from arXiv: 2607.08713 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic illustration of the experimental setup. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Two-stroke cycle of the CAS-2 engine. (a) Di [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Numerical calculations of the CAS-2 engine perfor [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Works this paper leans on

44 extracted references · 44 canonical work pages

  1. [35]

    V for further numerical details

    More precisely, the cycle closes strictly only after the den- sity matrix is projected onto the superselection sector of fixed total photon numberNand even parity ofn 2; see the Supplemental Material Sec. V for further numerical details

    work page

  2. [1]

    Carnot,Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power(Bachelier, Paris, 1824)

    S. Carnot,Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power(Bachelier, Paris, 1824)

    work page

  3. [2]

    H. B. Callen,Thermodynamics and an Introduction to Thermostatistics, 2nd ed. (John Wiley & Sons, New York, 1985)

    work page 1985

  4. [3]

    F. L. Curzon and B. Ahlborn, Am. J. Phys.43, 22 (1975)

    work page 1975

  5. [4]

    Esposito, R

    M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, Phys. Rev. Lett.105, 150603 (2010)

    work page 2010

  6. [5]

    Shiraishi, K

    N. Shiraishi, K. Saito, and H. Tasaki, Phys. Rev. Lett. 117, 190601 (2016)

    work page 2016

  7. [6]

    Shiraishi and K

    N. Shiraishi and K. Saito, J. Stat. Phys.174, 433 (2019)

    work page 2019

  8. [7]

    Tajima and K

    H. Tajima and K. Funo, Phys. Rev. Lett.127, 190604 (2021)

    work page 2021

Show all 44 references
  1. [8]

    Funo and H

    K. Funo and H. Tajima, Phys. Rev. Lett.134, 080401 (2025)

    2025

  2. [9]

    Uusn¨ akki, T

    T. Uusn¨ akki, T. M¨ orstedt, W. Teixeira, M. Rasola, and M. M¨ ott¨ onen, Nat. Commun. (2026), 10.1038/s41467- 026-72651-x

    2026 doi

  3. [10]

    Roßnagel, S

    J. Roßnagel, S. T. Dawkins, K. N. Tolazzi, O. Abah, E. Lutz, F. Schmidt-Kaler, and K. Singer, Science352, 325 (2016)

    2016

  4. [11]

    von Lindenfels, O

    D. von Lindenfels, O. Gr¨ ab, C. T. Schmiegelow, V. Kaushal, J. Schulz, M. T. Mitchison, J. Goold, F. Schmidt-Kaler, and U. G. Poschinger, Phys. Rev. Lett. 123, 080602 (2019)

    2019

  5. [12]

    Van Horne, D

    N. Van Horne, D. Yum, T. Dutta, P. H¨ anggi, J. Gong, D. Poletti, and M. Mukherjee, npj Quantum Inf.6, 37 (2020)

    2020

  6. [13]

    J. P. S. Peterson, T. B. Batalh˜ ao, M. Herrera, A. M. Souza, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, Phys. Rev. Lett.123, 240601 (2019)

    2019

  7. [14]

    R. J. de Assis, T. M. de Mendon¸ ca, C. J. Villas-Boas, A. M. de Souza, R. S. Sarthour, I. S. Oliveira, and N. G. de Almeida, Phys. Rev. Lett.122, 240602 (2019)

    2019

  8. [15]

    Klatzow, J

    J. Klatzow, J. N. Becker, P. M. Ledingham, C. Weinzetl, K. T. Kaczmarek, D. J. Saunders, J. Nunn, I. A. Walms- ley, R. Uzdin, and E. Poem, Phys. Rev. Lett.122, 110601 (2019)

    2019

  9. [16]

    Kim, S.-h

    J. Kim, S.-h. Oh, D. Yang, J. Kim, M. Lee, and K. An, Nat. Photonics16, 707 (2022)

    2022

  10. [17]

    Bouton, J

    Q. Bouton, J. Nettersheim, S. Burgardt, D. Adam, E. Lutz, and A. Widera, Nat. Commun.12, 2063 (2021)

  11. [18]

    Shirai, Y

    S. Shirai, Y. Okubo, K. Matsuura, A. Osada, Y. Naka- mura, and A. Noguchi, Phys. Rev. Lett.130, 260601 (2023)

    2023

  12. [19]

    Balembois, J

    L. Balembois, J. Travesedo, L. Pallegoix, A. May, E. Bil- laud, M. Villiers, D. Est` eve, D. Vion, P. Bertet, and E. Flurin, Phys. Rev. Appl.21, 014043 (2024)

    2024

  13. [20]

    Y. Y. Gao, B. J. Lester, Y. Zhang, C. Wang, S. Rosen- blum, L. Frunzio, L. Jiang, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. X8, 021073 (2018)

    2018

  14. [21]

    Y. Y. Gao, B. J. Lester, K. S. Chou, L. Frunzio, M. H. Devoret, L. Jiang, S. M. Girvin, and R. J. Schoelkopf, Nature566, 509 (2019)

    2019

  15. [22]

    Lescanne, S

    R. Lescanne, S. Del´ eglise, E. Albertinale, U. R´ eglade, T. Capelle, E. Ivanov, T. Jacqmin, Z. Leghtas, and E. Flurin, Phys. Rev. X10, 021038 (2020). 6

    2020

  16. [23]

    Throughout this work, the subscripts 1 and 2 refer to cavities 1 and 2,qto the qubit, andfto the Purcell filter

  17. [24]

    E. M. Purcell, Phys. Rev.69, 681 (1946)

    1946

  18. [25]

    E. A. Sete, J. M. Martinis, and A. N. Korotkov, Phys. Rev. A92, 012325 (2015)

    2015

  19. [26]

    Gorini, A

    V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, J. Math. Phys.17, 821 (1976)

    1976

  20. [27]

    Lindblad, Commun

    G. Lindblad, Commun. Math. Phys.48, 119 (1976)

    1976

  21. [28]

    More precisely, ∆ωdenotes the typical magnitude of the detunings appearing in the leading non-resonant pro- cesses of the Schrieffer–Wolff expansion

  22. [29]

    J. R. Schrieffer and P. A. Wolff, Phys. Rev.149, 491 (1966)

    1966

  23. [30]

    Nakajima, Prog

    S. Nakajima, Prog. Theor. Phys.20, 948 (1958)

    1958

  24. [31]

    Zwanzig, J

    R. Zwanzig, J. Chem. Phys.33, 1338 (1960)

    1960

  25. [32]

    Spohn, J

    H. Spohn, J. Math. Phys.19, 1227 (1978)

    1978

  26. [33]

    Esposito, K

    M. Esposito, K. Lindenberg, and C. Van den Broeck, New J. Phys.12, 013013 (2010)

    2010

  27. [34]

    TheseN-dependent parameters converge to finite values asN→ ∞, because their dependence onNenters only throughω qL = (βH /βL)ωqH +O(1/N)

  28. [36]

    Since the relaxation dynamics is not purely exponential, we chooseτ ν such that the engine cycle operates between n2− andn 2+

  29. [37]

    Krantz, M

    P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gus- tavsson, and W. D. Oliver, Applied Physics Reviews6, 021318 (2019)

    2019

  30. [38]

    Tominaga, S

    Y. Tominaga, S. Shirai, Y. Hishida, H. Terai, and A. Noguchi, (2025), 10.48550/arXiv.2502.17901, 2502.17901 [quant-ph]

    2025 doi arXiv

  31. [39]

    Somoroff, Q

    A. Somoroff, Q. Ficheux, R. A. Mencia, H. Xiong, R. Kuzmin, and V. E. Manucharyan, Phys. Rev. Lett. 130, 267001 (2023)

    2023

  32. [40]

    All other parameters are optimized so that the power is maximized

    Parameters:ω 1/2π= 3 GHz,ω 2/2π= 3.8 GHz, ωqH /2π= 5 GHz,ω qL/2π= 4.9 GHz (N→ ∞), g1/2π= 50 MHz,g 2/2π≈38 MHz,g f /2π= 300 kHz, Ω/2π= 100 MHz,κ/2π= 1 MHz,T H ≡(k BβH)−1 = 50 mK,T L ≡(k BβL)−1 = 49 mK,δ= 0.3,ϵ= 0.001. All other parameters are optimized so that the power is maximized

  33. [41]

    R. H. Dicke, Phys. Rev.93, 99 (1954)

    1954

  34. [42]

    R. M. Wilcox, J. Math. Phys.8, 962 (1967)

    1967

  35. [43]

    Lindblad, Commun

    G. Lindblad, Commun. Math. Phys.40, 147 (1975)

    1975

  36. [44]

    Uhlmann, Commun

    A. Uhlmann, Commun. Math. Phys.54, 21 (1977). End Matter CAS as superradiance on the Dicke ladder.—The O(N c) scaling of the activity has a transparent origin in a hidden superradiance structure of the CAS dynamics. The Schwinger-boson representation S− =a † 1a2, S z = (n2 −n ...

    1977

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