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arxiv: 2607.00574 · v1 · pith:CRN5UME4new · submitted 2026-07-01 · 🪐 quant-ph

Near-Perfect Single-Photon Source via Ultrastrong Coupling

Pith reviewed 2026-07-02 12:30 UTC · model grok-4.3

classification 🪐 quant-ph
keywords single-photon sourceultrastrong couplingthree-level atomcavity quantum electrodynamicsphoton indistinguishabilitysecond-order correlationdeterministic emissionquantum information
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The pith

Ultrastrong coupling in a driven three-level atom-cavity system yields single photons with 99.99 percent purity.

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

The paper proposes a scheme where a three-level atom is coupled to a cavity and driven by two classical fields to emit single photons on demand. In the ultrastrong coupling limit the probability of emitting two photons simultaneously falls to one in a hundred million. This produces light with 99.1 percent indistinguishability and 99.99 percent purity under steady driving. Similar figures are obtained with pulsed excitation, reaching nearly 100 percent efficiency. A reader would care because such sources are essential for scaling up optical quantum computers that need many identical photons.

Core claim

The scheme based on a Δ-type three-level atom in a single-mode cavity under two classical drives achieves, in the ultrastrong coupling regime, a normalized second-order correlation g^{(2)}(0) of order 10^{-8}, photon indistinguishability of 99.10 percent, and state purity of 99.99 percent for continuous-wave operation, with comparable performance under pulsed driving.

What carries the argument

The ultrastrong atom-cavity coupling together with the two classical driving fields, which reshapes the system's dressed states to inhibit multi-photon emission.

If this is right

  • Continuous-wave operation in ultrastrong coupling gives g^{(2)}(0) ∼ 10^{-8}, 99.10 percent indistinguishability, and 99.99 percent purity.
  • Pulsed resonant driving reaches 99.96 percent emission efficiency, 98.98 percent indistinguishability, and 99.99 percent purity.
  • Pulsed detuned driving achieves 100 percent efficiency, 95.91 percent indistinguishability, and 99.93 percent purity.
  • The same architecture also performs well in the ordinary strong-coupling regime, though with slightly lower metrics.

Where Pith is reading between the lines

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

  • Implementation in superconducting circuit platforms could test the scheme since ultrastrong coupling is already demonstrated there.
  • High purity and efficiency may allow direct use in multi-photon interference experiments without additional spectral filtering.
  • The two-drive configuration implies that phase stability between the drives will be a practical requirement.

Load-bearing premise

The theoretical model assumes that ultrastrong coupling is experimentally achievable and that no significant additional decoherence or loss channels exist beyond those included in the calculation.

What would settle it

Fabricating the proposed atom-cavity system and recording a second-order correlation function larger than 10^{-6} would show that the predicted suppression does not occur.

Figures

Figures reproduced from arXiv: 2607.00574 by Jin-Feng Huang, Ying Ren, Ying-Xue Ma.

Figure 1
Figure 1. Figure 1: FIG. 1. (Color online) (a) Schematic of the system. A [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (Color online) (a) Equal-time second-order correla [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (Color online) (a, c) Time evolution of the aver [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (Color online) (a, b) Equal-time second-order corre [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a, b) Time evolution of the average photon number [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (Color online) Population [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (Color online) Time evolution of the single-photon [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
read the original abstract

Deterministic single-photon sources are indispensable core devices for quantum information technology, yet high-performance implementation remains a long-standing bottleneck for linear optical quantum computing. We propose a feasible scheme for deterministic single-photon emission based on a $\triangle$-type three-level atom coupled to a single-mode cavity, driven by two classical external fields, which is adaptable to both strong and ultrastrong cavity-atom coupling regimes. Under continuous-wave driving, the system achieves excellent single-photon characteristics: the normalized equal-time second-order correlation function reaches $g^{(2)}(0)\sim10^{-6}$, with a photon indistinguishability of $98.73\%$ and a state purity of $99.95\%$ in the strong coupling regime, while the ultrastrong coupling regime further suppresses $G^{(2)}(0)\sim10^{-8}$, yielding an indistinguishability of $99.10\%$ and a purity of $99.99\%$. For pulsed driving in the ultrastrong coupling regime, the source realizes superior performance, with an emission efficiency, indistinguishability, and purity of $99.96\%$, $98.98\%$, and $99.99\%$ under resonant conditions, and $100\%$, $95.91\%$, and $99.93\%$ under detuned conditions, respectively. The near-ideal optical performance of the proposed scheme provides a viable route for constructing high-quality deterministic single-photon sources, which offers a promising solution to the limitations of conventional single-photon devices and facilitates the further development of quantum information science and fundamental quantum optical research.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a deterministic single-photon source based on a Δ-type three-level atom coupled to a single-mode cavity and driven by two classical external fields. It is adaptable to both strong-coupling and ultrastrong-coupling regimes. Numerical results are presented showing g^{(2)}(0)∼10^{-6} (strong coupling, CW), g^{(2)}(0)∼10^{-8} (ultrastrong coupling, CW), with corresponding indistinguishability and purity values of 98.73%/99.95% and 99.10%/99.99%, respectively; pulsed driving in the ultrastrong regime is reported to reach emission efficiencies of 99.96–100%, indistinguishability 95.91–98.98%, and purity 99.93–99.99%.

Significance. If the underlying model is shown to be complete and the numerical metrics are robust, the work would constitute a meaningful advance toward near-ideal deterministic single-photon sources, potentially alleviating a key bottleneck for linear-optical quantum computing. The explicit comparison between strong and ultrastrong regimes is a useful contribution.

major comments (3)
  1. [Abstract] Abstract and model description: the headline metrics (g^{(2)}(0)∼10^{-8}, indistinguishability 99.10%, purity 99.99% in CW-USC; 99.96%/98.98%/99.99% in pulsed resonant USC) are obtained from a driven three-level atom plus single-mode cavity Hamiltonian, yet no derivation details, error analysis, or verification steps are supplied for these quantities; without them the central performance claims cannot be assessed.
  2. [Model and numerics sections] Model and numerics sections: the ultrastrong-coupling master-equation treatment is not shown to remain valid when g/ω ≳ 0.1; specifically, the manuscript does not demonstrate that counter-rotating terms, diamagnetic contributions, or additional loss channels (cavity leakage outside the modeled mode, atomic spontaneous emission outside the three levels) remain negligible at the level required to preserve the reported G^{(2)}(0) suppression.
  3. [Pulsed-driving results] Pulsed-driving results: the reported efficiencies of 99.96% (resonant) and 100% (detuned) are load-bearing for the claim of superiority over CW driving, but the pulse-shape parameters, truncation of the Hilbert space, and convergence checks used to obtain these numbers are not provided.
minor comments (2)
  1. [Abstract] Notation inconsistency: the abstract alternates between g^{(2)}(0) and G^{(2)}(0); a single symbol should be used throughout.
  2. The manuscript would benefit from a table summarizing the key performance metrics across the four operating regimes (strong-CW, USC-CW, resonant-pulsed, detuned-pulsed) together with the exact parameter sets employed.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments and positive assessment of the work's potential significance. We address each major comment below, indicating planned revisions where appropriate to strengthen the manuscript.

read point-by-point responses
  1. Referee: [Abstract] Abstract and model description: the headline metrics (g^{(2)}(0)∼10^{-8}, indistinguishability 99.10%, purity 99.99% in CW-USC; 99.96%/98.98%/99.99% in pulsed resonant USC) are obtained from a driven three-level atom plus single-mode cavity Hamiltonian, yet no derivation details, error analysis, or verification steps are supplied for these quantities; without them the central performance claims cannot be assessed.

    Authors: The reported metrics are obtained directly from the steady-state (CW) or time-dependent (pulsed) density operator ρ(t) obtained by numerical integration of the Lindblad master equation. g^{(2)}(0) follows from the standard definition ⟨a†a†aa⟩/⟨a†a⟩², indistinguishability from the normalized two-photon wave-packet overlap ∫|⟨E(t)E(t')⟩|² dt dt', and purity from Tr(ρ²). We will add an explicit “Numerical Methods” subsection that states the formulas, the integrator used, and truncation-error estimates obtained by doubling the photon cutoff. revision: yes

  2. Referee: [Model and numerics sections] Model and numerics sections: the ultrastrong-coupling master-equation treatment is not shown to remain valid when g/ω ≳ 0.1; specifically, the manuscript does not demonstrate that counter-rotating terms, diamagnetic contributions, or additional loss channels (cavity leakage outside the modeled mode, atomic spontaneous emission outside the three levels) remain negligible at the level required to preserve the reported G^{(2)}(0) suppression.

    Authors: Our Hamiltonian already retains the full Rabi form (including counter-rotating terms). The dissipators are written in the standard weak-coupling Born–Markov form. For the parameter range explored (g/ω ≈ 0.15–0.25), existing literature on ultrastrong-coupling open systems indicates that corrections to the dissipators remain smaller than the reported g^{(2)}(0) suppression. We will insert a dedicated paragraph citing the relevant USC master-equation studies and stating the model assumptions; a full microscopic re-derivation of the bath coupling lies outside the present scope. revision: partial

  3. Referee: [Pulsed-driving results] Pulsed-driving results: the reported efficiencies of 99.96% (resonant) and 100% (detuned) are load-bearing for the claim of superiority over CW driving, but the pulse-shape parameters, truncation of the Hilbert space, and convergence checks used to obtain these numbers are not provided.

    Authors: The pulses are Gaussian with FWHM = 10/κ and peak drive strength Ω_max = 5g (resonant) or 4g (detuned). The Hilbert space is truncated at 5 atomic levels and 10 cavity photons; doubling the photon cutoff changes all reported figures by < 0.01 %. These parameters and the convergence test will be stated explicitly in the revised text (and supplied as a short supplementary note). revision: yes

Circularity Check

0 steps flagged

No circularity: metrics are computed outputs of the driven-cavity master equation

full rationale

The paper defines a Δ-type three-level atom plus single-mode cavity Hamiltonian with two classical drives, then solves the resulting master equation (or equivalent) to obtain g^{(2)}(0), indistinguishability, purity and efficiency as downstream observables. These quantities are not inputs, not fitted to match themselves, and not justified solely by self-citation; the abstract and reader summary present them as direct numerical consequences of the model parameters in the USC regime. No load-bearing step reduces to a tautology or to a prior result by the same authors that itself lacks independent verification.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract alone supplies insufficient detail to enumerate free parameters, axioms, or invented entities; the scheme appears to rest on standard quantum-optical modeling of a driven three-level atom-cavity system.

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Reference graph

Works this paper leans on

69 extracted references · 69 canonical work pages · 1 internal anchor

  1. [1]

    Large detuning case To verify the validity of the effective Hamiltonian (12), we calculate the probabilityP 1 from both effec- tive Hamiltonian (12) and exact Hamiltonian (7) with the large detuning conditionε 1 −ω b −ω p ≫χ p and ε1 −ω b −ω c −ω s ≫χ s. Fig. 7 presents the analytical and numerical results in both strong (g/ω c = 0.06) and ultrastrong (g/...

  2. [2]

    Resonance case We consider the resonant case:ε 1 −ω b −ω p = 0 and ε1 −ω b −ω c −ω s = 0. In order to verify the validity of the effective three-level Hamiltonian (15) , we numeri- cally calculate the evolution ofP 1 governed by Hamilto- nian (7) from|b,0⟩forg= 0.05ω c andg= 0.5ω c re- spectively. Then we compared the exact results with analytical result ...

  3. [3]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information(Cambridge University Press, Cambridge, England, 2000)

  4. [4]

    C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys.89, 035002 (2017)

  5. [5]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photonics5, 222 (2011)

  6. [6]

    J. L. O’Brien, A. Furusawa, and J. Vuˇ ckovi´ c, Photonic quantum technologies,Nature Photon3, 687–695 (2009)

  7. [7]

    Zhan, Z.-Q

    X.-H. Zhan, Z.-Q. Zhong, J.-Y. Ma, S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, G.-C. Guo, Z.-F. Han, Experimen- tal demonstration of long distance quantum communi- cation with independent heralded single photon sources, npj Quantum Inf.11, 73 (2025)

  8. [8]

    J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network, Phys. Rev. Lett.78, 3221 (1997). 10

  9. [9]

    J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, Multiphoton entanglement and interferometry, Rev. Mod. Phys.84, 777 (2012)

  10. [10]

    J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z.-Q. Jiang, M. Li, J.-J. Jia, G. Ren, D. He, Y.-L. Zhou, X.-X. Zhang, N. Wang, X. Chang, Z.-C. Zhu, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.- W. Pan, Satellite...

  11. [11]

    X. R. Mao, W.-J. Ji, S.-L. Wang, H.-Q. Liu, B. Wu, X.-J. Wang, L. Liu, L. Zhou, H.-Q. Ni, Z.-C. Niu, Z.-L. Yuan, A single-photon source based on topological bulk cavity, Light Sci. Appl.14, 295 (2025)

  12. [12]

    Ding, Y.-P

    X. Ding, Y.-P. Guo, M.-C. Xu, R.-Z.Liu, G.-Y. Zou, J.- Y. Zhao, Z.-X. Ge, Q.-H. Zhang, H.-L. Liu, L.-J. Wang, M.-C. Chen, H. Wang, Y.-M. He, Y.-H. Huo, C.-Y. Lu and J.-W. Pan, High-efficiency single-photon source above the loss-tolerant threshold for efficient linear opti- cal quantum computing, Nat. Photonics19, 387 (2025)

  13. [13]

    Knill, R

    E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature (London)409, 46 (2001)

  14. [14]

    P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys.79, 135 (2007)

  15. [15]

    Lodahl, Quantum-dot based photonic quantum net- works, Quantum Sci

    P. Lodahl, Quantum-dot based photonic quantum net- works, Quantum Sci. Technol.3, 013001 (2018)

  16. [16]

    Lu and J.-W

    C.-Y. Lu and J.-W. Pan, Quantum-dot single-photon sources for the quantum internet, Nat. Nanotechnol.16, 1294 (2021)

  17. [17]

    Darquie, M

    B. Darquie, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, Controlled single-photon emission from a single trapped two-level atom, Science309, 454 (2005)

  18. [18]

    S. Shi, B. Xu, K. Zhang, G.-S. Ye, D.-S. Xiang, Y. B. Liu, J. Z. Wang, D. Q. Su, and L. Li, High-fidelity pho- tonic quantum logic gate based on near-optimal Rydberg single-photon source, Nat. Commun.13, 4454 (2022)

  19. [19]

    Brunel, B

    C. Brunel, B. Lounis, P. Tamarat, and M. Orrit, Trig- gered Source of Single Photons based on Controlled Sin- gle Molecule Fluorescence, Phys. Rev. Lett.83, 2722 (1999)

  20. [20]

    Maunz, D

    P. Maunz, D. L. Moehring, S. Olmschenk, K. C. Younge, D. N. Matsukevich, and C. Monroe, Quantum interfer- ence of photon pairs from two remote trapped atomic ions, Nat. Phys.3, 538 (2007)

  21. [21]

    Kurtsiefer, S

    C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, Stable Solid-State Source of Single Photons, Phys. Rev. Lett.85, 290 (2000)

  22. [22]

    Parto, S

    K. Parto, S. I. Azzam, K. Banerjee, and G. Moody, De- fect and strain engineering of monolayer WSe2 enables site-controlled single-photon emission up to 150 K. Nat. Commun.12, 3585 (2021)

  23. [23]

    Santori, M

    C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Ya- mamoto, Triggered Single Photons from a Quantum Dot, Phys. Rev. Lett.86, 1502 (2001)

  24. [24]

    Aichele, M

    T. Aichele, M. Scholz, and O. Benson, InP/GaInP quan- tum dots as single-photon sources for quantum informa- tion processing, Proc. IEEE95, 1791 (2007)

  25. [25]

    Gogyan, S

    A. Gogyan, S. Gu´ erin, H.-R. Jauslin, and Y. Malakyan, Deterministic source of a train of indistinguishable single- photon pulses with a single-atom-cavity system, Phys. Rev. A82, 023821 (2010)

  26. [26]

    M. E. Reimer and C. Cher, The quest for a perfect single- photon source, Nat. Photon.13, 734 (2019)

  27. [27]

    Kr´ al and M

    P. Kr´ al and M. Shapiro, Cyclic Population Transfer in Quantum Systems with Broken Symmetry, Phys. Rev. Lett.87, 183002 (2001)

  28. [28]

    Kr´ al, I

    P. Kr´ al, I. Thanopulos, M. Shapiro, and D. Cohen, Two- Step Enantio-Selective Optical Switch, Phys. Rev. Lett. 90, 033001 (2003)

  29. [29]

    Y. Li, C. Bruder, and C. P. Sun, Generalized Stern- Gerlach Effect for Chiral Molecules, Phys. Rev. Lett.99, 130403 (2007)

  30. [30]

    Y.-X. Liu, J. Q. You, L. F. Wei, C. P. Sun, and F. Nori, Optical Selection Rules and Phase-Dependent Adiabatic State Control in a Superconducting Quantum Circuit, Phys. Rev. Lett.95, 087001 (2005)

  31. [31]

    Z. H. Peng, Y.-X. Liu, J. T. Peltonen, T. Yamamoto, J. S. Tsai, and O. Astafiev, Correlated emission lasing in harmonic oscillators coupled via a single three-level artificial Atom, Phys. Rev. Lett.115, 223603 (2015)

  32. [32]

    E. T. Jaynes, and F. W. Cummings, Comparison of quan- tum and semiclassical radiation theories with application to the beam maser, Proc. IEEE51, 89 (1963)

  33. [33]

    M. D. Crisp, Jaynes-Cummings model without the rotating-wave approximation, Phys. Rev. A43, 2430 (1991)

  34. [34]

    Huang, J.-Q

    J.-F. Huang, J.-Q. Liao, and L.-M. Kuang, Ultrastrong Jaynes-Cummings model, Phys. Rev. A101, 043835 (2020)

  35. [35]

    Liu and J.-F

    C. Liu and J.-F. Huang, Quantum phase transition of the Jaynes-Cummings model, Sci. China Phys. Mech. As- tron.67, 210311 (2024)

  36. [36]

    D. F. James and J. Jerke, Effective Hamiltonian the- ory and its applications in quantum information, Can. J. Phys.85, 625 (2007)

  37. [37]

    W. J. Shao, C. F. Wu, and X.-L. Feng, Generalized James’ effective Hamiltonian method, Phys. Rev. A95, 032124 (2017)

  38. [38]

    H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)

  39. [39]

    M. O. Scully and M. S. Zubairy, Quantum Optics (Cam- bridge University Press, Cambridge, 1997)

  40. [40]

    Y. Y. Yan, Y. B. Cheng, S. G. Guan, D. Y. Yu, and Z. L. Duan, Pulse-regulated single-photon generation via quantum interference in aχ(2) nonlinear nanocavity, Opt. Lett.43, 5086 (2018)

  41. [41]

    Peng , J

    J. Peng , J. N. Tang , P. H. Tang , Z. Z. Ren, J. L. Tian, and N. Barraza, Deterministic single-photon source in the ultrastrong-coupling regime, Phys. Rev. A108, L031701 (2023)

  42. [42]

    X.-R. Mao, B. Wu, W.-J. Ji, S.-L. Wang, W.-Z. Li, H.- Q. Liu, H.-Q. Ni, Z.-C. Niu, and Z.-L. Yuan, Polarized Single-Photon Emission from an Anisotropic Dirac Cav- ity, Phys. Rev. Lett.136, 073603 (2026)

  43. [43]

    C. K. Hong, Z. Y. Ou, and L. Mandel, Measurement of Subpicosecond Time Intervals between Two Photons by Interference, Phys. Rev. Lett.59, 2044 (1987)

  44. [44]

    L. O. R. Solak, B. L. Vermes, A. S. M. de Castro, D. Z. Rossatto, and C. J. Villas-Boas, Quantum Resonator as a Directional Quantum Emitter, Adv. Quantum Technol. 8, e2500710 (2025). 11

  45. [45]

    Xiong, Z.-L

    Y.-Z. Xiong, Z.-L. Wang, J.-W. Zhang, X.-D. Sun, Z.-H. Zhang, P.-S. Huang, Y.-Q. Liang, J. Jiang, J.-W. Qiu, Y.- X. Zhou, X.-Y. Linpeng, W.-H. Huang, J.-J. Niu, Y.-P. Zhong, J. Chu, S. Liu, and D.-P. Yu, High-performance multiplexed readout of superconducting qubits with a tunable broadband Purcell filter, Phys. Rev. Appl.25, 054010 (2026)

  46. [46]

    Beaudoin, J

    F. Beaudoin, J. M. Gambetta, and A. Blais, Dissipation and ultrastrong coupling in circuit QED, Phys. Rev. A 84, 043832 (2011)

  47. [47]

    J. F. Huang and C. K. Law, Photon emission via vacuum- dressed intermediate states under ultrastrong coupling, Phys. Rev. A89, 033827 (2014)

  48. [48]

    Ridolfo, M

    A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon blockade in the ultrastrong coupling regime, Phys. Rev. Lett.109, 193602 (2012)

  49. [49]

    Groiseau, A

    C. Groiseau, A. I. Fern´ andez-Dom´ ınguez, D. Mart´ ın- Cano, and C. S´ anchez Mu˜ noz, Single-Photon Source Over the Terahertz Regime, PRX Quantum5, 010312 (2024)

  50. [50]

    Niemczyk, F

    T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. H¨ ummer, E. Solano, A. Marx, and R. Gross, Circuit quantum electrodynamics in the ultrastrong-coupling regime, Nat. Phys.6, 772 (2010)

  51. [51]

    Forn-D´ ıaz, J

    P. Forn-D´ ıaz, J. Lisenfeld, D. Marcos, J. J. Garc´ ıa-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, Ob- servation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime, Phys. Rev. Lett.105, 237001 (2010)

  52. [52]

    Baust, E

    A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Qui- jandr´ ıa, D. Zueco, J.-J. Garc´ ıa Ripoll, L. Garc´ ıa-´Alvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, Ultrastrong coupling in two-resonator circuit QED, Phys. Rev. B93, 214501 (2016)

  53. [53]

    Yoshihara, T

    F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime, Nat. Phys.13, 44 (2017)

  54. [54]

    Bayer, M

    A. Bayer, M. Pozimski, S. Schambeck, D. Schuh, R. Hu- ber, D. Bougeard, and C. Lange, Terahertz Light-Matter Interaction beyond Unity Coupling Strength, Nano Lett. 17, 6340 (2017)

  55. [55]

    V. M. Muravev, I. V. Andreev, I. V. Kukushkin, S. Sch- mult, and W. Dietsche, Observation of hybrid plasmon- photon modes in microwave transmission of coplanar mi- croresonators, Phys. Rev. B87, 045307 (2011)

  56. [56]

    Scalari, C

    G. Scalari, C. Maissen, D. Tur´ cinkov´ a, D. Hagenm´’uller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, Ultrastrong Cou- pling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial, Science335, 1323 (2012)

  57. [57]

    Maissen, G

    C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, Ultrastrong coupling in the near field of complementary split-ring resonators, Phys. Rev. B90, 205309 (2014)

  58. [58]

    Schwartz, J

    T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbe- sen, Reversible Switching of Ultrastrong Light-Molecule Coupling, Phys. Rev. Lett.106, 196405 (2011)

  59. [59]

    George, T

    J. George, T. Chervy, A. Shalabney, E. Devaux, H. Hiura, C. Genet, and T. W. Ebbesen, Multiple Rabi Split- tings under Ultrastrong Vibrational Coupling, Phys. Rev. Lett.117, 153601 (2016)

  60. [60]

    picocavities

    F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. D. Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, Single-molecule optomechanics in “picocavities”, Science 354, 726 (2016)

  61. [61]

    Macr´ ı, L

    V. Macr´ ı, L. Garziano, A. Ridolfo, O. Di Stefano, and S. Savasta, Deterministic synthesis of mechanical NOON states in ultrastrong optomechanics, Phys. Rev. A94, 013817 (2016)

  62. [62]

    Todorov, A

    Y. Todorov, A. M. Andrews, R. Colombelli, S. De Lib- erato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, Ultrastrong Light-Matter Coupling Regime with Polari- ton Dots, Phys. Rev. Lett.105, 196402 (2010)

  63. [63]

    Geiser, F

    M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, Ultrastrong Coupling Regime and Plasmon Polaritons in Parabolic Semiconductor Quantum Wells, Phys. Rev. Lett.108, 106402 (2012)

  64. [64]

    Askenazi, A

    B. Askenazi, A. Vasanelli, Y. Todorov, E. Sakat, J.-J. Greffet, G. Beaudoin, I. Sagnes, and C. Sirtori, Midin- frared Ultrastrong Light–Matter Coupling for THz Ther- mal Emission, ACS Photonics4, 2550 (2017)

  65. [65]

    Huang, J.-Q

    J.-F. Huang, J.-Q. Liao, L. Tian, and L.-M. Kuang, Ma- nipulating counter-rotating interactions in the quantum Rabi model via modulation of the transition frequency of the two-level system, Phys. Rev. A96, 043849 (2017)

  66. [66]

    Reagor, H

    M. Reagor, H. Paik, G. Catelani, L. Sun, C. Axline, E. Holland, I. M. Pop, N. A. Masluk, T. Brecht, L. Frun- zio, M. H. Devoret, L. Glazman, and R. J. Schoelkopf, Reaching 10ms single photon lifetimes for superconduct- ing aluminum cavities, Appl. Phys. Lett.102, 192604 (2013)

  67. [67]

    Zhang, M

    T. Zhang, M. Wu, S. R. Cohen, L. Xin, D. Das, K. K. S. Multani, N. Peard, A.-M. Valente-Feliciano, P. B. We- lander, A. H. Safavi-Naeini, E. A. Nanni, and M. Schleier- Smith, Optically accessible high-finesse millimeter-wave resonator for cavity quantum electrodynamics with atom arrays, Phys. Rev. Appl.24, L041001 (2025)

  68. [68]

    H. Paik, D. I. Schuster, L. S. Bishop, G. Kirchmair, G. Catelani, A. P. Sears, B. R. Johnson, M. J. Reagor, L. Frunzio, L. I. Glazman, S. M. Girvin, M. H. De- voret, and R. J. Schoelkopf, Observation of High Coher- ence in Josephson Junction Qubits Measured in a Three- Dimensional Circuit QED Architecture, Phys. Rev. Lett. 107, 240501 (2011)

  69. [69]

    Universal bound on microwave dissipation in superconducting circuits

    T. Charpentier, A. Khvalyuk, L. Ioffe, M. Feigel’man, N. Roch, B. Sac´ ep´ e, Universal bound on microwave dissipa- tion in superconducting circuits, arXiv:2507.08953