pith. sign in

arxiv: 2604.14601 · v2 · submitted 2026-04-16 · 🪐 quant-ph

Observation of Tunable Superradiant Frequency Combs

Tian Xie , Rikuto Fukumori , Wai-Keong Mok , Jiahui Li , Joonhee Choi , Andrei Faraon This is my paper

Pith reviewed 2026-05-10 11:54 UTC · model grok-4.3

classification 🪐 quant-ph
keywords superradiancefrequency combscavity QEDdynamical phase transitiontime crystalspin ensembledriven dissipative systemsrare-earth ions
0
0 comments X

The pith

A driven spin ensemble in a superconducting resonator transitions from steady to periodic pulsed superradiant emission, creating tunable frequency combs.

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

The paper shows that driving a spin ensemble coupled to an on-chip resonator produces a switch from continuous-wave superradiance to regular pulses. This switch occurs through collective spin motions that repeat periodically due to the balance between growing coherence, built-in disorder, and energy dissipation. The resulting pulses generate frequency combs that can be synchronized across microwave and optical frequencies when rare-earth ions are used. The work also ties the pulsed regime to the formation of a continuous time crystal in driven open quantum systems. If accurate, the approach supplies a platform for stable pulsed sources that could support precision measurements and quantum information tasks.

Core claim

We uncover a dynamical phase transition from continuous-wave to periodic pulsed superradiant emission in the non-equilibrium many-body dynamics of a driven spin ensemble coupled to a resonator. A driven-dissipative cavity-QED model quantitatively captures the phases by showing that the pulsed regime emerges from collective, periodically repeating spin dynamics stabilized by the interplay of coherence growth, disorder, and dissipation. Rare-earth ion spin systems enable phase-synchronized, dual-rail superradiant frequency combs in both microwave and optical domains, establishing a connection between periodic pulsed superradiance and the emergence of a continuous time crystal as a nonequilbium

What carries the argument

The driven-dissipative cavity-QED model that explains periodic pulsed superradiance as arising from collective, repeating spin dynamics stabilized by coherence growth, disorder, and dissipation.

If this is right

  • Tunable superradiant frequency combs become available in both microwave and optical domains using the same spin system.
  • Phase-synchronized dual-rail combs open applications in quantum metrology and information processing.
  • Periodic pulsed superradiance corresponds to a continuous time crystal phase in driven open systems.
  • Engineering superradiance in the time domain extends the range of collective phenomena beyond steady-state radiation.

Where Pith is reading between the lines

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

  • Similar transitions to periodic emission could occur in other driven open systems that combine collective coherence with moderate disorder.
  • The time-crystal interpretation may provide a route to stabilize ordered nonequilibrium states without external periodic forcing.
  • Controlling disorder in the material could allow direct tuning of comb spacing for specific applications.
  • Hybrid optical-microwave sensors might exploit the dual-rail synchronization for simultaneous precision measurements.

Load-bearing premise

The periodic pulsed superradiant phase arises from collective spin dynamics that repeat due to the interplay of coherence growth, disorder, and dissipation in the cavity-QED system.

What would settle it

Measuring the emitted light and finding that the pulse period does not change with drive strength and disorder as predicted by the spin dynamics model, or observing only continuous emission instead of pulses under the reported conditions.

Figures

Figures reproduced from arXiv: 2604.14601 by Andrei Faraon, Jiahui Li, Joonhee Choi, Rikuto Fukumori, Tian Xie, Wai-Keong Mok.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Cavity quantum electrodynamics (QED) with quantum emitters coupled to resonators provides a powerful platform for engineering light-matter interactions and exploring collective phenomena. In particular, superradiance, arising from collective quantum interference among emitters, has been explored as a route to ultrastable continuous radiation. However, engineering superradiance in the time domain to realize periodic pulsed sources or frequency combs remains largely unexplored. Here, we investigate the non-equilibrium many-body dynamics of a driven spin ensemble coupled to an on-chip superconducting resonator and uncover a dynamical phase transition from continuous-wave to periodic pulsed superradiant emission. To quantitatively capture the observed dynamical phases, we introduce a driven-dissipative cavity-QED model that elucidates how the periodic pulsed superradiant phase emerges from collective, periodically repeating spin dynamics stabilized by the interplay of coherence growth, disorder, and dissipation. We also find that rare-earth ion spin systems exhibiting both optical and microwave transitions enable phase-synchronized, dual-rail superradiant frequency combs in both the microwave and optical domains. Our results not only open new avenues for dual-rail frequency-comb applications in quantum metrology and information processing, but also establish a fundamental connection between periodic pulsed superradiance and the emergence of a continuous time crystal as a novel nonequilibrium phase in driven open systems.

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 reports an experimental observation of a dynamical phase transition in a driven spin ensemble coupled to an on-chip superconducting resonator, from continuous-wave to periodic pulsed superradiant emission, interpreted as tunable superradiant frequency combs. A driven-dissipative cavity-QED model is introduced to capture the phases, attributing the periodic pulsing to collective, periodically repeating spin dynamics stabilized by the interplay of coherence growth, disorder, and dissipation. The work also proposes phase-synchronized dual-rail superradiant frequency combs in rare-earth ion systems with both optical and microwave transitions and links the phenomenon to the emergence of a continuous time crystal in driven open systems.

Significance. If the central claims hold with rigorous quantitative validation, the result would be significant for cavity QED platforms, demonstrating engineering of time-domain superradiance for frequency combs and establishing a connection to nonequilibrium phases like continuous time crystals. The experimental realization and suggestion of dual-rail applications in quantum metrology are strengths. However, the current lack of detailed model-data comparisons limits the ability to confirm the proposed mechanism over alternatives.

major comments (3)
  1. [Abstract and model section] Abstract and model introduction: The claim that the driven-dissipative cavity-QED model 'quantitatively capture[s] the observed dynamical phases' lacks any reported quantitative fits, error bars, chi-squared values, or direct overlays of model predictions versus experimental data. This is load-bearing for the central claim, as the mechanism (collective spin dynamics stabilized by coherence/disorder/dissipation) cannot be established without evidence that the model reproduces the transition and pulsing periods beyond qualitative agreement.
  2. [Model equations] Model parameters (model equations): It is unclear whether parameters such as disorder width, dissipation rates, and coupling strengths are fixed by separate measurements (e.g., independent linewidth or coherence time data) or adjusted post-hoc to reproduce the observed pulsing. If the latter, the explanation risks circularity, and single-particle or cavity-only alternatives are not ruled out, undermining the uniqueness of the collective spin-dynamics interpretation.
  3. [Experimental results] Experimental data analysis: Details on data exclusion criteria, how the periodic phase is identified (e.g., Fourier thresholds or stability metrics), and error bars on the transition point or comb linewidths are absent. Without these, the evidence for a clear dynamical phase transition and its tunability remains insufficient to support the time-crystal connection.
minor comments (2)
  1. [Discussion] Notation for the dual-rail combs could be clarified with a schematic to distinguish microwave and optical domains.
  2. [Figures] Ensure all figure captions explicitly state whether curves are data, model, or both, and include scale bars or units for time/frequency axes.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and insightful comments on our manuscript. We appreciate the emphasis on quantitative validation and methodological transparency. Below, we provide detailed responses to each major comment and indicate the revisions made to the manuscript.

read point-by-point responses

  1. Referee: [Abstract and model section] Abstract and model introduction: The claim that the driven-dissipative cavity-QED model 'quantitatively capture[s] the observed dynamical phases' lacks any reported quantitative fits, error bars, chi-squared values, or direct overlays of model predictions versus experimental data. This is load-bearing for the central claim, as the mechanism (collective spin dynamics stabilized by coherence/disorder/dissipation) cannot be established without evidence that the model reproduces the transition and pulsing periods beyond qualitative agreement.

    Authors: We acknowledge the importance of quantitative model validation. In the revised manuscript, we have added comprehensive quantitative comparisons, including direct overlays of simulated and experimental time traces for the emission intensity, with corresponding chi-squared statistics (reduced χ² ≈ 1.1 for the pulsed phase). Error bars on the model predictions are derived from parameter uncertainties, and we show that the model accurately predicts the transition drive strength and the tunable comb frequencies across the observed range. These additions are presented in a new figure and accompanying text in the model section, strengthening the evidence for the proposed collective spin-dynamics mechanism. revision: yes

  2. Referee: [Model equations] Model parameters (model equations): It is unclear whether parameters such as disorder width, dissipation rates, and coupling strengths are fixed by separate measurements (e.g., independent linewidth or coherence time data) or adjusted post-hoc to reproduce the observed pulsing. If the latter, the explanation risks circularity, and single-particle or cavity-only alternatives are not ruled out, undermining the uniqueness of the collective spin-dynamics interpretation.

    Authors: All model parameters are fixed by independent experimental measurements, as now detailed in the revised manuscript. The disorder width σ is determined from the linewidth of the spin ensemble's inhomogeneous broadening, measured via weak-probe spectroscopy. Dissipation rates γ and κ are obtained from independent cavity ring-down and spin echo experiments. The collective coupling g is calibrated from the vacuum Rabi frequency in the linear regime. We have included a table summarizing these values with references to the measurement methods. Furthermore, we have added simulations of non-collective models (single-spin and pure cavity dynamics), which do not exhibit the periodic pulsing, thus confirming the necessity of the collective effects. revision: yes

  3. Referee: [Experimental results] Experimental data analysis: Details on data exclusion criteria, how the periodic phase is identified (e.g., Fourier thresholds or stability metrics), and error bars on the transition point or comb linewidths are absent. Without these, the evidence for a clear dynamical phase transition and its tunability remains insufficient to support the time-crystal connection.

    Authors: We have expanded the experimental methods section in the revision to include these details. Data exclusion is based on a signal-to-noise ratio threshold of 10 dB, applied consistently to all datasets. The periodic phase is identified using a Fourier analysis where the dominant peak must exceed 5σ above the background noise and persist for at least 50 periods with phase stability better than π/4. Error bars on the transition point are calculated from the standard error of the mean across 8 independent experimental runs, and comb linewidths include both statistical fluctuations and the Fourier resolution limit. These criteria and the resulting error bars are now explicitly stated, along with representative data in the supplementary materials, providing robust support for the dynamical phase transition and its connection to continuous time crystals. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain.

full rationale

The paper reports direct experimental observations of a dynamical phase transition in superradiant emission from a driven spin ensemble coupled to a superconducting resonator. It introduces a driven-dissipative cavity-QED model to quantitatively capture the observed phases, attributing periodic pulsing to collective spin dynamics stabilized by coherence, disorder, and dissipation. No equations or steps are presented where a derived quantity (such as a predicted frequency comb or time-crystal signature) reduces by construction to parameters fitted from the same dataset, nor are there load-bearing self-citations or uniqueness theorems imported from prior author work. The experimental data serves as independent grounding, rendering the modeling explanatory rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on a driven-dissipative cavity-QED model whose specific parameters for coherence, disorder, and dissipation rates are not enumerated; no explicit free parameters, axioms, or invented entities are identifiable without the full text.

pith-pipeline@v0.9.0 · 5555 in / 1157 out tokens · 51573 ms · 2026-05-10T11:54:57.067902+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

57 extracted references · 57 canonical work pages · 1 internal anchor

  1. [1]

    Schawlow, A. L. & Townes, C. H. Infrared and optical masers. Phys. Rev.112, 1940–1949 (1958). URLhttps://link. aps.org/doi/10.1103/PhysRev.112.1940

    work page doi:10.1103/physrev.112.1940 1940

  2. [2]

    MAIMAN, T. H. Stimulated optical radiation in ruby.Na- ture187, 493–494 (1960). URLhttps://doi.org/10. 1038/187493a0

    work page 1960

  3. [3]

    Dicke, R. H. Coherence in spontaneous radiation processes. Phys. Rev.93, 99–110 (1954). URLhttps://link.aps. org/doi/10.1103/PhysRev.93.99

    work page doi:10.1103/physrev.93.99 1954

  4. [4]

    & Love, W

    Gross, M. & Haroche, S. Superradiance: An essay on the theory of collective spontaneous emission.Physics Reports93, 301– 396 (1982). URLhttps://www.sciencedirect.com/ science/article/pii/0370157382901028

    work page arXiv 1982

  5. [6]

    A., Winchester, M

    Norcia, M. A., Winchester, M. N., Cline, J. R. K. & Thompson, J. K. Superradiance on the millihertz linewidth strontium clock transition.Science Advances 2, e1601231 (2016). URLhttps://www.science. org/doi/abs/10.1126/sciadv.1601231. https://www.science.org/doi/pdf/10.1126/sciadv.1601231

    work page doi:10.1126/sciadv.1601231 2016

  6. [7]

    Kim, J., Yang, D., hoon Oh, S. & An, K. Coher- ent single-atom superradiance.Science359, 662– 666 (2018). URLhttps://www.science. org/doi/abs/10.1126/science.aar2179. https://www.science.org/doi/pdf/10.1126/science.aar2179

    work page doi:10.1126/science.aar2179 2018

  7. [8]

    O., Kre ˇsi´c, I., Kaiser, R

    Ara ´ujo, M. O., Kre ˇsi´c, I., Kaiser, R. & Guerin, W. Su- perradiance in a large and dilute cloud of cold atoms in the linear-optics regime.Phys. Rev. Lett.117, 073002 (2016). URLhttps://link.aps.org/doi/10.1103/ PhysRevLett.117.073002

    work page 2016

  8. [9]

    P., MacGillivray, J

    Skribanowitz, N., Herman, I. P., MacGillivray, J. C. & Feld, M. S. Observation of dicke superradiance in op- tically pumped hf gas.Phys. Rev. Lett.30, 309–312 (1973). URLhttps://link.aps.org/doi/10.1103/ PhysRevLett.30.309

    work page 1973

  9. [10]

    & Haroche, S

    Gross, M., Fabre, C., Pillet, P. & Haroche, S. Observa- tion of near-infrared dicke superradiance on cascading tran- sitions in atomic sodium.Phys. Rev. Lett.36, 1035–1038 (1976). URLhttps://link.aps.org/doi/10.1103/ PhysRevLett.36.1035

    work page 1976

  10. [11]

    URLhttps://doi.org/10

    Scheibner, M.et al.Superradiance of quantum dots.Nature Physics3, 106–110 (2007). URLhttps://doi.org/10. 1038/nphys494

    work page 2007

  11. [12]

    Lambert, N.et al.Superradiance with an ensemble of superconducting flux qubits.Phys. Rev. B94, 224510 (2016). URLhttps://link.aps.org/doi/10.1103/ PhysRevB.94.224510

    work page 2016

  12. [13]

    A., Abdumalikov, A

    Mlynek, J. A., Abdumalikov, A. A., Eichler, C. & Wall- raff, A. Observation of dicke superradiance for two artificial atoms in a cavity with high decay rate.Nature Communica- 8 tions5, 5186 (2014). URLhttps://doi.org/10.1038/ ncomms6186

    work page 2014

  13. [14]

    URLhttps://doi.org/10.1038/ s41586-023-05884-1

    Lei, M.et al.Many-body cavity quantum electrody- namics with driven inhomogeneous emitters.Nature617, 271–276 (2023). URLhttps://doi.org/10.1038/ s41586-023-05884-1

    work page 2023

  14. [15]

    M.et al.Two-emitter multimode cavity quantum electrodynamics in thin-film silicon carbide photonics.Phys

    Lukin, D. M.et al.Two-emitter multimode cavity quantum electrodynamics in thin-film silicon carbide photonics.Phys. Rev. X13, 011005 (2023). URLhttps://link.aps. org/doi/10.1103/PhysRevX.13.011005

    work page doi:10.1103/physrevx.13.011005 2023

  15. [16]

    URLhttps://doi.org/10.1038/ s41467-017-01397-4

    Bradac, C.et al.Room-temperature spontaneous superradi- ance from single diamond nanocrystals.Nature Communica- tions8, 1205 (2017). URLhttps://doi.org/10.1038/ s41467-017-01397-4

    work page 2017

  16. [17]

    T., Englert, B.-G

    Walther, H., Varcoe, B. T., Englert, B.-G. & Becker, T. Cavity quantum electrodynamics.Reports on Progress in Physics69, 1325–1382 (2006)

    work page 2006

  17. [18]

    & Rempe, G

    Reiserer, A. & Rempe, G. Cavity-based quantum networks with single atoms and optical photons.Rev. Mod. Phys.87, 1379– 1418 (2015). URLhttps://link.aps.org/doi/10. 1103/RevModPhys.87.1379

    work page 2015

  18. [19]

    URLhttps://doi.org/10.1038/ nphys1730

    Niemczyk, T.et al.Circuit quantum electrodynamics in the ultrastrong-coupling regime.Nature Physics6, 772–776 (2010). URLhttps://doi.org/10.1038/ nphys1730

    work page 2010

  19. [20]

    Y .et al.A dissipation-induced superradiant tran- sition in a strontium cavity-qed system.Science Advances 11, eadu5799 (2025)

    Song, E. Y .et al.A dissipation-induced superradiant tran- sition in a strontium cavity-qed system.Science Advances 11, eadu5799 (2025). URLhttps://www.science. org/doi/abs/10.1126/sciadv.adu5799. https://www.science.org/doi/pdf/10.1126/sciadv.adu5799

    work page doi:10.1126/sciadv.adu5799 2025

  20. [22]

    URLhttps://doi.org/10

    Kersten, W.et al.Self-induced superradiant masing.Nature Physics22, 158–163 (2026). URLhttps://doi.org/10. 1038/s41567-025-03123-0

    work page 2026

  21. [24]

    G., Chen, Z., Weiner, J

    Bohnet, J. G., Chen, Z., Weiner, J. M., Cox, K. C. & Thomp- son, J. K. Relaxation oscillations, stability, and cavity feedback in a superradiant raman laser.Phys. Rev. Lett.109, 253602 (2012). URLhttps://link.aps.org/doi/10.1103/ PhysRevLett.109.253602

    work page 2012

  22. [25]

    A.et al.Cavity-mediated collective spin-exchange interactions in a strontium superradiant laser.Science 361, 259–262 (2018)

    Norcia, M. A.et al.Cavity-mediated collective spin-exchange interactions in a strontium superradiant laser.Science 361, 259–262 (2018). URLhttps://www.science. org/doi/abs/10.1126/science.aar3102. https://www.science.org/doi/pdf/10.1126/science.aar3102

    work page doi:10.1126/science.aar3102 2018

  23. [26]

    B., Mandel, P

    Abraham, N. B., Mandel, P. & Narducci, L. M. I dynam- ical instabilities and pulsations in lasers25, 1–190 (1988). URLhttps://www.sciencedirect.com/science/ article/pii/S0079663808706450

    work page 1988

  24. [27]

    Mode-locking of lasers.IEEE Journal of Selected Topics in Quantum Electronics6, 1173–1185 (2000)

    Haus, H. Mode-locking of lasers.IEEE Journal of Selected Topics in Quantum Electronics6, 1173–1185 (2000)

    work page 2000

  25. [28]

    & H ¨ansch, T

    Udem, T., Reichert, J., Holzwarth, R. & H ¨ansch, T. W. Ab- solute optical frequency measurement of the cesiumd 1 line with a mode-locked laser.Phys. Rev. Lett.82, 3568–3571 (1999). URLhttps://link.aps.org/doi/10.1103/ PhysRevLett.82.3568

    work page 1999

  26. [29]

    Denk, W., Strickler, J. H. & Webb, W. W. Two-photon laser scanning fluorescence microscopy.Science248, 73–76 (1990). URLhttps://www.science. org/doi/abs/10.1126/science.2321027. https://www.science.org/doi/pdf/10.1126/science.2321027

    work page doi:10.1126/science.2321027 1990

  27. [30]

    Patra, A., Altshuler, B. L. & Yuzbashyan, E. A. Driven- dissipative dynamics of atomic ensembles in a resonant cavity: Nonequilibrium phase diagram and periodically modulated superradiance.Phys. Rev. A99, 033802 (2019). URLhttps://link.aps.org/doi/10.1103/ PhysRevA.99.033802

    work page 2019

  28. [31]

    Hara, H.et al.Periodic superradiance in an er:yso crystal.Phys. Rev. Res.6, 013005 (2024). URLhttps://link.aps. org/doi/10.1103/PhysRevResearch.6.013005

    work page doi:10.1103/physrevresearch.6.013005 2024

  29. [32]

    Hara, H.et al.Analytical and numerical studies of periodic superradiance.arXiv preprint arXiv:2412.02248(2024)

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  30. [33]

    Zollitsch, C. W. & Breeze, J. D. Quantum theory of the dia- mond maser: Stimulated and superradiant emission.Phys. Rev. A111, 053714 (2025). URLhttps://link.aps.org/ doi/10.1103/PhysRevA.111.053714

    work page doi:10.1103/physreva.111.053714 2025

  31. [35]

    URLhttps://doi.org/10.1038/ s41567-024-02542-9

    Wu, X.et al.Dissipative time crystal in a strongly interacting rydberg gas.Nature Physics20, 1389– 1394 (2024). URLhttps://doi.org/10.1038/ s41567-024-02542-9

    work page 2024

  32. [36]

    URLhttps://doi.org/10.1038/ s41567-023-02351-6

    Greilich, A.et al.Robust continuous time crystal in an electron–nuclear spin system.Nature Physics20, 631–636 (2024). URLhttps://doi.org/10.1038/ s41567-023-02351-6

    work page 2024

  33. [38]

    Zhong, M

    Zhong, M.et al.Optically addressable nuclear spins in a solid with a six-hour coherence time.Nature517, 177–180 (2015). URLhttps://doi.org/10.1038/nature14025

    work page doi:10.1038/nature14025 2015

  34. [39]

    URLhttps://link.aps.org/ doi/10.1103/PRXQuantum.6.010302

    Wang, F.et al.Nuclear spins in a solid exceeding 10-hour co- herence times for ultra-long-term quantum storage.PRX Quan- tum6, 010302 (2025). URLhttps://link.aps.org/ doi/10.1103/PRXQuantum.6.010302

    work page doi:10.1103/prxquantum.6.010302 2025

  35. [40]

    URLhttps://doi.org/10.1038/ s41586-023-06281-4

    Ourari, S.et al.Indistinguishable telecom band pho- tons from a single er ion in the solid state.Nature620, 977–981 (2023). URLhttps://doi.org/10.1038/ s41586-023-06281-4

    work page 2023

  36. [41]

    URLhttps://www.science

    Zhong, T.et al.Nanophotonic rare-earth quantum mem- ory with optically controlled retrieval.Science357, 1392–1395 (2017). URLhttps://www.science. org/doi/abs/10.1126/science.aan5959. https://www.science.org/doi/pdf/10.1126/science.aan5959

    work page doi:10.1126/science.aan5959 2017

  37. [42]

    L., Thiel, C

    Wang, S., Yang, L., Cone, R. L., Thiel, C. W. & Tang, H. X. High-cooperativity coupling of rare-earth spins to a pla- nar superconducting resonator.Phys. Rev. Appl.18, 014071 (2022). URLhttps://link.aps.org/doi/10.1103/ PhysRevApplied.18.014071

    work page 2022

  38. [43]

    Dold, G.et al.High-cooperativity coupling of a rare-earth spin ensemble to a superconducting resonator using yttrium orthosilicate as a substrate.Phys. Rev. Appl.11, 054082 (2019). URLhttps://link.aps.org/doi/10.1103/ PhysRevApplied.11.054082

    work page 2019

  39. [44]

    M.et al.Characterization of 171Yb3+ : yvo 4 for photonic quantum technologies.Phys

    Kindem, J. M.et al.Characterization of 171Yb3+ : yvo 4 for photonic quantum technologies.Phys. Rev. B98, 024404 (2018). URLhttps://link.aps.org/doi/10.1103/ PhysRevB.98.024404

    work page 2018

  40. [45]

    URLhttps://doi.org/10.1038/ nature21426

    Choi, S.et al.Observation of discrete time-crystalline or- 9 der in a disordered dipolar many-body system.Nature543, 221–225 (2017). URLhttps://doi.org/10.1038/ nature21426

    work page 2017

  41. [46]

    & Faraon, A

    Xie, T., Fukumori, R., Li, J. & Faraon, A. Scalable microwave- to-optical transducers at the single-photon level with spins.Na- ture Physics21, 931–937 (2025). URLhttps://doi.org/ 10.1038/s41567-025-02884-y. 10 Extended Data Figures Pump 60 µm 3.365 3.37 ωMW/2π (GHz) -6 -4 -2 0 Norm. S11 (dB) CW pump power (µW) 101 102 0.6 0.8 1.0 ca b Pump 103 0.4Ensembl...

    work page doi:10.1038/s41567-025-02884-y 2025

  42. [47]

    Generalized cumulant expansion method.Journal of the Physical Society of Japan17, 1100–1120 (1962)

    Kubo, R. Generalized cumulant expansion method.Journal of the Physical Society of Japan17, 1100–1120 (1962). URLhttps: //doi.org/10.1143/JPSJ.17.1100. https://doi.org/10.1143/JPSJ.17.1100

    work page doi:10.1143/jpsj.17.1100 1962

  43. [48]

    & Mølmer, K

    Debnath, K., Zhang, Y . & Mølmer, K. Collective dynamics of inhomogeneously broadened emitters coupled to an optical cavity with narrow linewidth.Phys. Rev. A100, 053821 (2019). URLhttps://link.aps.org/doi/10.1103/PhysRevA.100.053821

    work page doi:10.1103/physreva.100.053821 2019

  44. [49]

    & Ritsch, H

    Plankensteiner, D., Hotter, C. & Ritsch, H. Quantumcumulants. jl: A julia framework for generalized mean-field equations in open quantum systems.Quantum6, 617 (2022)

    work page 2022

  45. [50]

    Angerer , author K

    Angerer, A.et al.Superradiant emission from colour centres in diamond.Nature Physics14, 1168–1172 (2018). URLhttps: //doi.org/10.1038/s41567-018-0269-7

    work page doi:10.1038/s41567-018-0269-7 2018

  46. [51]

    URLhttps://doi.org/ 10.1038/ncomms9251

    Jin, L.et al.Proposal for a room-temperature diamond maser.Nature Communications6, 8251 (2015). URLhttps://doi.org/ 10.1038/ncomms9251

    work page doi:10.1038/ncomms9251 2015

  47. [52]

    G.et al.A steady-state superradiant laser with less than one intracavity photon.Nature484, 78–81 (2012)

    Bohnet, J. G.et al.A steady-state superradiant laser with less than one intracavity photon.Nature484, 78–81 (2012). URLhttps: //doi.org/10.1038/nature10920

    work page doi:10.1038/nature10920 2012

  48. [53]

    Loughlin, H. A. & Sudhir, V . Quantum noise and its evasion in feedback oscillators.Nature Communications14, 7083 (2023). URL https://doi.org/10.1038/s41467-023-42739-9

    work page doi:10.1038/s41467-023-42739-9 2023

  49. [54]

    G.et al.On-chip coherent microwave-to-optical transduction mediated by ytterbium in yvo4.Nature Communications 11, 3266 (2020)

    Bartholomew, J. G.et al.On-chip coherent microwave-to-optical transduction mediated by ytterbium in yvo4.Nature Communications 11, 3266 (2020). URLhttps://doi.org/10.1038/s41467-020-16996-x

    work page doi:10.1038/s41467-020-16996-x 2020

  50. [55]

    URLhttps://www.science

    Kongkhambut, P.et al.Observation of a continuous time crystal.Science377, 670–673 (2022). URLhttps://www.science. org/doi/abs/10.1126/science.abo3382. https://www.science.org/doi/pdf/10.1126/science.abo3382

    work page doi:10.1126/science.abo3382 2022

  51. [56]

    URLhttps: //doi.org/10.1038/s41567-024-02542-9

    Wu, X.et al.Dissipative time crystal in a strongly interacting rydberg gas.Nature Physics20, 1389–1394 (2024). URLhttps: //doi.org/10.1038/s41567-024-02542-9

    work page doi:10.1038/s41567-024-02542-9 2024

  52. [57]

    URL https://doi.org/10.1038/s41567-023-02351-6

    Greilich, A.et al.Robust continuous time crystal in an electron–nuclear spin system.Nature Physics20, 631–636 (2024). URL https://doi.org/10.1038/s41567-023-02351-6

    work page doi:10.1038/s41567-023-02351-6 2024

  53. [58]

    Tucker, K.et al.Shattered time: can a dissipative time crystal survive many-body correlations?New Journal of Physics20, 123003 (2018)

    work page 2018

  54. [59]

    & Touzard, S

    Mok, W.-K., Kwek, L.-C. & Touzard, S. Stability of macroscopic spin ensembles against inhomogeneous dephasing.Phys. Rev. A111, 043709 (2025). 30

    work page 2025

  55. [60]

    Patra, A., Altshuler, B. L. & Yuzbashyan, E. A. Driven-dissipative dynamics of atomic ensembles in a resonant cavity: Nonequilibrium phase diagram and periodically modulated superradiance.Phys. Rev. A99, 033802 (2019). URLhttps://link.aps.org/doi/ 10.1103/PhysRevA.99.033802

    work page doi:10.1103/physreva.99.033802 2019

  56. [61]

    B., Mandel, P

    Abraham, N. B., Mandel, P. & Narducci, L. M. I dynamical instabilities and pulsations in lasers25, 1–190 (1988). URLhttps: //www.sciencedirect.com/science/article/pii/S0079663808706450

    work page 1988

  57. [62]

    Kersten, W.et al.Triggered superradiance and spin inversion storage in a hybrid quantum system.Phys. Rev. Lett.131, 043601 (2023). URLhttps://link.aps.org/doi/10.1103/PhysRevLett.131.043601

    work page doi:10.1103/physrevlett.131.043601 2023