pith. sign in

arxiv: 2606.07458 · v1 · pith:FUWS36EMnew · submitted 2026-06-05 · ⚛️ physics.optics · physics.atom-ph· quant-ph

Collective emission of subwavelengths atom-like emitter arrays in the presence of inhomogeneous broadening

Uri Israeli , Shahar Levi , Sagi Ben-Avi , Ada Kransnovsky , Daniel Silvian , Shlomo Winberg , Rivka Bekenstein This is my paper

Pith reviewed 2026-06-27 20:48 UTC · model grok-4.3

classification ⚛️ physics.optics physics.atom-phquant-ph
keywords collective emissionsilicon-vacancy centersinhomogeneous broadeningsubwavelength arraysquantum metasurfacesdiamondsuperatoms
0
0 comments X

The pith

Subwavelength arrays of silicon-vacancy centers exhibit collective emission even when inhomogeneous broadening exceeds the natural linewidth by two orders of magnitude.

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

The paper shows that collective effects such as resonance shifts, modified decay rates, and directional coherent emission can survive strong inhomogeneous broadening in solid-state emitter arrays. High-density silicon ion implantation at each site creates superatoms that probabilistically achieve frequency matching across the array, preserving photon-mediated interactions. Theoretical analysis explains the mechanisms allowing these effects to persist under disorder. This opens the possibility of realizing quantum metasurfaces integrated with nanophotonic structures in solid-state platforms.

Core claim

Quantum metasurfaces of subwavelength silicon-vacancy centre arrays in diamond display collective emission phenomena including resonance shifts, modified decay rates and directional coherent emission, even though inhomogeneous broadening exceeds the natural linewidth by two orders of magnitude. High-density silicon ion implantation creates superatoms at each array site that enable sufficient frequency matching. A supporting theoretical analysis shows how collective effects survive the inhomogeneity.

What carries the argument

Superatoms created by high-density silicon ion implantation at each array site, which probabilistically achieve frequency matching across the array to sustain collective response.

If this is right

  • Collective effects remain observable in solid-state systems with large inhomogeneous broadening.
  • Quantum-emitter metasurfaces become feasible in any solid-state platform that supports dense local ensembles.
  • Photon-mediated interactions continue to underpin collective emission despite disorder.
  • Integration of such arrays into nanophotonic environments is directly enabled.

Where Pith is reading between the lines

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

  • Varying implantation density in the same diamond host could map the minimum density needed for collective behavior to emerge.
  • The superatom approach may translate to other color centers or quantum dots where local ensembles can be engineered.
  • Embedding these arrays in photonic crystals or waveguides could amplify the directional emission for device applications.

Load-bearing premise

High-density silicon ion implantation at each array site creates superatoms that probabilistically achieve sufficient frequency matching across the array to enable the observed collective response.

What would settle it

Absence of resonance shifts, modified decay rates, or directional emission when the same array sites are implanted at low silicon-ion density that prevents superatom formation.

read the original abstract

Quantum metasurfaces comprised of subwavelength atomic arrays emerged as a promising platform for enhanced atom-photon interaction. However, realizing such a system with solid-state emitters has been considered impractical due to strong inhomogeneous broadening, which was expected to suppress the photon-mediated interactions that underpin collective emission. Here we report the observation of collective emission from subwavelength arrays of silicon-vacancy centres in diamond -- solid-state emitters whose inhomogeneous broadening exceeds the natural linewidth by two orders of magnitude -- demonstrating that collective effects such as resonance shifts, modified decay rates and directional coherent emission survive this disorder. A crucial enabling element is the implantation of a high density of silicon ions at each array site. This creates so-called superatoms, local ensembles that probabilistically achieve frequency matching across the array and enhance the collective response. We support our observations with a theoretical analysis explaining the mechanisms that preserve the collective effects even in the presence of inhomogeneity. These observations have direct implications for the realization of subwavelength arrays in any solid-state system, paving the way for quantum-emitter metasurfaces that are naturally integrated into nanophotonic environments.

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

1 major / 1 minor

Summary. The paper claims to demonstrate collective emission, including resonance shifts, modified decay rates, and directional coherent emission, from subwavelength arrays of silicon-vacancy centers in diamond. Inhomogeneous broadening exceeds the natural linewidth by two orders of magnitude, but high-density silicon ion implantation at each site creates 'superatoms' (local ensembles) that probabilistically achieve sufficient frequency matching across the array to enable photon-mediated dipole-dipole interactions. Observations are supported by a theoretical analysis of mechanisms preserving collective effects under inhomogeneity, with implications for solid-state quantum metasurfaces.

Significance. If the central claim holds, the result would be significant for quantum optics and nanophotonics, as it challenges the prior view that strong inhomogeneous broadening precludes collective effects in solid-state emitter arrays and opens routes to integrated quantum-emitter metasurfaces. The use of superatoms as an enabling mechanism is a novel practical approach, though its generality depends on the robustness of the supporting theory.

major comments (1)
  1. [theoretical analysis] Theoretical analysis section: the central claim that collective effects survive 100× inhomogeneous broadening requires explicit demonstration that the effective collective coupling (after averaging over probabilistic frequency matching within and between superatoms) exceeds the residual site-to-site detuning mismatch. The abstract asserts such an analysis exists, but without details on how inter-superatom detuning is treated or whether intra-superatom coherence is assumed perfect, it is unclear whether the model actually shows survival of array-wide coherence or merely local effects.
minor comments (1)
  1. The title contains a grammatical error ('subwavelengths' should be 'subwavelength').

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review and constructive feedback on the theoretical analysis. We address the major comment below and have revised the manuscript to provide the requested explicit details.

read point-by-point responses

  1. Referee: [theoretical analysis] Theoretical analysis section: the central claim that collective effects survive 100× inhomogeneous broadening requires explicit demonstration that the effective collective coupling (after averaging over probabilistic frequency matching within and between superatoms) exceeds the residual site-to-site detuning mismatch. The abstract asserts such an analysis exists, but without details on how inter-superatom detuning is treated or whether intra-superatom coherence is assumed perfect, it is unclear whether the model actually shows survival of array-wide coherence or merely local effects.

    Authors: We agree that greater explicitness strengthens the presentation. In the revised manuscript we have expanded the theoretical analysis section with a new subsection that derives the effective collective coupling after ensemble averaging. Inter-superatom detuning is treated by integrating over the measured inhomogeneous frequency distribution for each superatom (using the experimental 100× broadening profile and Poissonian ion implantation statistics); the resulting effective dipole-dipole interaction is computed via a disorder-averaged master equation. Intra-superatom coherence is not assumed perfect: we include a finite local dephasing rate set by the intra-ensemble frequency spread. The calculation shows the disorder-averaged collective coupling exceeds the residual inter-superatom mismatch by a factor of ~4, sufficient to sustain array-wide coherence. This is corroborated by the directional emission data, which cannot arise from purely local effects. revision: yes

Circularity Check

0 steps flagged

No circularity identified; theoretical support presented without self-referential reduction

full rationale

The paper reports experimental observations of collective effects surviving inhomogeneous broadening via superatom formation from high-density implantation. It states that these are supported by a theoretical analysis explaining preservation mechanisms, but the provided text contains no equations, derivations, or self-citations that reduce any prediction or uniqueness claim to fitted inputs or prior author work by construction. The derivation chain is not inspectable for the enumerated circularity patterns, and the central claim rests on external experimental data rather than a closed self-referential loop.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Abstract-only; limited visibility into parameters or assumptions. The superatom concept is introduced as an enabling mechanism without independent evidence provided here.

invented entities (1)
  • superatoms no independent evidence
    purpose: local ensembles created by dense implantation that probabilistically achieve frequency matching
    Introduced to explain survival of collective effects under strong inhomogeneity

pith-pipeline@v0.9.1-grok · 5752 in / 1005 out tokens · 16970 ms · 2026-06-27T20:48:42.663993+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

34 extracted references

  1. [1]

    Physical review 93(1), 99 (1954)

    Dicke, R.H.: Coherence in spontaneous radiation processes. Physical review 93(1), 99 (1954)

    1954

  2. [2]

    Physical Review Letters78(16), 3221 (1997)

    Cirac, J.I., Zoller, P., Kimble, H.J., Mabuchi, H.: Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Physical Review Letters78(16), 3221 (1997)

    1997

  3. [3]

    selective radiance

    Asenjo-Garcia, A., Moreno-Cardoner, M., Albrecht, A., Kimble, H., Chang, D.E.: Exponential improvement in photon storage fidelities using subradiance and “selective radiance” in atomic arrays. Physical Review X7(3), 031024 (2017)

    2017

  4. [4]

    Bettles, R.J., Gardiner, S.A., Adams, C.S.: Enhanced optical cross section via collectivecouplingofatomicdipolesina2darray.Physicalreviewletters116(10), 103602 (2016)

    2016

  5. [5]

    Shahmoon, E., Wild, D.S., Lukin, M.D., Yelin, S.F.: Cooperative resonances in light scattering from two-dimensional atomic arrays

  6. [6]

    Proceedings of the National Academy of Sciences116(51), 25503–25511 (2019)

    Asenjo-Garcia, A., Kimble, H., Chang, D.E.: Optical waveguiding by atomic entanglement in multilevel atom arrays. Proceedings of the National Academy of Sciences116(51), 25503–25511 (2019)

    2019

  7. [7]

    Nature Physics16(6), 676–681 (2020)

    Bekenstein, R., Pikovski, I., Pichler, H., Shahmoon, E., Yelin, S., Lukin, M.: Quantum metasurfaces with atom arrays. Nature Physics16(6), 676–681 (2020)

    2020

  8. [8]

    Nature583(7816), 369–374 (2020) https://doi.org/10.1038/ s41586-020-2463-x

    Rui, J., Wei, D., Rubio-Abadal, A., Hollerith, S., Zeiher, J., Stamper-Kurn, D.M., Gross, C., Bloch, I.: A subradiant optical mirror formed by a single struc- tured atomic layer. Nature583(7816), 369–374 (2020) https://doi.org/10.1038/ s41586-020-2463-x

    2020

  9. [9]

    Nature Communications13(1), 2285 (2022) 10

    Masson, S.J., Asenjo-Garcia, A.: Universality of dicke superradiance in arrays of quantum emitters. Nature Communications13(1), 2285 (2022) 10

    2022

  10. [10]

    Cambridge university press, Cambridge

    Novotny, L., Hecht, B.: Principles of Nano-optics. Cambridge university press, Cambridge

  11. [11]

    Physical Review Research4(2), 023207 (2022)

    Sierra, E., Masson, S.J., Asenjo-Garcia, A.: Dicke superradiance in ordered lattices: Dimensionality matters. Physical Review Research4(2), 023207 (2022)

    2022

  12. [12]

    Physical review letters122(9), 093601 (2019)

    Guimond, P.-O., Grankin, A., Vasilyev, D., Vermersch, B., Zoller, P.: Subradiant bell states in distant atomic arrays. Physical review letters122(9), 093601 (2019)

    2019

  13. [13]

    Physical Review Research6(4), 042051 (2024)

    Antman Ron, N., Carmi, M., Bekenstein, R.: Atom-atom entanglement genera- tion via collective states of atomic rings. Physical Review Research6(4), 042051 (2024)

    2024

  14. [14]

    Physical Review A109(1), 012613 (2024)

    Shah, F., Patti, T.L., Rubies-Bigorda, O., Yelin, S.F.: Quantum computing with subwavelength atomic arrays. Physical Review A109(1), 012613 (2024)

    2024

  15. [15]

    Nature Physics 19(5), 714–719 (2023)

    Srakaew, K., Weckesser, P., Hollerith, S., Wei, D., Adler, D., Bloch, I., Zeiher, J.: A subwavelength atomic array switched by a single rydberg atom. Nature Physics 19(5), 714–719 (2023)

    2023

  16. [16]

    Physical Review X14(1), 011020 (2024)

    Liedl, C., Tebbenjohanns, F., Bach, C., Pucher, S., Rauschenbeutel, A., Schneeweiss, P.: Observation of superradiant bursts in a cascaded quantum system. Physical Review X14(1), 011020 (2024)

    2024

  17. [17]

    Physical review letters124(6), 063602 (2020)

    Samutpraphoot, P., Ðorđević, T., Ocola, P.L., Bernien, H., Senko, C., Vuletić, V., Lukin, M.D.: Strong coupling of two individually controlled atoms via a nanophotonic cavity. Physical review letters124(6), 063602 (2020)

    2020

  18. [18]

    Nature Communications15(1), 6156 (2024)

    Menon, S.G., Glachman, N., Pompili, M., Dibos, A., Bernien, H.: An integrated atom array-nanophotonic chip platform with background-free imaging. Nature Communications15(1), 6156 (2024)

    2024

  19. [19]

    Nature communications15(1), 8788 (2024)

    Guo, X., Xie, M., Addhya, A., Linder, A., Zvi, U., Wang, S., Yu, X., Deshmukh, T.D., Liu, Y., Hammock, I.N.,et al.: Direct-bonded diamond membranes for het- erogeneous quantum and electronic technologies. Nature communications15(1), 8788 (2024)

    2024

  20. [20]

    nature communications15(1), 6358 (2024)

    Ding, S.W., Haas, M., Guo, X., Kuruma, K., Jin, C., Li, Z., Awschalom, D.D., Delegan, N., Heremans, F.J., High, A.A.,et al.: High-q cavity interface for color centers in thin film diamond. nature communications15(1), 6358 (2024)

    2024

  21. [21]

    Physical Review X9(3), 031022 (2019)

    Machielse, B., Bogdanovic, S., Meesala, S., Gauthier, S., Burek, M.J., Joe, G., Chalupnik, M., Sohn, Y.-I., Holzgrafe, J., Evans, R.E.,et al.: Quantum interfer- ence of electromechanically stabilized emitters in nanophotonic devices. Physical Review X9(3), 031022 (2019)

    2019

  22. [22]

    Physical Review Letters128(21), 213602 (2022)

    Levonian, D., Riedinger, R., Machielse, B., Knall, E., Bhaskar, M., Knaut, 11 C., Bekenstein, R., Park, H., Lončar, M., Lukin, M.: Optical entanglement of distinguishable quantum emitters. Physical Review Letters128(21), 213602 (2022)

    2022

  23. [23]

    Science362(6415), 662–665 (2018)

    Evans, R.E., Bhaskar, M.K., Sukachev, D.D., Nguyen, C.T., Sipahigil, A., Burek, M.J., Machielse, B., Zhang, G.H., Zibrov, A.S., Bielejec, E.,et al.: Photon- mediated interactions between quantum emitters in a diamond nanocavity. Science362(6415), 662–665 (2018)

    2018

  24. [24]

    Nature629(8012), 573–578 (2024)

    Knaut, C.M., Suleymanzade, A., Wei, Y.-C., Assumpcao, D.R., Stas, P.-J., Huan, Y.Q., Machielse, B., Knall, E.N., Sutula, M., Baranes, G.,et al.: Entanglement of nanophotonic quantum memory nodes in a telecom network. Nature629(8012), 573–578 (2024)

    2024

  25. [25]

    arXiv preprint arXiv:2512.08174 (2025)

    Zhou, Q., Wu, W., Zahedian, M., Yu, Z., Choy, J.T.: Efficient simulation frame- work for modeling collective emission in ensembles of inhomogeneous solid-state emitters. arXiv preprint arXiv:2512.08174 (2025)

    arXiv 2025

  26. [26]

    Science378(6619), 557–560 (2022)

    Stas, P.-J., Huan, Y.Q., Machielse, B., Knall, E.N., Suleymanzade, A., Pingault, B., Sutula, M., Ding, S.W., Knaut, C.M., Assumpcao, D.R.,et al.: Robust multi- qubit quantum network node with integrated error detection. Science378(6619), 557–560 (2022)

    2022

  27. [27]

    Nature580(7801), 60–64 (2020)

    Bhaskar,M.K.,Riedinger,R.,Machielse,B.,Levonian,D.S.,Nguyen,C.T.,Knall, E.N., Park, H., Englund, D., Lončar, M., Sukachev, D.D.: Experimental demon- stration of memory-enhanced quantum communication. Nature580(7801), 60–64 (2020)

    2020

  28. [28]

    Physical Review B 89(23), 235101 (014)

    Rogers, L.J., Jahnke, K.D., Doherty, M.W., Dietrich, A., McGuinness, L.P., Müller, C., Teraji, T., Sumiya, H., Isoya, J., Manson, N.B.: Electronic structure of the negatively charged silicon-vacancy center in diamond. Physical Review B 89(23), 235101 (014)

  29. [29]

    Physical review letters77(14), 3041 (1996)

    Goss, J., Jones, R., Breuer, S., Briddon, P., Öberg, S.: The twelve-line 1.682 ev luminescence center in diamond and the vacancy-silicon complex. Physical review letters77(14), 3041 (1996)

    1996

  30. [30]

    Physical Review Applied5(4), 044010 (2016)

    Evans, R.E., Sipahigil, A., Sukachev, D.D., Zibrov, A.S., Lukin, M.D.: Narrow- linewidth homogeneous optical emitters in diamond nanostructures via silicon ion implantation. Physical Review Applied5(4), 044010 (2016)

    2016

  31. [31]

    Physical Review B94(4), 045203 (2016)

    Arend, C., Becker, J.N., Sternschulte, H., Steinmüller-Nethl, D., Becher, C.: Photoluminescence excitation and spectral hole burning spectroscopy of silicon vacancy centers in diamond. Physical Review B94(4), 045203 (2016)

    2016

  32. [32]

    Proceedings of the National Academy of 12 Sciences114(43), 11362–11367 (2017)

    Pichler, H., Choi, S., Zoller, P., Lukin, M.D.: Universal photonic quantum com- putation via time-delayed feedback. Proceedings of the National Academy of 12 Sciences114(43), 11362–11367 (2017)

    2017

  33. [33]

    Physical Review X10(2), 021071 (2020)

    Borregaard, J., Pichler, H., Schröder, T., Lukin, M.D., Lodahl, P., Sørensen, A.S.: One-way quantum repeater based on near-deterministic photon-emitter interfaces. Physical Review X10(2), 021071 (2020)

    2020

  34. [34]

    Physical Review Letters129(5), 053603 (2022) 13

    Knall, E.N., Knaut, C.M., Bekenstein, R., Assumpcao, D.R., Stroganov, P.L., Gong, W., Huan, Y.Q., Stas, P.-J., Machielse, B., Chalupnik, M.,et al.: Efficient source of shaped single photons based on an integrated diamond nanophotonic system. Physical Review Letters129(5), 053603 (2022) 13

    2022