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Subradiant Dimer Excitations of Emitter Chains Coupled to a 1D Waveguide

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Pith's one-line read Dimer states of two nearby excitations in an emitter chain coupled to a 1D waveguide can decay more slowly than even the most subradiant single-excitation state, and become perfectly subradiant in the infinite-chain limit.

desk verdict A solid waveguide-QED paper with a real analytical technique and a genuine subradiant-dimer claim; the printed qII sign is wrong and the k>π/4 domain needs clarification, but the central result holds. read the letter →

arxiv 1908.01818 v2 pith:2Y7QEPZG submitted 2019-08-05 quant-ph

Yu-Xiang Zhang , Chuan Yu , Klaus M{o}lmer This is my paper · ORCID
classification quant-ph PACS 42.50.Nn
keywords subradianceemitterchainsone-dimensionalwaveguidetwo-excitationdimersconfinement-localizationmappingdefect-localizedstatescollectivedecayquantumoptics
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

The paper claims that two nearby excited emitters in a chain coupled to a one-dimensional waveguide can form subradiant dimer states whose collective decay is slower than that of any state with a single excitation. This contradicts the common expectation that more excitations necessarily decay faster, and it shows that emitter saturation does not merely perturb few-excitation physics but can create a new protection mechanism. For infinite chains the dimers have exactly zero decay rate in the effective model, with analytical expressions for their energies and spatial profiles. The authors explain the mechanism through a mapping that identifies a dimer with a single excitation localized around an unoccupied site, and they extend the same argument to chains emitting into three-dimensional free space, where the dimers keep finite but strongly suppressed decay rates.

What carries the argument

The argument is carried by the effective non-Hermitian Hamiltonian $H_{\mathrm{eff}}$ plus a confinement-localization mapping. Acting on dimer basis states $|K;\Delta\rangle$ with center-of-mass wave number $K$ and separation $\Delta$, $H_{\mathrm{eff}}$ reduces for infinite chains to a matrix $H^K_{\Delta,\Delta'}$ acting only on the relative coordinate. The paper proves that eigenstates of $H^K$ with positive separations are in one-to-one correspondence with even-parity eigenstates of a defect Hamiltonian $H^K_{\mathrm{def}}$, which describes a single excitation localized around an empty site. Since an excited emitter blocks a second excitation on the same site, each excitation acts as a defect that localizes the other, explaining the dimer's stability. The mapping also shows that type-II dimers at $K=\pi/d$ are equivalent to type-I dimers at $K=0$ after replacing $d$ by $2d$ and applying alternating sign flips, and it extends by linearity to Hamiltonians of the form $\int d\mu(k_{1\mathrm{D}})H_{\mathrm{eff}}(k_{1\mathrm{D}})$, covering coupling to 3D free-space modes.

What would settle it

Prepare an $N=48$ emitter chain with spacing $k_{1\mathrm{D}}d=0.1676\pi$, initialize the type-II dimer (two excitations separated by $2d$ with center-of-mass quasimomentum $\pi/d$), and measure the decay rate of the two-excitation population alongside the most subradiant one-excitation state; if the dimer decays faster, the central claim is wrong. The prediction is sharpest at $k_{1\mathrm{D}}d=\pi/6$, where the dimer rate should fall faster than $N^{-3}$ as $N$ grows.

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Extended reading notes

Core claim

The paper establishes that the non-Hermitian Hamiltonian $H_{\mathrm{eff}} = -\frac{i}{2}\Gamma_{1\mathrm{D}}\sum_{m,n}e^{ik_{1\mathrm{D}}|z_m-z_n|}\sigma_m^\dagger\sigma_n$ has, in the two-excitation sector, two families of subradiant dimer eigenstates. Type-I dimers have center-of-mass wave number $K\approx0$ and dominant separation $\Delta=d$; type-II dimers have $K\approx\pi/d$ and dominant separation $\Delta=2d$. For infinite chains, these eigenvalues are real: $\omega_\mathrm{I}=2\Gamma_{1\mathrm{D}}\cot(k_{1\mathrm{D}}d)$ and $\omega_\mathrm{II}=2\Gamma_{1\mathrm{D}}\cot(2k_{1\mathrm{D}}d)$, with separation distributions $p_\mathrm{I}(\Delta)\propto(\cos k_{1\mathrm{D}}d)^{2\Delta/d}$ and $p_\mathrm{II}(\Delta)\propto(\cos2k_{1\mathrm{D}}d)^{\Delta/d}$ on even separations. On finite chains the decay rates are small but nonzero, and exact diagonalization shows that for $k_{1\mathrm{D}}d\simeq0.1676\pi$ a chain of $N=48$ emitters already supports a type-II dimer whose minimal decay rate is smaller than that of the most subradiant fermionic two-excitation state and of the most subradiant one-excitation state, whose rate at this spacing scales as $N^{-3}$.

Load-bearing premise

The central claim rests on the effective model in which the waveguide is eliminated to give emitters instantaneous, distance-dependent interactions and decay (the Born-Markov approximation with a linear dispersion); if non-Markovian retardation or band curvature is significant, the predicted vanishing dimer decay rates are not guaranteed.

Editorial extensions

If this is right

  • A finite chain of about 50 emitters with spacing $k_{1\mathrm{D}}d\simeq0.1676\pi$ should already show a two-excitation state decaying more slowly than the best single-excitation state, giving an experimentally accessible signature of the effect.
  • At $k_{1\mathrm{D}}d=\pi/6$ the type-II dimer decay rate dips sharply and falls faster than $N^{-3}$, so increasing chain length can produce a qualitatively stronger lifetime boost than the standard one-excitation scaling.
  • At $k_{1\mathrm{D}}d=\pi/4$ the type-II dimer becomes an eigenstate of both total momentum and relative position, a travelling EPR-like two-excitation state with no amplitude for separations beyond $2d$.
  • Because the mapping is linear, chains coupled to 3D free-space vacuum fields also support subradiant dimers; their decay rates remain finite in the infinite-chain limit but are strongly suppressed, for both transverse and parallel emitter polarizations.
  • Proposed verification: excite emitters around a missing or suitably perturbed site to address the single-defect localized state, or use interactions to prepare correlated dimers; the long-lived state should survive as orthogonal modes decay.

Reading between the lines

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

  • The defect picture suggests a direct experimental test of the mechanism: compare the decay of a single excitation next to a missing site with that of a dimer with the same effective separation; the mapping predicts matching exponential suppression governed by the shorter side of the chain.
  • The sharp dip at $k_{1\mathrm{D}}d=\pi/6$ may reflect a commensurability between the dimer bond length and the resonant wavelength, so varying the chain length modulo four emitters (a half-wavelength) could be used to steer the decay rate in finite systems.
  • If the confinement-localization equivalence holds in other lattice models with long-range hopping, two-particle bound states in cold-atom, ion, or Rydberg arrays might be designed to inherit defect-mode lifetimes, turning 'anti-blockade' into a resource rather than a loss channel.
  • One could test the non-Markovian sensitivity by repeating the exact diagonalization with a finite-bandwidth waveguide dispersion; the dimer decay rates should generically acquire corrections, and the perfect subradiance at $k_{1\mathrm{D}}d=\pi/6$ would be the first quantity to move.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript studies two-excitation eigenstates of the effective non-Hermitian Hamiltonian (1) for a chain of two-level emitters coupled to a one-dimensional waveguide. It identifies two families of 'dimer' states, derives exponential separation distributions for their amplitudes, Eqs. (3) and (4), and shows that on infinite chains these states have real eigenvalues, i.e., vanishing decay rates. The authors also present a formal mapping between these confined dimer states and single-excitation states localized around an unoccupied defect site, and they extend the mapping to emitter chains coupled to the three-dimensional free-space field. For finite chains, numerical diagonalization of Heff shows that type-II dimer states can have decay rates below those of the most subradiant fermionic states and even below the most subradiant one-excitation states in a narrow parameter window around k1Dd ≈ 0.1676π, with unusual non-monotonic dependence on emitter number N.

Significance. If the central claims hold, this is a significant result: two-excitation subradiant states that outlive the best single-excitation states challenge a common expectation, and the confinement-localization mapping is elegant and potentially generalizable. The Letter is largely self-contained: the analytical expressions are derived from the stated Hamiltonian without fitted parameters and are compared with direct numerical diagonalization, and the finite-chain benchmark at k1Dd = 0.1676π is clearly identified. However, the infinite-chain claims currently rest on an incorrectly printed exponent and an unstated domain restriction, so the paper needs revision before the result can be fully assessed.

major comments (3)
  1. [Subradiant dimer excited states, Eq. (4)] The main-text expression qIId = [π + i ln cos(2k1Dd)]/2 has the wrong sign for the imaginary part. With this sign, |e^{iqII Δ/d}| = (cos 2k1Dd)^{-Δ/(2d)}, which grows with Δ and makes the type-II state non-normalizable. The supplemental expression qII = π − (i/2) ln cos(2k1Dd) repairs the sign and is consistent with the stated probability pII(Δ) ∝ (cos 2k1Dd)^{Δ/d}, but the printed main-text formula contradicts its own Eq. (4). This error is load-bearing because the exponential localization of the type-II dimer is the basis for the infinite-chain eigenvalue ωII = 2Γ1D cot(2k1Dd).
  2. [Subradiant dimer excited states and Figs. 2–3] The type-II ansatz with the real (cos 2k1Dd)^{Δ/d} weighting is defined only when cos(2k1Dd) > 0, i.e., 0 < k1Dd < π/4. The paper states the lattice domain as 0 < k1Dd < π/2 and plots type-II data up to k1Dd = 0.4π in Figs. 2 and 3, while the unqualified claim of perfectly subradiant dimers on infinite chains and the EPR discussion at k1Dd = 0.25π rely on the branch where cos(2k1Dd) < 0. The region k1Dd > π/4 must either be explicitly excluded from the infinite-chain analytical statements and the affected figure ranges, or a continuation analysis must be provided. As written, the statement that these dimers are perfectly subradiant on infinite chains is not supported in that region.
  3. [Confinement-localization mapping and Supplemental Sec. H] The equivalence H^{π/d}_{def}(k1Dd) ≅ H^{0}_{def}(2k1Dd) used to derive the type-II states inherits the same restriction on 2k1Dd. The supplemental derivation of qII and ωII is therefore valid only for 0 < k1Dd < π/4. The paper should state this restriction explicitly where the type-II asymptotic eigenvalue is quoted, since the unqualified 'vanishing decay rates on infinite chains' statement appears in the main text before the defect mapping is introduced.
minor comments (5)
  1. [Subradiant dimer excited states] In the sentence introducing Eq. (4), the prime on the summation is said to include only even values of Δ/d, but the notation is not defined until later; please define the prime explicitly at first use.
  2. [Fig. 2 caption] The caption reads 'emitter number' in the axis label; please write 'emitter number N' or simply 'N' to avoid ambiguity with the separation Δ.
  3. [References] Ref. [31] is cited as 'Supplemental Material' without an arXiv or journal anchor; please state where the supplement is available or include it as a clearly labelled appendix.
  4. [Conclusions] The phrase 'unwritten orthodoxy' is informal for a Letter; consider replacing it with 'common expectation' or 'common assumption'.
  5. [Spin Model, Eq. (1)] The right-hand side of Eq. (1) is an operator expression, but the ordering of σ_m^† and σ_n is conventional; please specify that this is the Born-Markov reduced Hamiltonian with normal ordering and state any sign convention explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the dimer states, their eigenvalues, and the confinement-localization mapping are derived from the effective Hamiltonian and checked against exact diagonalization.

full rationale

I walked the derivation chain from the effective Hamiltonian Heff (Eq. 1) through the dimer ansatze and the confinement-localization mapping. The type-I and type-II wave vectors qI and qII are not fitted or renamed inputs; they are obtained by solving the eigenvector condition derived in Supplement B, where Eq. (3) yields q = -i ln cos(k1Dd) and the analogous type-II solution is obtained by the same construction. These analytical expressions are then compared with exact numerical diagonalization, so the comparison is not circular. The mapping from HK to H^K_def is proved algebraically in Supplement F rather than assumed, and the resulting equivalence is used to explain, not to define, the dimer states. Reference [18] is self-cited but is used for context and for the fermionic-state comparison and the 3D free-space kernel; it does not supply the dimer wavefunctions or eigenvalues, and the paper explicitly notes that the Holstein-Primakoff analysis of [18] does not reveal the dimer mechanism. There are no fitted parameters, and no 'prediction' is constructed from the quantity it claims to predict. The possible domain restriction for type-II states when cos(2k1Dd) < 0 is a mathematical correctness caveat, not a circularity, and does not affect the circularity score.

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

No free parameters are fitted; Γ1D, k1D, d, and N are physical inputs to the model. The analysis assumes the Born-Markov/linear-dispersion effective model, standard in waveguide QED. No new particles, forces, or dimensions are introduced.

assumptions (4)
  • domain assumption Born-Markov approximation and adiabatic elimination of the waveguide modes yield the non-Hermitian spin Hamiltonian Eq. (1).
    Invoked in the 'Spin Model' section with citation to Ref. [33]; all subsequent subradiance claims are made within this effective description.
  • domain assumption The waveguide modes have a linear dispersion, so the interaction phase is e^{i k1D |z_m - z_n|}.
    Stated in the 'Spin Model' section; required for the translation-invariant form of H_eff and for the existence of the K-conserving sectors.
  • standard math In the infinite-chain limit, the 'tails' in Eq. (5) vanish, so H_K fully determines the two-excitation eigenstates for a given center-of-mass wave number K.
    The tails involve sums restricted to intervals of length Δ at the chain ends; they vanish as N→∞, but the limiting argument is asserted rather than proven in full detail.
  • standard math The localized ansatz with positive imaginary part for q, leading to e^{iqNd} ≈ 0 for large N, gives the correct bound-state solution.
    Used in Sec. B of the supplement to solve for q_I = -i ln cos(k1Dd); this is the standard exponential-decay boundary condition for localized states.

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Pith. "Pith review of Subradiant Dimer Excitations of Emitter Chains Coupled to a 1D Waveguide." pith.science (2026). https://pith.science/paper/2Y7QEPZG

@misc{pith2026190801818,
  author       = {Pith},
  title        = {Pith review of: Subradiant Dimer Excitations of Emitter Chains Coupled to a 1D Waveguide},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2Y7QEPZG}},
  note         = {Machine review of arXiv:1908.01818}
}
read the original abstract

This Letter shows that chains of optical or microwave emitters coupled to a 1D waveguide support subradiant states with close pairs of excited emitters, which have longer lifetimes than even the most subradiant states with only a single excitation. Exact, analytical expressions for non-radiative excitation dimer states are obtained in the limit of infinite chains. To understand the mechanism underlying these states, we present a formal equivalence between subradiant dimers and single localized excitations around a chain defect (unoccupied site). Our analytical mapping permits extension to emitter chains coupled to the 3D free space vacuum field.

Figures

Figures reproduced from arXiv: 1908.01818 by the authors.

Figure 1
Figure 1. (a) A chain of two-level emitters couple to a 1D [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Decay rates of the most subradiant type-II dimers [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Decay rates of the most subradiant type-II dimer [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: (a) The confinement of excitation pairs is equiva [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 2
Figure 2. Figure 2: The dotted (solid) lines show the deviation between [PITH_FULL_IMAGE:figures/full_fig_p007_2.png]
Figure 1
Figure 1. Figure 1: The eigenvalues of the two-excitation sector [PITH_FULL_IMAGE:figures/full_fig_p007_1.png]
Figure 3
Figure 3. Figure 3: Compared with the results for the type-II states, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png]
Figure 3
Figure 3. Figure 3: Decay rates of the most subradiant type-I dimer [PITH_FULL_IMAGE:figures/full_fig_p008_3.png]
Figure 4
Figure 4. Figure 4: Effects of spatial disorder on the decay rates of the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Bottom panels: phase profiles of the localized [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Inelastic scattering of photon pairs in qubit arrays with subradiant states

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    Photon-pair scattering in qubit arrays is resonantly enhanced at double-excited subradiant states, and newly identified twilight states generate long-lived photon-photon correlations.

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Works this paper leans on

50 extracted references · 34 canonical work pages · cited by 1 Pith paper

  1. [18]

    Zhang and K

    Y.-X. Zhang and K. Mølmer, Phys. Rev. Lett. 122, 203605 (2019)

    2019

  2. [1]

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

    1954

  3. [2]

    Guerin, M

    W. Guerin, M. O. Ara´ ujo, and R. Kaiser, Phys. Rev. Lett. 116, 083601 (2016)

    2016

  4. [3]

    Weiss, M

    P. Weiss, M. O. Ara´ ujo, R. Kaiser, and W. Guerin, New J. Phys. 20, 063024 (2018)

    work page 2018

  5. [4]

    S. D. Jenkins, J. Ruostekoski, N. Papasimakis, S. Savo, and N. I. Zheludev, Phys. Rev. Lett. 119, 053901 (2017)

    work page 2017

  6. [5]

    Paulisch, H

    V. Paulisch, H. Kimble, and A. Gonz´ alez-Tudela, New J. Phys. 18, 043041 (2016)

    work page 2016

  7. [6]

    H. R. Haakh, S. Faez, and V. Sandoghdar, Phys. Rev. A 94, 053840 (2016)

    work page 2016

  8. [7]

    Ruostekoski and J

    J. Ruostekoski and J. Javanainen, Phys. Rev. Lett. 117, 143602 (2016)

    2016

Show all 50 references
  1. [8]

    Ruostekoski and J

    J. Ruostekoski and J. Javanainen, Phys. Rev. A 96, 033857 (2017)

    2017

  2. [9]

    Zoubi, Phys

    H. Zoubi, Phys. Rev. A 89, 043831 (2014)

    2014

  3. [10]

    D. F. Kornovan, A. S. Sheremet, and M. I. Petrov, Phys. Rev. B 94, 245416 (2016)

    2016

  4. [11]

    R. T. Sutherland and F. Robicheaux, Phys. Rev. A 94, 013847 (2016)

    2016

  5. [12]

    Olmos, D

    B. Olmos, D. Yu, Y. Singh, F. Schreck, K. Bongs, and I. Lesanovsky, Phys. Rev. Lett. 110, 143602 (2013)

    2013

  6. [13]

    R. J. Bettles, S. A. Gardiner, and C. S. Adams, Phys. Rev. A 94, 043844 (2016)

    2016

  7. [14]

    H. H. Jen, M.-S. Chang, and Y.-C. Chen, Phys. Rev. A 94, 013803 (2016)

    2016

  8. [15]

    Asenjo-Garcia, M

    A. Asenjo-Garcia, M. Moreno-Cardoner, A. Albrecht, H. J. Kimble, and D. E. Chang, Phys. Rev. X 7, 031024 (2017)

    2017

  9. [16]

    Albrecht, L

    A. Albrecht, L. Henriet, A. Asenjo-Garcia, P. B. Dieterle, O. Painter, and D. E. Chang, New J. Phys. 21, 025003 (2019)

    2019

  10. [17]

    Henriet, J

    L. Henriet, J. S. Douglas, D. E. Chang, and A. Albrecht, Phys. Rev. A 99, 023802 (2019)

    2019

  11. [19]

    Solano, P

    P. Solano, P. Barberis-Blostein, F. K. Fatemi, L. A. Orozco, and S. L. Rolston, Nat. Commun. 8, 1857 (2017)

    2017

  12. [20]

    Asenjo-Garcia, H

    A. Asenjo-Garcia, H. J. Kimble, and D. E. Chang, arXiv:1906.02204

    1906 arXiv

  13. [21]

    D. F. Kornovan, N. V. Corzo, J. Laurat, and A. S. Sheremet, arXiv:1906.07423

    1906 arXiv

  14. [22]

    Zhang, X

    A. Zhang, X. Chen, V. V. Yakovlev, and L. Yuan, arXiv:1907.07252

    1907 arXiv

  15. [23]

    B. X. Wang and C. Y. Zhao, Phys. Rev. A 98, 023808 (2018)

    2018

  16. [24]

    Perczel, J

    J. Perczel, J. Borregaard, D. E. Chang, H. Pichler, S. F. Yelin, P. Zoller, and M. D. Lukin, Phys. Rev. Lett. 119, 023603 (2017)

    2017

  17. [25]

    Facchinetti, S

    G. Facchinetti, S. D. Jenkins, and J. Ruostekoski, Phys. Rev. Lett. 117, 243601 (2016)

    2016

  18. [26]

    Guimond, A

    P.-O. Guimond, A. Grankin, D. V. Vasilyev, B. Vermer- sch, and P. Zoller, Phys. Rev. Lett. 122, 093601 (2019)

    2019

  19. [27]

    J. A. Needham, I. Lesanovsky, and B. Olmos, arXiv:1905.00508

    1905 arXiv

  20. [28]

    Moreno-Cardoner, D

    M. Moreno-Cardoner, D. Plankensteiner, L. Ostermann, D. E. Chang, and H. Ritsch, Phys. Rev. A 100, 023806 (2019)

    2019

  21. [29]

    P. S. Lee and Y. C. Lee, Phys. Rev. A 8, 1727 (1973)

    1973

  22. [30]

    Porras and J

    D. Porras and J. I. Cirac, Phys. Rev. A78, 053816 (2008)

    2008

  23. [31]

    Supplemental Material

  24. [32]

    This is reminiscent of the recent theoretical discovery of a range of different power law dependences of the decay rates of single excitation states for very specific values of the atomic distances [21]

  25. [33]

    H. T. Dung, L. Kn¨ oll, and D.-G. Welsch, Phys. Rev. A 66, 063810 (2002)

    2002

  26. [34]

    D. E. Chang, L. Jiang, A. Gorshkov, and H. Kimble, New J. Phys. 14, 063003 (2012)

    2012

  27. [35]

    Caneva, M

    T. Caneva, M. T. Manzoni, T. Shi, J. S. Douglas, J. I. Cirac, and D. E. Chang, New J. Phys. 17, 113001 (2015)

    2015

  28. [36]

    D. Roy, C. M. Wilson, and O. Firstenberg, Rev. Mod. Phys. 89, 021001 (2017)

    2017

  29. [37]

    X. Zang, J. Yang, R. Faggiani, C. Gill, P. G. Petrov, J.- P. Hugonin, K. Vynck, S. Bernon, P. Bouyer, V. Boyer, and P. Lalanne, Phys. Rev. Applied 5, 024003 (2016)

    2016

  30. [38]

    D. E. Chang, J. S. Douglas, A. Gonz´ alez-Tudela, C.-L. Hung, and H. J. Kimble, Rev. Mod. Phys. 90, 031002 (2018)

    2018

  31. [39]

    Astafiev, A

    O. Astafiev, A. Zagoskin, A. Abdumalikov, Y. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. Tsai, Science 327, 840 (2010)

    2010

  32. [40]

    I.-C. Hoi, C. M. Wilson, G. Johansson, T. Palomaki, B. Peropadre, and P. Delsing, Phys. Rev. Lett. 107, 073601 (2011)

    2011

  33. [41]

    A. F. Van Loo, A. Fedorov, K. Lalumi` ere, B. C. Sanders, A. Blais, and A. Wallraff, Science 342, 1494 (2013)

    2013

  34. [42]

    Mirhosseini, E

    M. Mirhosseini, E. Kim, X. Zhang, A. Sipahigil, P. B. Dieterle, A. J. Keller, A. Asenjo-Garcia, D. E. Chang, and O. Painter, Nature 569, 692 (2019)

    2019

  35. [43]

    Mølmer, Y

    K. Mølmer, Y. Castin, and J. Dalibard, J. Opt. Soc. Am. B 10, 524 (1993)

    1993

  36. [44]

    Hernandez, J

    V. Hernandez, J. E. Roman, and V. Vidal, ACM Trans. Math. Software 31, 351 (2005)

    2005

  37. [45]

    Stewart, SIAM J

    G. Stewart, SIAM J. Matrix Anal. Appl. 23, 601 (2002)

    2002

  38. [46]

    Saad, Numerical Methods for Large Eigenvalue Prob- lems (Society for Industrial and Applied Mathematics, 2011)

    Y. Saad, Numerical Methods for Large Eigenvalue Prob- lems (Society for Industrial and Applied Mathematics, 2011)

    2011

  39. [47]

    Einstein, B

    A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 6 777 (1935)

    1935

  40. [48]

    J. S. Douglas, T. Caneva, and D. E. Chang, Phys. Rev. X 6, 031017 (2016)

    2016

  41. [49]

    Gonz´ alez-Tudela, V

    A. Gonz´ alez-Tudela, V. Paulisch, D. E. Chang, H. J. Kimble, and J. I. Cirac, Phys. Rev. Lett. 115, 163603 (2015)

    2015

  42. [50]

    F. Liu, R. Lundgren, P. Titum, G. Pagano, J. Zhang, C. Monroe, and A. V. Gorshkov, Phys. Rev. Lett. 122, 150601 (2019). 7 SUPPLEMENTAL MATERIAL A. Distributions of the eigenvalues in the two-excitation sector The fermionic states and the dimers constitute all the subradiant st...

    2019

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