Pith. sign in

REVIEW 3 major objections 6 minor 63 references

Correlation Localization in Waveguide QED with Delayed Interactions

T0 review · 3 major / 6 minor · reviewed 2026-07-09 · glm-5.2

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Photon delay traps correlations: ξ scales as (γτ)^{-1/2}

desk verdict Clean power-law scaling for correlation localization in delayed waveguide QED, but finite-size control of the numerics is thin and the steady state requires idealized conditions read the letter →

arxiv 2607.06888 v1 pith:HP2GY5CS submitted 2026-07-08 quant-ph physics.atom-ph

N. Vera , F. M. Quinteros , P. Barberis-Blostein , P. Solano This is my paper · ORCID
classification quant-phphysics.atom-ph PACS 42.50.Nn42.50.Ct03.67.-a
keywords correlationwaveguideatomatom-atomdelayedexcitationexcitedinteractions
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

This paper studies a one-dimensional array of atoms coupled to a waveguide, where adjacent atoms are spaced so that the photon propagation phase between them satisfies the Bragg condition (a mirror-like resonance). When one atom is initially excited, the excitation partially spreads through the array via photon-mediated interactions. In the standard Markovian limit—where photon travel time is treated as negligible—the excitation distributes evenly across all atoms. The authors show that when the finite photon propagation time τ between neighbors is retained (a non-Markovian, delay-differential regime), a fraction of the excitation instead remains trapped near the initially excited atom. The atom-atom correlation function decays exponentially with distance from the central atom, defining a correlation length ξ. The central analytical result is that this correlation length obeys a power law: ξ is proportional to (γτ)^{-1/2}, where γ is the single-atom decay rate into the waveguide. This scaling is derived by substituting an evanescent Bloch-wave ansatz into the delay equations of motion and expanding in the short-delay limit, yielding a localization length set by the geometric mean of the photon coherence time γ^{-1} and the delay time τ. The power law is confirmed numerically (ξ ~ (γτ)^{-0.48}). Positional disorder further shortens the correlation length, with delay and disorder acting as independent but combinable localization mechanisms.

What carries the argument

The machinery consists of delay-differential equations of motion for the atomic excitation amplitudes β_j(t), which include retarded arguments β_{j'}(t − τ_{j,j'}) weighted by Bragg-condition phase factors e^{-iω₀τ}. The correlation length is extracted from the spin-spin correlation function g(j) = ⟨σ₀^(z) σ_j^(z)⟩ − ⟨σ₀^(z)⟩⟨σ_j^(z)⟩, which decays exponentially as e^{-|j|/ξ}. The power-law scaling is derived by inserting a Bloch-wave ansatz with imaginary wavevector (evanescent profile) into the delay equations, evaluating the resulting geometric series in the dispersion relation, and expanding in the short-delay limit |η| ≪ 1 to obtain κd ≈ √(2γτ), giving ξ ∝ (κd)^{-1} ∝ (γτ)^{-1/2}.

What would settle it

If the Bragg condition is not exactly satisfied or if atoms couple to non-guided modes, the retained excitation would eventually decay and no true steady-state correlation length would exist, making the power-law scaling inapplicable to the asymptotic regime.

Watch

Extended reading notes

Core claim

The central discovery is that delayed photon-mediated interactions in a Bragg-configured waveguide-QED array cause steady-state atom-atom correlations to localize exponentially around the initially excited atom, with a correlation length that scales as the inverse square root of the dimensionless delay parameter γτ. This is distinct from the Markovian regime, where correlations spread uniformly across the entire array. The scaling ξ ∝ (γτ)^{-1/2} emerges analytically from the structure of the delay-differential equations under the Bragg condition, connecting the photon coherence time to the spatial extent of correlation confinement.

Load-bearing premise

The existence of a true steady state with non-zero retained excitation depends on the Bragg condition (the photon propagation phase between adjacent atoms being an exact multiple of 2π) combined with perfect coupling of atoms to the guided modes and no loss to unguided radiation. The authors acknowledge that deviations from either condition introduce additional decay channels that prevent a true steady state, reducing the localization to a transient quasi-stationary effect to

Editorial extensions

If this is right

  • The power-law scaling ξ ∝ (γτ)^{-1/2} provides a tunable knob for controlling the spatial range of correlations and entanglement in waveguide-QED arrays by adjusting interatomic spacing (and thus τ) or by engineering the waveguide group velocity v.
  • Because the Markovian limit is never perfectly realized in extended arrays, the intrinsic delay-induced localization identified here sets a practical lower bound on correlation transport even in nominally Markovian systems, affecting quantum network design.
  • The interplay between delay-induced localization and disorder-induced Anderson-like localization suggests a two-parameter landscape for engineering localized quantum states, potentially relevant for decoherence-free subspaces and quantum memory protocols.
  • The resemblance to bound states in the continuum (BIC) in extended arrays opens a path toward photonic bound states in non-Markovian many-emitter systems, which remain experimentally and theoretically unexplored beyond few-atom configurations.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. This manuscript studies atom-atom correlations in a finite array of atoms coupled to a waveguide under the Bragg condition, focusing on the regime where the photon propagation delay between adjacent atoms is non-negligible. Starting from a single centrally excited atom, the authors solve the delay-differential equations of motion (Eq. 3) numerically and find that the steady-state excitation localizes near the initially excited atom. The central quantitative result is that the spin-spin correlation length $g(j) = e^{-|j|/ξ}$ scales as $ξ ∝ (γτ)^{-1/2}$, which is derived analytically in the Supplemental Material (Eqs. S14–S22) via a Bloch-wave ansatz on an infinite lattice and confirmed numerically (Fig. 4, giving exponent $-0.48$). The paper also examines the interplay between delay-induced localization and positional disorder (Fig. 5).

Significance. The paper addresses a timely question in waveguide QED: how retardation effects modify correlation transport in collective atomic arrays. The analytical derivation of the power-law scaling $ξ ∝ (γτ)^{-1/2}$ is a genuine strength—it is parameter-free, follows from a standard Bloch ansatz into the exact delay equation, and the geometric series evaluation is exact. The numerical exponent $-0.48$ agrees well with the analytical $-1/2$. The study of disorder-induced localization and its interplay with delay is a natural extension. The results are falsifiable and the model is clearly specified. The main conceptual novelty is the identification of a steady-state (rather than transient) correlation localization mechanism in non-chiral wQED, which connects to broader localization phenomena.

major comments (3)
  1. Finite-size control for the power-law fit (Fig. 4 and Supplemental Eq. S22): The analytical derivation assumes an infinite, translationally invariant lattice (the sum in Eq. S18 runs from $-∞$ to $+∞$), but the numerics use $N=21$ with open boundaries and a central initially excited atom. The manuscript states that 'the simulation ensures that the solution converges and that boundary effects are eliminated,' but provides no quantitative evidence. At the smallest delays in the fit range ($γτ ≈ 0.01$), the predicted $ξ ≈ 10$ is comparable to the half-array size of 10 sites, meaning the correlation function $g(j)$ may be truncated before reaching the asymptotic regime. This could artificially flatten the fitted slope. The authors should either (a) demonstrate convergence by showing that the fitted exponent is stable when $N$ is increased (e.g., $N=31, 41$), or (b) restrict the fit range toγ
  2. Steady-state existence and robustness: The true steady state with non-zero excitation retention depends critically on the exact Bragg condition ($ω_0 τ = 2π$) and perfect emitter-waveguide coupling (no loss to non-guided modes). The Discussion acknowledges that deviations lead to eventual excitation loss, but the main text and figures present the localization as a steady-state phenomenon without quantifying how sensitive the power-law scaling is to small deviations from the Bragg condition. Since the Bragg condition $ω_0 τ = 2π$ ties the delay to the atomic frequency, it would strengthen the paper to show (even briefly) how the correlation length behaves for a small detuning from the Bragg condition, or to state explicitly that the power-law applies only in the quasi-stationary window.
  3. Disorder section (Fig. 5): The disorder study states that 'arbitrarily close to the Bragg condition, the atomic excitation always decays at infinitely long times; however, this decay is slow enough to allow us to compute the correlation lengths at long times as a quasi-stationary process.' However, no timescale or criterion for 'long times' is specified, and it is unclear whether the quasi-stationary $ξ$ depends on the measurement time. The authors should specify the time at which $ξ$ is extracted and demonstrate that it is in a well-defined quasi-stationary plateau, or at least state the sensitivity of the extracted $ξ$ to this choice.
minor comments (6)
  1. The disorder scaling exponents in Fig. 5 are described as $σ^{-0.75}, σ^{-0.5}, σ^{-0.3}, σ^{-0.2}$ 'with increasing τ,' but the specificτ values corresponding to each curve are not labeled in the figure or caption. Please add labels.
  2. In the caption of Fig. 4, the inset is described as showing 'the exponential fit to the spin-spin correlation function for the point indicated by an arrow,' but no arrow is visible in the main panel. Please add the arrow or clarify.
  3. The Markovian steady-state formula $|β_c(t→∞)|^2 = ((N-1)/N)^2$ is given in the main text; the Supplemental Material derives it (Eq. S12), but the main text does not clearly state that this is for the initially excited atom specifically. A brief clarification would help.
  4. The phrase 'the localization effects stem from the interplay between the interaction delay timeτand the temporal coherence length of the spontaneously emitted photons, given by $γ^{-1}$' could be made more precise: the scaling $ξ ∝ (γτ)^{-1/2}$ is dimensionally $√(γτ)$ in the denominator, but the physical interpretation of the geometric mean is not elaborated.
  5. Reference [16] is cited as 'Phys. Rev. A113, 013701 (2026)' — please verify the year and volume.
  6. The notation $g^{(6)}$ in the inset of Fig. 4 is unclear; the main text defines $g(j)$ in Eq. (5) without a superscript. Please reconcile.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: power-law scaling derived analytically from delay-differential equations, confirmed independently by numerics

full rationale

The paper's central result—the power-law scaling ξ ∝ (γτ)^{-1/2}—is derived analytically in the Supplemental Material (Eq. S22) from the delay-differential equations of motion (Eq. S6) without introducing any fitted parameters. The derivation proceeds by substituting a standard Bloch-wave ansatz into the equations, evaluating a geometric series exactly (Eq. S20), and expanding in the short-delay limit (|η|≪1, κd≪1) to obtain κd ≃ √(2γτ), yielding ξ ∝ (γτ)^{-1/2}. No step in this chain reduces to its own inputs by construction. The numerical simulations (Fig. 4, showing ξ ∼ (γτ)^{-0.48}) serve as independent confirmation and are not used to derive or fit the exponent. The Markovian steady-state formula |β_c|² = ((N-1)/N)² is likewise derived from the eigenvector decomposition of the decay matrix (Eqs. S10–S13) without circularity. Self-citations (e.g., to [57] for the non-Markovian derivation method, to [56] for Markovian eigenvector structure) reference standard techniques or prior results that are not equivalent to the present paper's target claim. The derivation is self-contained against external benchmarks, and no 'prediction' reduces to a fitted input or a self-defitional step. The reader's concern about finite-size effects on the numerical exponent is a correctness/robustness issue, not a circularity issue—the analytical derivation itself is parameter-free and independent of the numerics. Score 0 is warranted: no significant circularity found.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No new physical entities are postulated. The system (atoms + waveguide) is standard in waveguide QED. The localization phenomenon emerges from the known delay-differential equations under known conditions (Bragg spacing). All axioms are domain assumptions standard to the wQED literature, with the Bragg condition and perfect coupling being the most restrictive.

free parameters (3)
  • γτ (delay parameter)
    Not fitted; γ is the single-atom decay rate and τ is the photon propagation time, both physical parameters of the system. The scaling is derived as a function of this dimensionless ratio.
  • N (number of atoms) = 21 (for simulations)
    System size chosen for numerical convergence; not a fitted parameter of the theory.
  • σ (disorder strength)
    Gaussian random deviation from Bragg spacing; scanned as a control parameter, not fitted.
assumptions (5)
  • domain assumption Single-excitation manifold suffices to describe the dynamics
    The state ansatz (Eq. 2) restricts to one excitation shared among atoms and field modes. Justified by the initial condition of a single excited atom and the linearity of the equations in this manifold.
  • domain assumption Bragg condition: ω₀τ = 2π (integer multiple)
    Invoked in Eq. S17 to simplify the phase factors. This is the mirror configuration that enables the steady state. The paper acknowledges deviations break the steady state.
  • domain assumption Perfect coupling to waveguide (no loss to non-guided modes)
    The model assumes γ_1D is the only decay channel. Stated in the text after Eq. 3: 'the only decay channel is into the guided modes.'
  • domain assumption Short-delay expansion |η| ≪ 1, κd ≪ 1 is valid for the scaling regime
    Used in Eq. S22 to expand hyperbolic functions to leading order. The numerical simulations use γτ up to ~0.1, which is in this regime.
  • standard math Weisskopf-Wigner theory of spontaneous emission applies
    Standard quantum optics framework; invoked at the start of the 'Atomic dynamics' section.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Correlation Localization in Waveguide QED with Delayed Interactions." pith.science (2026). https://pith.science/paper/HP2GY5CS

@misc{pith2026260706888,
  author       = {Pith},
  title        = {Pith review of: Correlation Localization in Waveguide QED with Delayed Interactions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HP2GY5CS}},
  note         = {Machine review of arXiv:2607.06888}
}
read the original abstract

We study the atom-atom correlation length in an atomic array coupled to a waveguide under the Bragg condition with delayed non-Markovian interactions caused by a finite photon propagation time. Starting from a single excited atom, the excitation partially spreads among all atoms, reaching a steady state. The remaining excitation localizes near the initially excited atom, and the atom-atom correlation length decreases as a power law with the interaction delay. This localization phenomenon reveals how the delay-induced non-Markovian behavior affects the correlation transport in waveguide QED systems.

Figures

Figures reproduced from arXiv: 2607.06888 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic of an atomic array coupled to a waveguide [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Correlation length [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 63 canonical work pages

  1. [1]

    for a detailed derivation): ˙βj(t) =−γ X j′ e−iω0τj,j′ βj′ (t−τ j,j′) Θ (t−τ j,j′) (3) whereτ j,j′ = |xj −xj′ | v is the delayed interaction time be- tween theith andjth atoms. We conveniently write this expression in a more concise vector form as ˙B(t) =−γDiag [Γ·B(t−τ j,j′)],(4) whereΓis the matrix of elements Γ j,j′ =e −iω0τj,j′ and B(t−τ j,j′) is the ...

    work page 2022

  2. [2]

    Colloquium: Strongly interacting photons in one- dimensional continuum,

    Dibyendu Roy, C. M. Wilson, and Ofer Firsten- berg, “Colloquium: Strongly interacting photons in one- dimensional continuum,” Rev. Mod. Phys.89, 021001 (2017)

    work page 2017

  3. [3]

    Colloquium: Quantum matter built from nanoscopic lattices of atoms and photons,

    D. E. Chang, J. S. Douglas, A. Gonz´ alez-Tudela, C.-L. Hung, and H. J. Kimble, “Colloquium: Quantum matter built from nanoscopic lattices of atoms and photons,” Rev. Mod. Phys.90, 031002 (2018)

    work page 2018

  4. [4]

    Waveguide quantum electrodynamics: collective radiance and photon–photon correlations,

    Alexandra S. Sheremet, Mihail I. Petrov, Ivan V. Iorsh, Alexander V. Poshakinskiy, and Alexander N. Pod- dubny, “Waveguide quantum electrodynamics: collective radiance and photon–photon correlations,” Rev. Mod. Phys.95, 015002 (2023)

    work page 2023

  5. [5]

    Waveguide quantum electrodynamics,

    Francesco Ciccarello, Peter Lodahl, and Dominik Schneble, “Waveguide quantum electrodynamics,” Op- tics & Photonics News35, 34–41 (2024)

    work page 2024

  6. [6]

    Optical interface cre- ated by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,

    E. Vetsch, D. Reitz, G. Sagu´ e, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface cre- ated by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett.104, 203603 (2010)

    work page 2010

  7. [7]

    Optical nanofibres and neutral atoms,

    Thomas Nieddu, Vandna Gokhroo, and S´ ıle Nic Chor- maic, “Optical nanofibres and neutral atoms,” Journal of Optics18, 053001 (2016)

    work page 2016

  8. [8]

    Optical nanofibers: A new platform for quantum optics,

    P. Solano, J. A. Grover, J. E. Hoffman, S. Ravets, F. K. Fatemi, L. A. Orozco, and S. L. Rolston, “Optical nanofibers: A new platform for quantum optics,” Adv. At. Mol. Opt. Phys.66, 439–505 (2017)

    work page 2017

Show all 63 references
  1. [9]

    Light-matter interaction at the transition between cavity and waveguide qed,

    Daniel Lechner, Riccardo Pennetta, Martin Blaha, Philipp Schneeweiss, Arno Rauschenbeutel, and J¨ urgen Volz, “Light-matter interaction at the transition between cavity and waveguide qed,” Phys. Rev. Lett.131, 103603 (2023)

    2023

  2. [10]

    Cavity qed with atomic mirrors,

    D E Chang, L Jiang, A V Gorshkov, and H J Kim- ble, “Cavity qed with atomic mirrors,” New Journal of Physics14, 063003 (2012)

    2012

  3. [11]

    Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions,

    Huaixiu Zheng and Harold U. Baranger, “Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions,” Phys. Rev. Lett.110, 113601 (2013)

    2013

  4. [12]

    Superradiance for atoms trapped along a photonic crystal waveguide,

    A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett.115, 063601 (2015)

    2015

  5. [13]

    Exponential improve- ment in photon storage fidelities using subradiance and “selective radiance

    A. Asenjo-Garcia, M. Moreno-Cardoner, A. Albrecht, H. J. Kimble, and D. E. Chang, “Exponential improve- ment in photon storage fidelities using subradiance and “selective radiance” in atomic arrays,” Phys. Rev. X7, 031024 (2017)

    2017

  6. [14]

    Waveguide-coupled single collective excitation of atomic arrays,

    Neil V. Corzo, J´ er´ emy Raskop, Aveek Chandra, Alexan- dra S Sheremet, Baptiste Gouraud, and Julien Laurat, “Waveguide-coupled single collective excitation of atomic arrays,” Nature566, 359–362 (2019)

    2019

  7. [15]

    Photonic band gaps in one-dimensionally ordered cold atomic vapors,

    Alexander Schilke, Claus Zimmermann, Philippe W. 6 Courteille, and William Guerin, “Photonic band gaps in one-dimensionally ordered cold atomic vapors,” Phys. Rev. Lett.106, 223903 (2011)

    2011

  8. [16]

    Bragg condition for scattering into a guided optical mode,

    B. Olmos, C. Liedl, I. Lesanovsky, and P. Schneeweiss, “Bragg condition for scattering into a guided optical mode,” Phys. Rev. A104, 043517 (2021)

    2021

  9. [17]

    Flat-band-mediated photon-photon interactions in two- dimensional waveguide qed networks,

    Matija Teˇ cer, Giuseppe Calaj´ o, and Marco Di Liberto, “Flat-band-mediated photon-photon interactions in two- dimensional waveguide qed networks,” Phys. Rev. A113, 013701 (2026)

    2026

  10. [18]

    Waveguide-qed-based photonic quantum computation,

    Huaixiu Zheng, Daniel J. Gauthier, and Harold U. Baranger, “Waveguide-qed-based photonic quantum computation,” Phys. Rev. Lett.111, 090502 (2013)

    2013

  11. [19]

    Uni- versal quantum computation in waveguide qed using de- coherence free subspaces,

    V Paulisch, H J Kimble, and A Gonz´ alez-Tudela, “Uni- versal quantum computation in waveguide qed using de- coherence free subspaces,” New Journal of Physics18, 043041 (2016)

    2016

  12. [20]

    Universal photonic quantum compu- tation via time-delayed feedback,

    Hannes Pichler, Soonwon Choi, Peter Zoller, and Mikhail D. Lukin, “Universal photonic quantum compu- tation via time-delayed feedback,” Proc. Natl. Acad. Sci. U.S.A.114, 11362–11367 (2017)

    2017

  13. [21]

    Quantum state transfer and entanglement distribution among distant nodes in a quantum network,

    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, 3221–3224 (1997)

    1997

  14. [22]

    The quantum internet,

    H. J. Kimble, “The quantum internet,” Nature453, 1023–1030 (2008)

    2008

  15. [23]

    Non-markovian dy- namics in chiral quantum networks with spins and pho- tons,

    Tom´ as Ramos, Benoˆ ıt Vermersch, Philipp Hauke, Hannes Pichler, and Peter Zoller, “Non-markovian dy- namics in chiral quantum networks with spins and pho- tons,” Phys. Rev. A93, 062104 (2016)

    2016

  16. [24]

    Quantum many-body models with cold atoms coupled to photonic crystals,

    J. S. Douglas, H. Habibian, C.-L. Hung, A. V. Gorshkov, H. J. Kimble, and D. E. Chang, “Quantum many-body models with cold atoms coupled to photonic crystals,” Nat. Photonics9, 326–331 (2015)

    2015

  17. [25]

    Many-body superradiance and dy- namical mirror symmetry breaking in waveguide qed,

    Silvia Cardenas-Lopez, Stuart J. Masson, Zoe Zager, and Ana Asenjo-Garcia, “Many-body superradiance and dy- namical mirror symmetry breaking in waveguide qed,” Phys. Rev. Lett.131, 033605 (2023)

    2023

  18. [26]

    Effects of retardation on many-body superra- diance in chiral waveguide qed,

    Bennet Windt, Miguel Bello, Daniel Malz, and J. Igna- cio Cirac, “Effects of retardation on many-body superra- diance in chiral waveguide qed,” Phys. Rev. Lett.134, 173601 (2025)

    2025

  19. [27]

    Radiation from ann-atom system. i. general formalism,

    R. H. Lehmberg, “Radiation from ann-atom system. i. general formalism,” Phys. Rev. A2, 883–888 (1970)

    1970

  20. [28]

    On the generators of quantum dy- namical semigroups,

    G¨ oran Lindblad, “On the generators of quantum dy- namical semigroups,” Communications in Mathematical Physics48, 119–130 (1976)

    1976

  21. [29]

    Quantum trajectory theory for cas- caded open systems,

    H. J. Carmichael, “Quantum trajectory theory for cas- caded open systems,” Phys. Rev. Lett.70, 2273–2276 (1993)

    1993

  22. [30]

    Photon-mediated interactions between distant ar- tificial atoms,

    Arjan F. van Loo, Arkady Fedorov, Kevin Lalumi` ere, Barry C. Sanders, Alexandre Blais, and Andreas Wall- raff, “Photon-mediated interactions between distant ar- tificial atoms,” Science342, 1494–1496 (2013)

    2013

  23. [31]

    Super-radiance reveals infinite-range dipole interactions through a nanofiber,

    Pablo Solano, Pablo Barberis-Blostein, Fredrik K. Fatemi, Luis A. Orozco, and Steven L. Rolston, “Super-radiance reveals infinite-range dipole interactions through a nanofiber,” Nature Communications8, 1857 (2017)

    2017

  24. [32]

    Microwave quantum link between superconducting circuits housed in spatially separated cryogenic systems,

    P. Magnard, S. Storz, P. Kurpiers, J. Sch¨ ar, F. Marxer, J. L¨ utolf, T. Walter, J.-C. Besse, M. Gabureac, K. Reuer, A. Akin, B. Royer, A. Blais, and A. Wallraff, “Microwave quantum link between superconducting circuits housed in spatially separated cryogenic systems,” Phys. ...

    2020

  25. [33]

    Collapse and revival of an artificial atom coupled to a structured photonic reservoir,

    V´ ıctor S. Ferreira, Jash Banker, Alp Sipahigil, Matthew H. Matheny, Andrew J. Keller, Eunjong Kim, Mohammad Mirhosseini, and Oskar Painter, “Collapse and revival of an artificial atom coupled to a structured photonic reservoir,” Phys. Rev. X11, 041043 (2021)

    2021

  26. [34]

    Long-distance cascaded flu- orescence of cold cesium atoms coupled to an optical nanofiber,

    Mohammad Sadeghi, Wayne Crump, Scott Parkins, and Maarten Hoogerland, “Long-distance cascaded flu- orescence of cold cesium atoms coupled to an optical nanofiber,” (2025), arXiv:2412.01099

    2025 arXiv

  27. [35]

    Res- onance fluorescence of an artificial atom with a time- delayed coherent feedback,

    Ching-Yeh Chen, Gavin Crowder, Zheng-Qi Niu, Ping Yi Wen, Yen-Hsiang Lin, Jeng-Chung Chen, Zhi-Rong Lin, Franco Nori, Stephen Hughes, and Io-Chun Hoi, “Res- onance fluorescence of an artificial atom with a time- delayed coherent feedback,” (2026), arXiv:2603.28004

    2026

  28. [36]

    Non-markovian collective emission from macro- scopically separated emitters,

    Kanupriya Sinha, Pierre Meystre, Elizabeth A. Gold- schmidt, Fredrik K. Fatemi, S. L. Rolston, and Pablo Solano, “Non-markovian collective emission from macro- scopically separated emitters,” Phys. Rev. Lett.124, 043603 (2020)

    2020

  29. [37]

    Exact solution for the collective non-markovian decay of two fully ex- cited quantum emitters,

    Alfonso Lanuza and Dominik Schneble, “Exact solution for the collective non-markovian decay of two fully ex- cited quantum emitters,” Phys. Rev. Res.6, 033196 (2024)

    2024

  30. [38]

    Non- markovian spontaneous emission in a tunable cavity formed by atomic mirrors,

    Annyun Das, Pablo Solano, and Kanu Sinha, “Non- markovian spontaneous emission in a tunable cavity formed by atomic mirrors,” Phys. Rev. A112, 043723 (2025)

    2025

  31. [39]

    Spontaneous emission in the presence of quantum mirrors,

    Kanu Sinha, Jennifer Parra-Contreras, Annyun Das, and Pablo Solano, “Spontaneous emission in the presence of quantum mirrors,” New Journal of Physics27, 054101 (2025)

    2025

  32. [40]

    Exciting a bound state in the continuum through multiphoton scattering plus delayed quantum feedback,

    Giuseppe Calaj´ o, Yao-Lung L. Fang, Harold U. Baranger, and Francesco Ciccarello, “Exciting a bound state in the continuum through multiphoton scattering plus delayed quantum feedback,” Phys. Rev. Lett.122, 073601 (2019)

    2019

  33. [41]

    Delay-induced spontaneous dark-state gener- ation from two distant excited atoms,

    W. Alvarez-Giron, P. Solano, K. Sinha, and P. Barberis- Blostein, “Delay-induced spontaneous dark-state gener- ation from two distant excited atoms,” Phys. Rev. Res. 6, 023213 (2024)

    2024

  34. [42]

    Non-markovian dynamics of gener- ation of bound states in the continuum via single-photon scattering,

    Giuseppe Magnifico, Maria Maffei, Domenico Pomarico, Debmalya Das, Paolo Facchi, Saverio Pascazio, and Francesco V. Pepe, “Non-markovian dynamics of gener- ation of bound states in the continuum via single-photon scattering,” Phys. Rev. Res.7, 033249 (2025)

    2025

  35. [43]

    Non-markovian delay-assisted sens- ing with waveguide-coupled quantum emitters,

    Prajit Dhara, Isack Padilla, Saikat Guha, Annyun Das, and Kanu Sinha, “Non-markovian delay-assisted sens- ing with waveguide-coupled quantum emitters,” (2026), arXiv:2605.05434

    2026 arXiv

  36. [44]

    Photonic circuits with time delays and quantum feedback,

    Hannes Pichler and Peter Zoller, “Photonic circuits with time delays and quantum feedback,” Phys. Rev. Lett. 116, 093601 (2016)

    2016

  37. [45]

    Pronounced non-markovian features in multiply excited, multiple emitter waveguide qed: Retar- dation induced anomalous population trapping,

    Alexander Carmele, Nikolett Nemet, Victor Canela, and Scott Parkins, “Pronounced non-markovian features in multiply excited, multiple emitter waveguide qed: Retar- dation induced anomalous population trapping,” Phys. Rev. Res.2, 013238 (2020)

    2020

  38. [46]

    Non-markovian collec- tive emission of giant emitters in the zeno regime,

    Qing-Yang Qiu and Xin-You L¨ u, “Non-markovian collec- tive emission of giant emitters in the zeno regime,” Phys. Rev. Res.6, 033243 (2024)

    2024

  39. [47]

    Collective radiation from distant emitters,

    Kanupriya Sinha, Alejandro Gonz´ alez-Tudela, Yong Lu, and Pablo Solano, “Collective radiation from distant emitters,” Phys. Rev. A102, 043718 (2020). 7

    2020

  40. [48]

    Dissim- ilar collective decay and directional emission from two quantum emitters,

    P. Solano, P. Barberis-Blostein, and K. Sinha, “Dissim- ilar collective decay and directional emission from two quantum emitters,” Phys. Rev. A107, 023723 (2023)

    2023

  41. [49]

    Superra- diant decay in non-markovian waveguide quantum elec- trodynamics,

    Rosa Lucia Capurso, Giuseppe Calaj´ o, Simone Mon- tangero, Saverio Pascazio, Francesco V. Pepe, Maria Maffei, Giuseppe Magnifico, and Paolo Facchi, “Superra- diant decay in non-markovian waveguide quantum elec- trodynamics,” (2025), arXiv:2511.22332

    2025

  42. [50]

    Distant emitters in ultrastrong waveguide qed: Ground-state properties and non-markovian dy- namics,

    C. A. Gonz´ alez-Guti´ errez, J. Rom´ an-Roche, and D. Zueco, “Distant emitters in ultrastrong waveguide qed: Ground-state properties and non-markovian dy- namics,” Phys. Rev. A104, 053701 (2021)

    2021

  43. [51]

    Oscillating bound states for a giant atom,

    Lingzhen Guo, Anton Frisk Kockum, Florian Marquardt, and G¨ oran Johansson, “Oscillating bound states for a giant atom,” Phys. Rev. Res.2, 043014 (2020)

    2020

  44. [52]

    Controlling atom-photon bound states in an array of josephson-junction resonators,

    Marco Scigliuzzo, Giuseppe Calaj` o, Francesco Ciccarello, Daniel Perez Lozano, Andreas Bengtsson, Pasquale Scar- lino, Andreas Wallraff, Darrick Chang, Per Delsing, and Simone Gasparinetti, “Controlling atom-photon bound states in an array of josephson-junction resonators,” P...

    2022

  45. [53]

    Multimode- cavity picture of non-markovian waveguide qed,

    Dario Cilluffo, Luca Ferialdi, G. Massimo Palma, Giuseppe Calaj` o, and Francesco Ciccarello, “Multimode- cavity picture of non-markovian waveguide qed,” Phys. Rev. Res.8, 023172 (2026)

    2026

  46. [54]

    Absence of diffusion in certain random lattices,

    P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev.109, 1492–1505 (1958)

    1958

  47. [55]

    Colloquium: Many-body localization, thermalization, and entanglement,

    Dmitry A. Abanin, Ehud Altman, Immanuel Bloch, and Maksym Serbyn, “Colloquium: Many-body localization, thermalization, and entanglement,” Rev. Mod. Phys.91, 021001 (2019)

    2019

  48. [56]

    Berechnung der nat¨ urlichen linienbreite auf grund der diracschen licht- theorie,

    V. Weisskopf and E. Wigner, “Berechnung der nat¨ urlichen linienbreite auf grund der diracschen licht- theorie,” Zeitschrift f¨ ur Physik63, 54–73 (1930)

    1930

  49. [57]

    Cooperative spontaneous emission as a many-body eigenvalue prob- lem,

    Anatoly Svidzinsky and Jun-Tao Chang, “Cooperative spontaneous emission as a many-body eigenvalue prob- lem,” Phys. Rev. A77, 043833 (2008)

    2008

  50. [58]

    Photode- tection and causality in quantum optics,

    PW Milonni, DFV James, and Heidi Fearn, “Photode- tection and causality in quantum optics,” Physical Re- view A52, 1525 (1995)

    1995

  51. [59]

    Quantum optics of chiral spin networks,

    Hannes Pichler, Tom´ as Ramos, Andrew J. Daley, and Peter Zoller, “Quantum optics of chiral spin networks,” Phys. Rev. A91, 042116 (2015)

    2015

  52. [60]

    See Supplemental Material at URL-will-be-inserted-by- publisher for detailed calculations

  53. [61]

    Entanglement of formation of an arbitrary state of two qubits,

    William K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett.80, 2245– 2248 (1998)

    1998

  54. [62]

    The kuramoto model: A simple paradigm for synchronization phenom- ena,

    Juan A. Acebr´ on, L. L. Bonilla, Conrad J. P´ erez Vi- cente, F´ elix Ritort, and Renato Spigler, “The kuramoto model: A simple paradigm for synchronization phenom- ena,” Rev. Mod. Phys.77, 137–185 (2005)

    2005

  55. [63]

    Critical behavior of several lattice models with long-range interaction,

    Mark Kac and Colin J. Thompson, “Critical behavior of several lattice models with long-range interaction,” Jour- nal of Mathematical Physics10, 1373–1386 (1969). 1 SUPPLEMENT AL MA TERIAL FOR: DELA YED-INDUCED EXCIT A TION LOCALIZA TION IN A TOMIC ARRA YS COUPLED TO A W A VEGU...

    1969

Pith tools

Reviewed July 9, 2026 · model on record in the stance chip above.