Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Emergence of Second-Order Coherence in Superfluorescence

Phys. Rev. Lett. 136, 063402 – Published 10 February, 2026

DOI: https://doi.org/10.1103/r3kg-c4x9

Abstract

We experimentally investigate the second-order quantum coherence function of a superradiant burst in a cascaded quantum system. We chirally (i.e., direction dependently) couple about 900 cesium atoms to the forward-propagating mode of an optical nanofiber. We then prepare the ensemble close to the maximally excited state, where the subsequent collective emission of a burst is known as superfluorescence. Here, we observe that second-order coherence emerges in the course of the decay. This is a clear signature of the underlying collective dynamics that is also at the origin of the superradiant burst itself. We furthermore study the dynamics of the second-order coherence function of the emission in relation to the initial average dipole moment of the ensemble. In addition, by investigating the correlation of early and late photon emission events, we obtain evidence for fundamental shot-to-shot fluctuations in the delay of the emission of the burst. Our findings thus reveal surprising similarities between superradiance in cascaded and symmetrically coupled systems, despite the fact that they are described by fundamentally different coupling Hamiltonians.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (61)

  1. V. Letokhov and S. Johansson, Astrophysical Lasers (Oxford University Press, New York, 2009).
  2. M. R. W. Guerin and R. Kaiser, Light interacting with atomic ensembles: Collective, cooperative and mesoscopic effects, J. Mod. Opt. 64, 895 (2017).
  3. 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).
  4. R. H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev. 93, 99 (1954).
  5. N. Skribanowitz, I. Herman, J. MacGillivray, and M. Feld, Observation of Dicke superradiance in optically pumped HF gas, Phys. Rev. Lett. 30, 309 (1973).
  6. M. Gross, C. Fabre, P. Pillet, and S. Haroche, Observation of near-infrared Dicke superradiance on cascading transitions in atomic sodium, Phys. Rev. Lett. 36, 1035 (1976).
  7. M. Gross and S. Haroche, Superradiance: An essay on the theory of collective spontaneous emission, Phys. Rep. 93, 301 (1982).
  8. S. Cardenas-Lopez, S. J. Masson, Z. Zager, and A. Asenjo-Garcia, Many-body superradiance and dynamical mirror symmetry breaking in waveguide QED, Phys. Rev. Lett. 131, 033605 (2023).
  9. C. Liedl, F. Tebbenjohanns, C. Bach, S. Pucher, A. Rauschenbeutel, and P. Schneeweiss, Observation of superradiant bursts in a cascaded quantum system, Phys. Rev. X 14, 011020 (2024).
  10. C. W. Gardiner, Driving a quantum system with the output field from another driven quantum system, Phys. Rev. Lett. 70, 2269 (1993).
  11. H. J. Carmichael, Quantum trajectory theory for cascaded open systems, Phys. Rev. Lett. 70, 2273 (1993).
  12. N. Stiesdal, H. Busche, K. Kleinbeck, J. Kumlin, M. G. Hansen, H. P. Büchler, and S. Hofferberth, Controlled multi-photon subtraction with cascaded Rydberg superatoms as single-photon absorbers, Nat. Commun. 12, 4328 (2021).
  13. G. Calajó, M. J. A. Schuetz, H. Pichler, M. D. Lukin, P. Schneeweiss, J. Volz, and P. Rabl, Quantum acousto-optic control of light-matter interactions in nanophotonic networks, Phys. Rev. A 99, 053852 (2019).
  14. T. Ramos, H. Pichler, A. J. Daley, and P. Zoller, Quantum spin dimers from chiral dissipation in cold-atom chains, Phys. Rev. Lett. 113, 237203 (2014).
  15. 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).
  16. R. Bonifacio and L. A. Lugiato, Cooperative radiation processes in two-level systems: Superfluorescence, Phys. Rev. A 11, 1507 (1975).
  17. Q. Vrehen, M. Schuurmans, and D. Polder, Superfluorescence: Macroscopic quantum fluctuations in the time domain, Nature (London) 285, 70 (1980).
  18. J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, A steady-state superradiant laser with less than one intracavity photon, Nature (London) 484, 78 (2012).
  19. T. Bienaimé, R. Bachelard, N. Piovella, and R. Kaiser, Cooperativity in light scattering by cold atoms, Fortschr. Phys. 61, 377 (2013).
  20. K. Cong, Q. Zhang, Y. Wang, G. T. Noe, A. Belyanin, and J. Kono, Dicke superradiance in solids [invited], J. Opt. Soc. Am. B 33, C80 (2016).
  21. T. Laske, H. Winter, and A. Hemmerich, Pulse delay time statistics in a superradiant laser with calcium atoms, Phys. Rev. Lett. 123, 103601 (2019).
  22. G. Ferioli, A. Glicenstein, F. Robicheaux, R. T. Sutherland, A. Browaeys, and I. Ferrier-Barbut, Laser-driven superradiant ensembles of two-level atoms near Dicke regime, Phys. Rev. Lett. 127, 243602 (2021).
  23. R. Pennetta, D. Lechner, M. Blaha, A. Rauschenbeutel, P. Schneeweiss, and J. Volz, Observation of coherent coupling between super- and subradiant states of an ensemble of cold atoms collectively coupled to a single propagating optical mode, Phys. Rev. Lett. 128, 203601 (2022).
  24. M. Reitz, C. Sommer, and C. Genes, Cooperative quantum phenomena in light-matter platforms, PRX Quantum 3, 010201 (2022).
  25. A. C. Santos and R. Bachelard, Generation of maximally entangled long-lived states with giant atoms in a waveguide, Phys. Rev. Lett. 130, 053601 (2023).
  26. G. Ferioli, S. Pancaldi, A. Glicenstein, D. Clément, A. Browaeys, and I. Ferrier-Barbut, Non-Gaussian correlations in the steady state of driven-dissipative clouds of two-level atoms, Phys. Rev. Lett. 132, 133601 (2024).
  27. S. Ostermann, O. Rubies-Bigorda, V. Zhang, and S. F. Yelin, Breakdown of steady-state superradiance in extended driven atomic arrays, Phys. Rev. Res. 6, 023206 (2024).
  28. F. Haake and R. J. Glauber, Quantum statistics of superradiant pulses, Phys. Rev. A 5, 1457 (1972).
  29. R. Lopes, A. Imanaliev, M. Bonneau, J. Ruaudel, M. Cheneau, D. Boiron, and C. I. Westbrook, Second-order coherence of superradiance from a Bose-Einstein condensate, Phys. Rev. A 90, 013615 (2014).
  30. F. Jahnke, C. Gies, M. Aßmann, M. Bayer, H. Leymann, A. Foerster, J. Wiersig, C. Schneider, M. Kamp, and S. Höfling, Giant photon bunching, superradiant pulse emission and excitation trapping in quantum-dot nanolasers, Nat. Commun. 7, 11540 (2016).
  31. S. Stryzhenko, A. Bruns, and T. Peters, N scaling of large-sample collective decay in inhomogeneous ensembles, Phys. Rev. Res. 6, 013091 (2024).
  32. R. J. Glauber, The quantum theory of optical coherence, Phys. Rev. 130, 2529 (1963).
  33. E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber, Phys. Rev. Lett. 104, 203603 (2010).
  34. N. Schlosser, G. Reymond, and P. Grangier, Collisional blockade in microscopic optical dipole traps, Phys. Rev. Lett. 89, 023005 (2002).
  35. Y. Meng, A. Dareau, P. Schneeweiss, and A. Rauschenbeutel, Near-ground-state cooling of atoms optically trapped 300 nm away from a hot surface, Phys. Rev. X 8, 031054 (2018).
  36. R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide, Nat. Commun. 5, 5713 (2014).
  37. C. Liedl, S. Pucher, F. Tebbenjohanns, P. Schneeweiss, and A. Rauschenbeutel, Collective radiation of a cascaded quantum system: From timed Dicke states to inverted ensembles, Phys. Rev. Lett. 130, 163602 (2023).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/r3kg-c4x9 for detailed analysis, which includes Refs. [39–44].
  39. O. Somech and E. Shahmoon, Quantum entangled states of a classically radiating macroscopic spin, PRX Quantum 5, 010349 (2024).
  40. U. Van Bürck, Coherent pulse propagation through resonant media, Hyperfine Interact. 123, 483 (1999).
  41. D. Su, Y. Jiang, S. Cardenas-Lopez, A. Asenjo-Garcia, P. Solano, L. A. Orozco, and Y. Zhao, Dynamical beats of short pulses in waveguide QED, Phys. Rev. Res. 5, L042041 (2023).
  42. K. Stannigel, P. Rabl, and P. Zoller, Driven-dissipative preparation of entangled states in cascaded quantum-optical networks, New J. Phys. 14, 063014 (2012).
  43. H. Pichler, T. Ramos, A. J. Daley, and P. Zoller, Quantum optics of chiral spin networks, Phys. Rev. A 91, 042116 (2015).
  44. H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations, Vol. 1 (Springer Science & Business Media, New York, 1999).
  45. C. D. Mink and M. Fleischhauer, Collective radiative interactions in the discrete truncated Wigner approximation, SciPost Phys. 15, 233 (2023).
  46. F. Tebbenjohanns, C. D. Mink, C. Bach, A. Rauschenbeutel, and M. Fleischhauer, Predicting correlations in superradiant emission from a cascaded quantum system, Phys. Rev. A 110, 043713 (2024).
  47. L. Ostermann, H. Zoubi, and H. Ritsch, Cascaded collective decay in regular arrays of cold trapped atoms, Opt. Express 20, 29634 (2012).
  48. T. Caneva, M. T. Manzoni, T. Shi, J. S. Douglas, J. I. Cirac, and D. E. Chang, Quantum dynamics of propagating photons with strong interactions: A generalized input–output formalism, New J. Phys. 17, 113001 (2015).
  49. S. Mahmoodian, G. Calajó, D. E. Chang, K. Hammerer, and A. S. Sørensen, Dynamics of many-body photon bound states in chiral waveguide QED, Phys. Rev. X 10, 031011 (2020).
  50. F. Robicheaux and D. A. Suresh, Beyond lowest order mean-field theory for light interacting with atom arrays, Phys. Rev. A 104, 023702 (2021).
  51. S. Arranz Regidor, G. Crowder, H. Carmichael, and S. Hughes, Modeling quantum light-matter interactions in waveguide QED with retardation, nonlinear interactions, and a time-delayed feedback: Matrix product states versus a space-discretized waveguide model, Phys. Rev. Res. 3, 023030 (2021).
  52. K. J. Kusmierek, S. Mahmoodian, M. Cordier, J. Hinney, A. Rauschenbeutel, M. Schemmer, P. Schneeweiss, J. Volz, and K. Hammerer, Higher-order mean-field theory of chiral waveguide QED, SciPost Phys. Core 6, 041 (2023).
  53. O. Rubies-Bigorda, S. Ostermann, and S. F. Yelin, Dynamic population of multiexcitation subradiant states in incoherently excited atomic arrays, Phys. Rev. A 107, L051701 (2023).
  54. K. Kleinbeck, H. Busche, N. Stiesdal, S. Hofferberth, K. Mølmer, and H. P. Büchler, Creation of nonclassical states of light in a chiral waveguide, Phys. Rev. A 107, 013717 (2023).
  55. E. Vlasiuk, A. V. Poshakinskiy, and A. N. Poddubny, Two-photon pulse-scattering spectroscopy for arrays of two-level atoms coupled to a waveguide, Phys. Rev. A 108, 033705 (2023).
  56. J. Schachenmayer, A. Pikovski, and A. M. Rey, Many-body quantum spin dynamics with Monte Carlo trajectories on a discrete phase space, Phys. Rev. X 5, 011022 (2015).
  57. D. Ferreira, R. Bachelard, W. Guerin, R. Kaiser, and M. Fouché, Connecting field and intensity correlations: The Siegert relation and how to test it, Am. J. Phys. 88, 831 (2020).
  58. The normalized, equal-time first-order coherence function is by definition equal to unity, g(1)(t,t)=1 [32, 59].

  59. R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University Press, New York, 2000).
  60. R. Florian, L. O. Schwan, and D. Schmid, Time-resolving experiments on Dicke superfluorescence of O2− centers in KCl. Two-color superfluorescence, Phys. Rev. A 29, 2709 (1984).
  61. G. Ferioli, I. Ferrier-Barbut, and A. Browaeys, Emergence of second-order coherence in the superradiant emission from a free-space atomic ensemble, Phys. Rev. Lett. 134, 153602 (2025).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation