- Physical Review Journals
All JournalsPhysics Magazine

PRX Quantum

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

Extracting Information from a Superradiant Burst Using Simple Measurements

Federico Belliardo1,*, Anjun Chu1, Martin Koppenhöfer2, and Aashish A. Clerk1,†

  • *Contact author: federico.belliardo@gmail.com
  • †Contact author: aaclerk@uchicago.edu
PDF

PRX Quantum 7, 043029 – Published 12 November, 2026

DOI: https://doi.org/10.1103/1m4s-kky2

Abstract

It is well known that superradiant decay of an ensemble of N spins generates a complex non-classical state of light. Here, we consider the estimation of a phase encoded in the initial spin state from a superradiant burst of photons: how is information about this phase distributed among the emitted photons and can the phase be estimated using simple measurements? Despite the complexity of the photonic burst state, we show that a simple homodyne measurement combined with an optimized filter and linear estimator recovers the N-scaling of the quantum Fisher information of the initial spin state (including cases exhibiting N2 Heisenberg scaling). Even more surprising, the temporal mode with optimal information content contains a vanishing fraction of the total emitted photons in the large-N limit, suggesting an effective compression of phase information. Our results and setup represent a new approach to quantum metrology for spin systems, in that they enable cavity-based readout of solid-state spin ensembles that utilizes resonant spin-photon interactions.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Quantum sensors can detect tiny changes in their surroundings, but extracting the information stored in a collection of spins can be difficult. We show theoretically that this information can be read from the light the spins emit in a superradiant burst, using a standard homodyne measurement and carefully designed signal processing. Surprisingly, the mode of light we choose to measure contains only a small fraction of the emitted photons but carries half of the information encoded in the spins. This fraction shrinks as the sensor gets larger, revealing that useful information can be concentrated into a small fraction of the total emitted photons. These results suggest a new way to read out quantum sensors, with potential applications to systems such as defects in diamond coupled to optical or microwave resonators.

Article Text

References (74)

  1. R. H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev. 93, 99 (1954).
  2. M. Gross and S. Haroche, Superradiance: An essay on the theory of collective spontaneous emission, Phys. Rep. 93, 301 (1982).
  3. N. E. Rehler and J. H. Eberly, Superradiance, Phys. Rev. A 3, 1735 (1971).
  4. A. Asenjo-Garcia, M. Moreno-Cardoner, A. Albrecht, H. Kimble, and D. Chang, Exponential improvement in photon storage fidelities using subradiance and “selective radiance” in atomic arrays, Phys. Rev. X 7, 031024 (2017).
  5. F. Mivehvar, H. Ritsch, and F. Piazza, Superradiant topological peierls insulator inside an optical cavity, Phys. Rev. Lett. 118, 073602 (2017).
  6. S. J. Masson and A. Asenjo-Garcia, Universality of Dicke superradiance in arrays of quantum emitters, Nat. Commun. 13, 2285 (2022).
  7. D. Malz, R. Trivedi, and J. I. Cirac, Large-N limit of Dicke superradiance, Phys. Rev. A 106, 013716 (2022).
  8. O. Rubies-Bigorda, S. Ostermann, and S. F. Yelin, Characterizing superradiant dynamics in atomic arrays via a cumulant expansion approach, Phys. Rev. Res. 5, 013091 (2023).
  9. B. Sundar, D. Barberena, A. M. Rey, and A. P. n. Orioli, Squeezing multilevel atoms in dark states via cavity superradiance, Phys. Rev. Lett. 132, 033601 (2024).
  10. X. H. H. Zhang, D. Malz, and P. Rabl, Unraveling superradiance: Entanglement and mutual information in collective decay, Phys. Rev. Lett. 135, 033602 (2025).
  11. 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).
  12. Z. Yan, J. Ho, Y.-H. Lu, S. J. Masson, A. Asenjo-Garcia, and D. M. Stamper-Kurn, Superradiant and subradiant cavity scattering by atom arrays, Phys. Rev. Lett. 131, 253603 (2023).
  13. S. L. Kristensen, E. Bohr, J. Robinson-Tait, T. Zelevinsky, J. W. Thomsen, and J. H. Müller, Subnatural linewidth superradiant lasing with cold 88Sr atoms, Phys. Rev. Lett. 130, 223402 (2023).
  14. 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).
  15. E. Y. Song, D. Barberena, D. J. Young, E. Chaparro, A. Chu, S. Agarwal, Z. Niu, J. T. Young, A. M. Rey, and J. K. Thompson, A dissipation-induced superradiant transition in a strontium cavity-QED system, Sci. Adv. 11, eadu5799 (2025).
  16. W. Kersten, N. de Zordo, O. Diekmann, E. S. Redchenko, A. N. Kanagin, A. Angerer, W. J. Munro, K. Nemoto, I. E. Mazets, S. Rotter, T. Pohl, and J. Schmiedmayer, Self-induced superradiant masing, Nat. Phys. 22, 158 (2026).
  17. F. E. van Dorsselaer and G. Nienhuis, Collective decay as a stochastic process, Phys. Rev. A 56, 958 (1997).
  18. M. Perarnau-Llobet, A. González-Tudela, and J. I. Cirac, Multimode Fock states with large photon number: Effective descriptions and applications in quantum metrology, Quantum Sci. Technol. 5, 025003 (2020).
  19. B. Lemberger and K. Mølmer, Radiation eigenmodes of Dicke superradiance, Phys. Rev. A 103, 033713 (2021).
  20. 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).
  21. V. Paulisch, M. Perarnau-Llobet, A. González-Tudela, and J. I. Cirac, Quantum metrology with one-dimensional superradiant photonic states, Phys. Rev. A 99, 043807 (2019).
  22. E. Abbasgholinejad, D. Malz, A. Asenjo-Garcia, and R. Trivedi, Theory of quantum-enhanced interferometry with general Markovian light sources, arXiv:2504.05111.
  23. M. Jirasek, I. Lesanovsky, and A. Cabot, Boundary time crystal as a light source for collectively enhanced sensing, Phys. Rev. A 114, 032611 (2026).
  24. S. Gammelmark and K. Mølmer, Fisher information and the quantum Cramér-Rao sensitivity limit of continuous measurements, Phys. Rev. Lett. 112, 170401 (2014).
  25. F. Albarelli, M. A. C. Rossi, M. G. A. Paris, and M. G. Genoni, Ultimate limits for quantum magnetometry via time-continuous measurements, New J. Phys. 19, 123011 (2017).

  26. Strictly speaking, the emitted field contains exactly N photons at the reference point φ=0; for any non-zero φ there is population for smaller numbers of photons, but we are interested in infinitesimal rotation angles and in studying the metrological properties of the N-photon state.

  27. P. M. Woodward, Probability and Information Theory: With Applications to Radar (McGraw-Hill, New York, 1953).
  28. G. Turin, An introduction to matched filters, IRE Trans. Inf. Theory 6, 311 (1960).
  29. B. Picinbono, Generalized matched filters, in Fifth ASSP Workshop on Spectrum Estimation and Modeling (1990), pp. 182–186.
  30. V. Olshevsky and L. Sakhnovich, Matched filtering for generalized stationary processes, IEEE Trans. Inf. Theory 51, 3308 (2005).
  31. E. Davis, G. Bentsen, and M. Schleier-Smith, Approaching the Heisenberg limit without single-particle detection, Phys. Rev. Lett. 116, 053601 (2016).
  32. O. Hosten, R. Krishnakumar, N. J. Engelsen, and M. A. Kasevich, Quantum phase magnification, Science 352, 1552 (2016).
  33. F. Albarelli and M. G. Genoni, A pedagogical introduction to continuously monitored quantum systems and measurement-based feedback, Phys. Lett. A 494, 129260 (2024).
  34. R. Mattes, A. Cabot, F. Carollo, and I. Lesanovsky, Designing open quantum systems for enabling quantum enhanced sensing through classical measurements, Phys. Rev. Lett. 135, 230402 (2025).
  35. A. Angerer, K. Streltsov, T. Astner, S. Putz, H. Sumiya, S. Onoda, J. Isoya, W. J. Munro, K. Nemoto, J. Schmiedmayer, and J. Majer, Superradiant emission from colour centres in diamond, Nat. Phys. 14, 1168 (2018).
  36. C. Bradac, M. T. Johnsson, M. v. Breugel, B. Q. Baragiola, R. Martin, M. L. Juan, G. K. Brennen, and T. Volz, Room-temperature spontaneous superradiance from single diamond nanocrystals, Nat. Commun. 8, 1205 (2017).
  37. J. J. Borkowski, A. Czerwinski, and P. Kolenderski, Revisiting superradiance dynamics from single diamond nanocrystals with a physically consistent model for fluorescence decay, Nat. Commun. 17, 58 (2026).
  38. M. Mamaev, J. Venkatraman, M. Koppenhöfer, A. C. B. Jayich, and A. A. Clerk, Detecting quantum noise of a solid-state spin ensemble with dispersive measurement, Phys. Rev. Res. 8, 023331 (2026).
  39. J. G. Bohnet, Z. Chen, J. M. Weiner, K. C. Cox, and J. K. Thompson, Active and passive sensing of collective atomic coherence in a superradiant laser, Phys. Rev. A 88, 013826 (2013).
  40. J. M. Weiner, K. C. Cox, J. G. Bohnet, Z. Chen, and J. K. Thompson, Superradiant Raman laser magnetometer, Appl. Phys. Lett. 101, 261107 (2012).
  41. A. A. Svidzinsky, L. Yuan, and M. O. Scully, Quantum amplification by superradiant emission of radiation, Phys. Rev. X 3, 041001 (2013).
  42. O. Somech and E. Shahmoon, Quantum entangled states of a classically radiating macroscopic spin, PRX Quantum 5, 010349 (2024).
  43. D. Meiser and M. J. Holland, Intensity fluctuations in steady-state superradiance, Phys. Rev. A 81, 063827 (2010).
  44. M. Koppenhöfer, P. Groszkowski, H.-K. Lau, and A. A. Clerk, Dissipative superradiant spin amplifier for enhanced quantum sensing, PRX Quantum 3, 030330 (2022).
  45. M. Koppenhöfer, P. Groszkowski, and A. A. Clerk, Squeezed superradiance enables robust entanglement-enhanced metrology even with highly imperfect readout, Phys. Rev. Lett. 131, 060802 (2023).
  46. E. A. Bohr, S. L. Kristensen, C. Hotter, S. A. Schäffer, J. Robinson-Tait, J. W. Thomsen, T. Zelevinsky, H. Ritsch, and J. H. Müller, Collectively enhanced Ramsey readout by cavity sub- to superradiant transition, Nat. Commun. 15, 1084 (2024).
  47. R. Bonifacio, P. Schwendimann, and F. Haake, Quantum statistical theory of superradiance. I, Phys. Rev. A 4, 302 (1971).

  48. Our results should therefore be understood for a scaling of the physical parameters in N for which this condition remains satisfied as N is varied.

  49. M. A. Norcia, R. J. Lewis-Swan, J. R. K. Cline, B. Zhu, A. M. Rey, and J. K. Thompson, Cavity-mediated collective spin-exchange interactions in a strontium superradiant laser, Science 361, 259 (2018).
  50. V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photonics 5, 222 (2011).
  51. L. Pezzè, Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys. 90, 035005 (2018).
  52. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  53. M. S. Scharnagl, T. Kielinski, and K. Hammerer, Optimal Ramsey interferometry with echo protocols based on one-axis twisting, Phys. Rev. A 108, 062611 (2023).
  54. M. Koppenhöfer and A. A. Clerk, Revisiting the impact of dissipation on time-reversed one-axis-twist quantum-sensing protocols, Phys. Rev. Res. 5, 043279 (2023).
  55. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys. 82, 1155 (2010).
  56. C. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer Science & Business Media, Berlin and Heidelberg, Germany, 2004).
  57. V. V. Albert and L. Jiang, Symmetries and conserved quantities in Lindblad master equations, Phys. Rev. A 89, 022118 (2014).
  58. D. F. Walls and G. J. Milburn, Quantum Optics (Springer Science & Business Media, Berlin and Heidelberg, Germany, 2024).
  59. C. K. Law and S. K. Y. Lee, Dynamic photon-mode selection in Dicke superradiance, Phys. Rev. A 75, 033813 (2007).

  60. Note that one does not have to worry about SII(t,t′) being non-invertible. Non-invertibility would imply the existence of one or more modes that have zero fluctuations in one quadrature. This would in turn imply infinite squeezing, something that is impossible with a finite number of photons. In our case, there is even a stronger constraint, as the superradiant decay dynamics never generates squeezing correlations in the output field.

  61. D. Yang, M. Ketkar, K. Audenaert, S. F. Huelga, and M. B. Plenio, Quantum Cramér-Rao precision limit of noisy continuous sensing, Phys. Rev. Lett. 136, 070802 (2026).
  62. G. Tóth and I. Apellaniz, Quantum metrology from a quantum information science perspective, J. Phys. A 47, 424006 (2014).
  63. M. Hayashi, Asymptotic Theory of Quantum Statistical Inference: Selected Papers (World Scientific, Singapore, 2005), 10.1142/5630.
  64. A. Khan, F. Albarelli, and A. Datta, A tensor network approach to sensing quantum light-matter interactions, PRX Quantum 6, 040343 (2025).
  65. A. H. Kiilerich and K. Mølmer, Input-output theory with quantum pulses, Phys. Rev. Lett. 123, 123604 (2019).
  66. A. H. Kiilerich and K. Mølmer, Quantum interactions with pulses of radiation, Phys. Rev. A 102, 023717 (2020).
  67. J. Combes, K., and M. Sarovar, The SLH framework for modeling quantum input-output networks, Adv. Phys. 2, 784 (2017).
  68. H. J. Carmichael, Quantum trajectory theory for cascaded open systems, Phys. Rev. Lett. 70, 2273 (1993).
  69. C. Catana, L. Bouten, and M. Guta, Fisher informations and local asymptotic normality for continuous-time quantum Markov processes, J. Phys. A 48, 365301 (2015) 10.1088/1751-8113/48/36/365301.
  70. D. Yang, M. Ketkar, K. Audenaert, S. F. Huelga, and M. B. Plenio, Quantum Cramer-Rao precision limit of noisy continuous sensing, Phys. Rev. Lett. 136, 070802 (2025).
  71. D. Yang, S. F. Huelga, and M. B. Plenio, Efficient information retrieval for sensing via continuous measurement, Phys. Rev. X 13, 031012 (2023).
  72. F. Girotti, A. Godley, and M. Guta, Estimating quantum Markov chains using coherent absorber post-processing and pattern counting estimator, Quantum 9, 1835 (2025).
  73. F. Ciccarello, S. Lorenzo, V. Giovannetti, and G. M. Palma, Quantum collision models: Open system dynamics from repeated interactions, Phys. Rep. 954, 1 (2022).
  74. H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, 2009).

Outline

Information

PRX Quantum 7, 043029– Published 12 November, 2026
  • Received 31 March 2026
  • Revised 4 August 2026
  • Accepted 21 October 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation