- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Nonequilibrium universality of Rydberg-excitation spreading on a dynamic network

Simon Ohler1, Daniel Brady1, Patrick Mischke1,2, Jana Bender1, Herwig Ott1, Thomas Niederprüm1, Winfried Ripken3,4, Johannes S. Otterbach5, and Michael Fleischhauer1

PDF

Phys. Rev. Research 7, 033167 – Published 19 August, 2025

DOI: https://doi.org/10.1103/8rlg-169g

Abstract

Understanding the universal properties of nonequilibrium phase transitions of spreading processes is a challenging problem. This applies in particular to irregular and dynamically varying networks. We here investigate an experimentally accessible model system for such processes, namely, the absorbing-state phase transition (ASPT) of Rydberg-excitation spreading, known as Rydberg facilitation, in a laser-driven gas of mobile atoms. It occurs on an irregular graph, set by the random atom positions in the gas, and, depending on temperature, changes its character from static to dynamic. By studying the behavior of the order parameter in the work of Brady et al. [Phys. Rev. Lett. 133, 173401 (2024)], we showed numerical evidence for a crossover from directed percolation (DP) universality through various phases of anomalous directed percolation (ADP) to mean-field (MF) behavior when the temperature of the gas is increased. As the behavior of the order parameter is not sufficient to uniquely determine the universality class, we here analyze the distribution of avalanches—characteristic of nonequilibrium critical behavior—to fully characterize the ASPT. Performing extended numerical calculations and experiments on a cold Rb87 atom gas, we confirm our earlier numerical findings and our phenomenological model that maps the dynamic network to a static one with power-law tails of the distribution of excitation distances. Furthermore, we discuss the influence of dissipation, present in the experiment and a necessary ingredient for the self-organization of the system to the critical point. In particular, we study the potential modification of the universality class by losses as a function of dissipation strength.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (48)

  1. P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality: An explanation of the 1/f noise, Phys. Rev. Lett. 59, 381 (1987).
  2. P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality, Phys. Rev. A 38, 364 (1988).
  3. C. Tang and P. Bak, Critical exponents and scaling relations for self-organized critical phenomena, Phys. Rev. Lett. 60, 2347 (1988).
  4. N. W. Watkins, G. Pruessner, S. C. Chapman, N. B. Crosby, and H. J. Jensen, 25 years of self-organized criticality: Concepts and controversies, Space Sci. Rev. 198, 3 (2016).
  5. A. Sornette and D. Sornette, Self-organized criticality and earthquakes, Europhys. Lett. 9, 197 (1989).
  6. E. T. Lu and R. J. Hamilton, Avalanches and the distribution of solar flares, Astrophysical Journal, Part 2-Letters 380, L89 (1991).
  7. M. J. Aschwanden, N. B. Crosby, M. Dimitropoulou, M. K. Georgoulis, S. Hergarten, J. McAteer, A. V. Milovanov, S. Mineshige, L. Morales, N. Nishizuka et al., 25 years of self-organized criticality: solar and astrophysics, Space Sci. Rev. 198, 47 (2016).
  8. D. Plenz, T. L. Ribeiro, S. R. Miller, P. A. Kells, A. Vakili, and E. L. Capek, Self-organized criticality in the brain, Front. Phys. 9, 639389 (2021).
  9. J. Hesse and T. Gross, Self-organized criticality as a fundamental property of neural systems, Front. Syst. Neurosci. 8, 166 (2014).
  10. S. S. Manna, Two-state model of self-organized criticality, J. Phys. A: Math. Gen. 24, L363 (1991).
  11. B. Drossel and F. Schwabl, Self-organized critical forest-fire model, Phys. Rev. Lett. 69, 1629 (1992).
  12. Z. Olami, H. J. S. Feder, and K. Christensen, Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes, Phys. Rev. Lett. 68, 1244 (1992).
  13. F. Caruso, V. Latora, A. Pluchino, A. Rapisarda, and B. Tadić, Olami-Feder-Christensen model on different networks, Eur. Phys. J. B 50, 243 (2006).
  14. M. Dottori and G. Fabricius, Sir model on a dynamical network and the endemic state of an infectious disease, Physica A 434, 25 (2015).
  15. S. Lise and M. Paczuski, Nonconservative earthquake model of self-organized criticality on a random graph, Phys. Rev. Lett. 88, 228301 (2002).
  16. J. A. Bonachela and M. A. Munoz, Self-organization without conservation: true or just apparent scale-invariance? J. Stat. Mech. (2009) P09009.
  17. M. Henkel, H. Hinrichsen, and S. Lübeck, Non-Equilibrium Phase Transitions, 1st ed., Theoretical and Mathematical Physics (Springer Science+Business Media, Dordrecht, 2008), Vol. 1.
  18. K. A. Takeuchi, M. Kuroda, H. Chaté, and M. Sano, Directed percolation criticality in turbulent liquid crystals, Phys. Rev. Lett. 99, 234503 (2007).
  19. A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16, 132 (2020).
  20. M. Saffman, T. G. Walker, and K. Mølmer, Quantum information with Rydberg atoms, Rev. Mod. Phys. 82, 2313 (2010).
  21. C. S. Adams, J. D. Pritchard, and J. P. Shaffer, Rydberg atom quantum technologies, J. Phys. B: At. Mol. Opt. Phys. 53, 012002 (2019).
  22. D. Brady and M. Fleischhauer, Mean-field approach to Rydberg facilitation in a gas of atoms at high and low temperatures, Phys. Rev. A 108, 052812 (2023).
  23. T. Wintermantel, M. Buchhold, S. Shevate, M. Morgado, Y. Wang, G. Lochead, S. Diehl, and S. Whitlock, Epidemic growth and Griffiths effects on an emergent network of excited atoms, Nat. Commun. 12, 103 (2021).
  24. S. Helmrich, A. Arias, G. Lochead, T. Wintermantel, M. Buchhold, S. Diehl, and S. Whitlock, Signatures of self-organized criticality in an ultracold atomic gas, Nature (London) 577, 481 (2020).
  25. M. Marcuzzi, E. Levi, W. Li, J. P. Garrahan, B. Olmos, and I. Lesanovsky, Non-equilibrium universality in the dynamics of dissipative cold atomic gases, New J. Phys. 17, 072003 (2015).
  26. R. Gutiérrez, C. Simonelli, M. Archimi, F. Castellucci, E. Arimondo, D. Ciampini, M. Marcuzzi, I. Lesanovsky, and O. Morsch, Experimental signatures of an absorbing-state phase transition in an open driven many-body quantum system, Phys. Rev. A 96, 041602 (2017).
  27. I. Lesanovsky and J. P. Garrahan, Out-of-equilibrium structures in strongly interacting Rydberg gases with dissipation, Phys. Rev. A 90, 011603 (2014).
  28. D. Brady, S. Ohler, J. Otterbach, and M. Fleischhauer, Anomalous directed percolation on a dynamic network using Rydberg facilitation, Phys. Rev. Lett. 133, 173401 (2024).
  29. G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976).
  30. W. Li, C. Ates, and I. Lesanovsky, Nonadiabatic motional effects and dissipative blockade for Rydberg atoms excited from optical lattices or microtraps, Phys. Rev. Lett. 110, 213005 (2013).
  31. T. Schlegel, E. Konstantinidou, M. Fleischhauer, and D. Brady arXiv:2505.09314.
  32. C. Ates, T. Pohl, T. Pattard, and J. Rost, Strong interaction effects on the atom counting statistics of ultracold Rydberg gases, J. Phys. B: At. Mol. Opt. Phys. 39, L233 (2006).
  33. E. Levi, R. Gutiérrez, and I. Lesanovsky, Quantum non-equilibrium dynamics of Rydberg gases in the presence of dephasing noise of different strengths, J. Phys. B: At. Mol. Opt. Phys. 49, 184003 (2016).
  34. D. Brady, J. Bender, P. Mischke, S. Ohler, T. Niederprüm, H. Ott, and M. Fleischhauer, Griffiths phase in a facilitated Rydberg gas at low temperatures, Phys. Rev. Res. 6, 013052 (2024).
  35. P. Erdős and A. Rényi, On the evolution of random graphs, Publ. math. inst. hung. acad. sci 5, 17 (1960).
  36. H. Hinrichsen and M. Howard, A model for anomalous directed percolation, Eur. Phys. J. B 7, 635 (1999).
  37. M. A. Munoz, R. Dickman, A. Vespignani, and S. Zapperi, Avalanche and spreading exponents in systems with absorbing states, Phys. Rev. E 59, 6175 (1999).
  38. M. A. Munoz, R. Juhász, C. Castellano, and G. Ódor, Griffiths phases on complex networks, Phys. Rev. Lett. 105, 128701 (2010).
  39. H. Hinrichsen, Non-equilibrium phase transitions with long-range interactions, J. Stat. Mech. (2007) P07006.
  40. S. Manna, Large-scale simulation of avalanche cluster distribution in sand pile model, J. Stat. Phys. 59, 509 (1990).
  41. S. Lübeck and K. Usadel, Numerical determination of the avalanche exponents of the Bak-Tang-Wiesenfeld model, Phys. Rev. E 55, 4095 (1997).
  42. K. B. Lauritsen, S. Zapperi, and H. E. Stanley, Self-organized branching processes: Avalanche models with dissipation, Phys. Rev. E 54, 2483 (1996).
  43. S. Lise and H. J. Jensen, Transitions in nonconserving models of self-organized criticality, Phys. Rev. Lett. 76, 2326 (1996).
  44. P. Grassberger, H. Chaté, and G. Rousseau, Spreading in media with long-time memory, Phys. Rev. E 55, 2488 (1997).
  45. A. Jiménez-Dalmaroni and H. Hinrichsen, Epidemic processes with immunization, Phys. Rev. E 68, 036103 (2003).
  46. S. Ohler, D. Brady, P. Mischke, J. Bender, H. Ott, T. Niederprüm, W. Ripken, J. S. Otterbach, and M. Fleischhauer, Nonequilibrium universality of Rydberg-excitation spreading on a dynamic network [dataset] RPTU Kaiserslautern-Landau (2025), 10.26204/data/9.
  47. V. R. Barlett, J. Bigeón, M. Hoyuelos, and H. Mártin, Differences between fixed time step and kinetic Monte Carlo methods for biased diffusion, J. Comput. Phys. 228, 5740 (2009).
  48. J. P. Sethna, K. A. Dahmen, and C. R. Myers, Crackling noise, Nature (London) 410, 242 (2001).

Outline

Information

Phys. Rev. Research 7, 033167– Published 19 August, 2025
  • Received 27 February 2025
  • Accepted 13 July 2025
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