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Correlated many-body quantum dynamics of the Peregrine soliton

D. Diplaris1,2,*, G. A. Bougas3, P. G. Kevrekidis4, C.-L. Hung5,6, P. Schmelcher1,2, and S. I. Mistakidis3

  • *Contact author: dimitrios.diplaris@uni-hamburg.de
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Phys. Rev. Research 8, 023355 – Published 29 June, 2026

DOI: https://doi.org/10.1103/z9xj-9m24

Abstract

We explore the correlated dynamics underlying the formation of the quantum Peregrine soliton, a prototypical rogue-wave excitation, utilizing interaction quenches from repulsive to attractive couplings in an ultracold bosonic gas confined in a one-dimensional box trap. The latter emulates the so-called semiclassical initial conditions and the associated gradient catastrophe scenario facilitating the emergence of a high-density, doubly localized waveform. The ensuing multiorbital variant of the Peregrine soliton features notable deviations from its mean-field sibling, including a reduced peak amplitude, wider core, absence of the side density dips, and earlier formation times. Moreover, Peregrine soliton generation yields coherence losses, while experiencing two-body bunching within each of its sides, which show anti-bunching between each other. Controllable seeding of the Peregrine soliton is also demonstrated by tuning the atom number or the box length, while reducing the latter favors the generation of the time-periodic Kuznetsov-Ma breather. Our results highlight that correlations reshape the morphology of rogue waves in the genuinely quantum, nonintegrable realm, while setting the stage for the emergent field of quantum dispersive hydrodynamics.

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References (98)

  1. N. Akhmediev, A. Ankiewicz, and M. Taki, Waves that appear from nowhere and disappear without a trace, Phys. Lett. A 373, 675 (2009).
  2. C. Kharif, E. Pelinovsky, and A. Slunyaev, Rogue Waves in the Ocean (Springer Science & Business Media, Berlin Heidelberg, Germany, 2008).
  3. A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, Rogue wave observation in a water wave tank, Phys. Rev. Lett. 106, 204502 (2011).
  4. A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Super rogue waves: Observation of a higher-order breather in water waves, Phys. Rev. X 2, 011015 (2012).
  5. H. Bailung, S. K. Sharma, and Y. Nakamura, Observation of Peregrine solitons in a multicomponent plasma with negative ions, Phys. Rev. Lett. 107, 255005 (2011).
  6. B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, The Peregrine soliton in nonlinear fibre optics, Nat. Phys. 6, 790 (2010).
  7. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Optical rogue waves, Nature (London) 450, 1054 (2007).
  8. S. Perkins, Dashing rogues: Freak ocean waves pose threat to ships, deep-sea oil platforms, Science News 170, 328 (2006).
  9. A. Romero-Ros, G. C. Katsimiga, S. I. Mistakidis, S. Mossman, G. Biondini, P. Schmelcher, P. Engels, and P. G. Kevrekidis, Experimental realization of the Peregrine soliton in repulsive two-component Bose-Einstein condensates, Phys. Rev. Lett. 132, 033402 (2024).
  10. D. H. Peregrine, Water waves, nonlinear Schrödinger equations and their solutions, Aust. N. Z. Ind. Appl. Math. J. 25, 16 (1983).
  11. E. A. Kuznetsov, Solitons in parametrically unstable plasma, Dokl. Akad. Nauk SSSR 236, 575 (1977).
  12. Y.-C. Ma, The perturbed plane-wave solutions of the cubic Schrödinger equation, Stud. Appl. Math. 60, 43 (1979).
  13. J. Chen and D. E. Pelinovsky, Rogue waves arising on the standing periodic waves in the Ablowitz–Ladik equation, Stud. Appl. Math. 152, 147 (2024).
  14. E. A. Kuznetsov and A. V. Mikhailov, Stability of stationary waves in nonlinear weakly dispersive media, Zh. Eksp. Teor. Fiz 67, 1717 (1974) [Sov. Phys. JETP 40, 855 (1975)].
  15. M. S. Ruderman, Freak waves in laboratory and space plasmas: Freak waves in plasmas, Eur. Phys. J. Spec. Top. 185, 57 (2010).
  16. F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, Vector rogue waves and baseband modulation instability in the defocusing regime, Phys. Rev. Lett. 113, 034101 (2014).
  17. V. E. Zakharov and L. A. Ostrovsky, Modulation instability: The beginning, Physica D 238, 540 (2009).
  18. M. Bertola and A. Tovbis, Universality for the focusing nonlinear Schrödinger equation at the gradient catastrophe point: Rational breathers and poles of the tritronquée solution to Painlevé I, Commun. Pure Appl. Math. 66, 678 (2013).
  19. G. A. El, E. G. Khamis, and A. Tovbis, Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves, Nonlinearity 29, 2798 (2016).
  20. G. Biondini and D. Mantzavinos, Universal nature of the nonlinear stage of modulational instability, Phys. Rev. Lett. 116, 043902 (2016).
  21. G. A. El’A. V. Gurevich, V. V. Khodorovskiî, A. L. Krylov, et al., Modulational instability and formation of a nonlinear oscillatory structure in a “focusing” medium, Phys. Lett. A 177, 357 (1993).
  22. G. El and M. Hoefer, Dispersive shock waves and modulation theory, Physica D 333, 11 (2016).
  23. W. Wan, D. V. Dylov, C. Barsi, and J. W. Fleischer, Diffraction from an edge in a self-focusing medium, Opt. Lett. 35, 2819 (2010).
  24. M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Dispersive and classical shock waves in Bose-Einstein condensates and gas dynamics, Phys. Rev. A 74, 023623 (2006).
  25. S. Mossman, S. I. Mistakidis, G. C. Katsimiga, A. Romero-Ros, G. Biondini, P. Schmelcher, P. Engels, and P. G. Kevrekidis, Nonlinear stage of modulational instability in repulsive two-component Bose-Einstein condensates, Phys. Rev. Lett. 135, 113401 (2025).
  26. C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Rev. Mod. Phys. 82, 1225 (2010).
  27. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  28. K. Henderson, C. Ryu, C. MacCormick, and M. Boshier, Experimental demonstration of painting arbitrary and dynamic potentials for Bose–Einstein condensates, New J. Phys. 11, 043030 (2009).
  29. K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, Formation and propagation of matter-wave soliton trains, Nature (London) 417, 150 (2002).
  30. J. H. Nguyen, D. Luo, and R. G. Hulet, Formation of matter-wave soliton trains by modulational instability, Science 356, 422 (2017).
  31. P. J. Everitt, M. A. Sooriyabandara, M. Guasoni, P. B. Wigley, C. H. Wei, G. D. McDonald, K. S. Hardman, P. Manju, J. D. Close, C. C. N. Kuhn, S. S. Szigeti, Y. S. Kivshar, and N. P. Robins, Observation of a modulational instability in Bose-Einstein condensates, Phys. Rev. A 96, 041601(R) (2017).
  32. A. Di Carli, C. D. Colquhoun, G. Henderson, S. Flannigan, G.-L. Oppo, A. J. Daley, S. Kuhr, and E. Haller, Excitation modes of bright matter-wave solitons, Phys. Rev. Lett. 123, 123602 (2019).
  33. C.-A. Chen and C.-L. Hung, Observation of universal quench dynamics and Townes soliton formation from modulational instability in two-dimensional Bose gases, Phys. Rev. Lett. 125, 250401 (2020).
  34. S. Banerjee, K. Zhou, S. K. Tiwari, H. Tamura, R. Li, P. Kevrekidis, S. I. Mistakidis, V. Walther, and C.-L. Hung, Collapse of a quantum vortex in an attractive two-dimensional Bose gas, Phys. Rev. Lett. 135, 073401 (2025).
  35. H. Tamura, S. Banerjee, R. Li, P. Kevrekidis, S. I. Mistakidis, and C.-L. Hung, Observation of many-body coherence in quasi-one-dimensional attractive Bose gases, arXiv:2506.13597.
  36. Z. Dutton and C. W. Clark, Effective one-component description of two-component Bose-Einstein condensate dynamics, Phys. Rev. A 71, 063618 (2005).
  37. G. A. Bougas, G. C. Katsimiga, S. Mossman, P. Engels, P. G. Kevrekidis, and S. I. Mistakidis, Observation of vector rogue waves in repulsive three-component atomic mixtures, arXiv:2510.24917.
  38. B. Bakkali-Hassani, C. Maury, Y.-Q. Zou, E. Le Cerf, R. Saint-Jalm, P. C. M. Castilho, S. Nascimbene, J. Dalibard, and J. Beugnon, Realization of a Townes soliton in a two-component planar Bose gas, Phys. Rev. Lett. 127, 023603 (2021).
  39. B. Bakkali-Hassani and J. Dalibard, Townes soliton and beyond: Non-miscible Bose mixtures in 2D, arXiv:2210.14045.
  40. F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Solutions of the vector nonlinear Schrödinger equations: Evidence for deterministic rogue waves, Phys. Rev. Lett. 109, 044102 (2012).
  41. C. B. Ward, P. G. Kevrekidis, and N. Whitaker, Evaluating the robustness of rogue waves under perturbations, Phys. Lett. A 383, 2584 (2019).
  42. E. G. Charalampidis, J. Cuevas-Maraver, D. J. Frantzeskakis, and P. G. Kevrekidis, Rogue waves in ultracold bosonic seas, Rom. Rep. Phys. 70, 504 (2018).
  43. S. Chandramouli, S. I. Mistakidis, G. C. Katsimiga, D. J. Ratliff, D. J. Frantzeskakis, and P. G. Kevrekidis, Rogue waves in extended Gross-Pitaevskii models with a Lee-Huang-Yang correction, Phys. Rev. A 113, 013308 (2026).
  44. E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman, Dynamics of collapsing and exploding Bose-Einstein condensates, Nature (London) 412, 295 (2001).
  45. J. Adriazola and P. G. Kevrekidis, Experimentally tractable generation of high-order rogue waves in Bose-Einstein condensates, Phys. Rev. E 112, 064207 (2025).
  46. L. Cao, S. Krönke, O. Vendrell, and P. Schmelcher, The multi-layer multi-configuration time-dependent Hartree method for bosons: Theory, implementation, and applications, J. Chem. Phys. 139, 134103 (2013).
  47. L. Cao, V. Bolsinger, S. I. Mistakidis, G. M. Koutentakis, S. Krönke, J. M. Schurer, and P. Schmelcher, A unified ab initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures, J. Chem. Phys. 147, 044106 (2017).
  48. S. Krönke, L. Cao, O. Vendrell, and P. Schmelcher, Non-equilibrium quantum dynamics of ultra-cold atomic mixtures: The multi-layer multi-configuration time-dependent Hartree method for bosons, New J. Phys. 15, 063018 (2013).
  49. L. Pitaevskii and S. Stringari, Bose-Einstein Condensation, International Series of Monographs on Physics (Clarendon Press, Oxford, United Kingdom, 2003).
  50. N. Navon, R. P. Smith, and Z. Hadzibabic, Quantum gases in optical boxes, Nat. Phys. 17, 1334 (2021).
  51. M. Tajik, B. Rauer, T. Schweigler, F. Cataldini, J. Sabino, F. S. Møller, S.-C. Ji, I. E. Mazets, and J. Schmiedmayer, Designing arbitrary one-dimensional potentials on an atom chip, Opt. Express 27, 33474 (2019).
  52. M. Olshanii, Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons, Phys. Rev. Lett. 81, 938 (1998).
  53. T. Bergeman, M. G. Moore, and M. Olshanii, Atom-atom scattering under cylindrical harmonic confinement: Numerical and analytic studies of the confinement induced resonance, Phys. Rev. Lett. 91, 163201 (2003).
  54. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U.S. Government Printing Office, Washington, D.C., USA, 1948), Vol. 55.
  55. T. Köhler, K. Góral, and P. S. Julienne, Production of cold molecules via magnetically tunable Feshbach resonances, Rev. Mod. Phys. 78, 1311 (2006).
  56. J. I. Kim, V. S. Melezhik, and P. Schmelcher, Suppression of quantum scattering in strongly confined systems, Phys. Rev. Lett. 97, 193203 (2006).
  57. O. E. Alon, A. I. Streltsov, and L. S. Cederbaum, Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems, Phys. Rev. A 77, 033613 (2008).
  58. O. E. Alon, A. I. Streltsov, and L. S. Cederbaum, Unified view on multiconfigurational time propagation for systems consisting of identical particles, J. Chem. Phys. 127, 154103 (2007).
  59. J. H. V. Nguyen, M. C. Tsatsos, D. Luo, A. U. J. Lode, G. D. Telles, V. S. Bagnato, and R. G. Hulet, Parametric excitation of a Bose-Einstein condensate: From Faraday waves to granulation, Phys. Rev. X 9, 011052 (2019).
  60. G. C. Katsimiga, G. Koutentakis, S. I. Mistakidis, P. G. Kevrekidis, and P. Schmelcher, Dark–bright soliton dynamics beyond the mean-field approximation, New J. Phys. 19, 073004 (2017).
  61. S. I. Mistakidis, G. C. Katsimiga, P. G. Kevrekidis, and P. Schmelcher, Correlation effects in the quench-induced phase separation dynamics of a two species ultracold quantum gas, New J. Phys. 20, 043052 (2018).
  62. A. U. J. Lode, C. Lévêque, L. B. Madsen, A. I. Streltsov, and O. E. Alon, Colloquium: Multiconfigurational time-dependent Hartree approaches for indistinguishable particles, Rev. Mod. Phys. 92, 011001 (2020).
  63. S. I. Mistakidis, A. Volosniev, R. Barfknecht, T. Fogarty, T. Busch, A. Foerster, P. Schmelcher, and N. Zinner, Few-body Bose gases in low dimensions—A laboratory for quantum dynamics, Phys. Rep. 1042, 1 (2023).
  64. J. Light, I. Hamilton, and J. Lill, Generalized discrete variable approximation in quantum mechanics, J. Chem. Phys. 82, 1400 (1985).
  65. J. Frenkel, Wave Mechanics: Elementary Theory (Clarendon Press, Oxford, United Kingdom, 1934).
  66. D. Bilman, L. Ling, and P. D. Miller, Extreme superposition: Rogue waves of infinite order and the Painlevé-III hierarchy, Duke Math. J. 169, 671 (2020).
  67. J. S. He, H. R. Zhang, L. H. Wang, K. Porsezian, and A. S. Fokas, Generating mechanism for higher-order rogue waves, Phys. Rev. E 87, 052914 (2013).
  68. D. Bilman and P. D. Miller, Broader universality of rogue waves of infinite order, Physica D 435, 133289 (2022).
  69. M. Frometa, P. Dias, P. Magnani, M. Martins, M. Hugbart, A. Cipris, P. W. Courteille, and R. C. Teixeira, Phase-contrast imaging of a dense atomic cloud, Rev. Sci. Instrum. 96, 083203 (2025).
  70. L. Wolswijk, L. Cavicchioli, G. Vinelli, M. Chiarotti, L. Donati, M. F. Fernandez, D. H. Rajkov, C. Mancini, P. Vezio, T. Zhou, et al., Trapping, manipulating and probing ultracold atoms: A quantum technologies tutorial, arXiv:2510.20790.
  71. C.-L. Hung and C. Chin, In situ imaging of atomic quantum gases, in Quantum Gas Experiments: Exploring Many-Body States (World Scientific, 2015), pp. 101–120.
  72. K. Sakmann, A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Reduced density matrices and coherence of trapped interacting bosons, Phys. Rev. A 78, 023615 (2008).
  73. R. Roy, A. Gammal, M. C. Tsatsos, B. Chatterjee, B. Chakrabarti, and A. U. J. Lode, Phases, many-body entropy measures, and coherence of interacting bosons in optical lattices, Phys. Rev. A 97, 043625 (2018).
  74. M. Hoefer and M. Ablowitz, Dispersive shock waves, Scholarpedia 4, 5562 (2009).
  75. J. J. Chang, P. Engels, and M. A. Hoefer, Formation of dispersive shock waves by merging and splitting Bose-Einstein condensates, Phys. Rev. Lett. 101, 170404 (2008).
  76. N. Gemelke, X. Zhang, C.-L. Hung, and C. Chin, In situ observation of incompressible Mott-insulating domains in ultracold atomic gases, Nature (London) 460, 995 (2009).
  77. C. Gross and W. S. Bakr, Quantum gas microscopy for single atom and spin detection, Nat. Phys. 17, 1316 (2021).
  78. R. Yao, S. Chi, M. Wang, R. J. Fletcher, and M. Zwierlein, Measuring pair correlations in Bose and Fermi gases via atom-resolved microscopy, Phys. Rev. Lett. 134, 183402 (2025).
  79. J. Xiang, E. Cruz-Colón, C. C. Chua, W. R. Milner, J. de Hond, J. F. Fricke, and W. Ketterle, In situ imaging of the thermal de Broglie wavelength in an ultracold Bose gas, Phys. Rev. Lett. 134, 183401 (2025).
  80. T. de Jongh, J. Verstraten, M. Dixmerias, C. Daix, B. Peaudecerf, and T. Yefsah, Quantum gas microscopy of fermions in the continuum, Phys. Rev. Lett. 134, 183403 (2025).
  81. M. McDonald, J. Trisnadi, K.-X. Yao, and C. Chin, Superresolution microscopy of cold atoms in an optical lattice, Phys. Rev. X 9, 021001 (2019).
  82. S. Subhankar, Y. Wang, T.-C. Tsui, S. L. Rolston, and J. V. Porto, Nanoscale atomic density microscopy, Phys. Rev. X 9, 021002 (2019).
  83. D. Delande and K. Sacha, Many-body matter-wave dark soliton, Phys. Rev. Lett. 112, 040402 (2014).
  84. A. Syrwid and K. Sacha, Quantum dark solitons in a Bose gas confined in a hard-wall box, Phys. Rev. A 96, 043602 (2017).
  85. G. C. Katsimiga, S. I. Mistakidis, G. M. Koutentakis, P. G. Kevrekidis, and P. Schmelcher, Many-body dissipative flow of a confined scalar Bose-Einstein condensate driven by a Gaussian impurity, Phys. Rev. A 98, 013632 (2018).
  86. G. C. Katsimiga, S. I. Mistakidis, G. Koutentakis, P. G. Kevrekidis, and P. Schmelcher, Many-body quantum dynamics in the decay of bent dark solitons of Bose–Einstein condensates, New J. Phys. 19, 123012 (2017).
  87. E. J. Mueller, T.-L. Ho, M. Ueda, and G. Baym, Fragmentation of Bose-Einstein condensates, Phys. Rev. A 74, 033612 (2006).
  88. M. Naraschewski and R. J. Glauber, Spatial coherence and density correlations of trapped Bose gases, Phys. Rev. A 59, 4595 (1999).
  89. S. Hodgman, R. Dall, A. Manning, K. Baldwin, and A. Truscott, Direct measurement of long-range third-order coherence in Bose-Einstein condensates, Science 331, 1046 (2011).
  90. P. E. Tavares, A. R. Fritsch, G. D. Telles, M. S. Hussein, F. Impens, R. Kaiser, and V. S. Bagnato, Matter wave speckle observed in an out-of-equilibrium quantum fluid, Proc. Natl. Acad. Sci. USA 114, 12691 (2017).
  91. G. Gauthier, I. Lenton, N. McKay Parry, M. Baker, M. Davis, H. Rubinsztein-Dunlop, and T. Neely, Direct imaging of a digital-micromirror device for configurable microscopic optical potentials, Optica 3, 1136 (2016).
  92. A. Wenz, G. Zürn, S. Murmann, I. Brouzos, T. Lompe, and S. Jochim, From few to many: Observing the formation of a Fermi sea one atom at a time, Science 342, 457 (2013).
  93. B. J. Lester, Y. Lin, M. O. Brown, A. M. Kaufman, R. J. Ball, E. Knill, A. M. Rey, and C. A. Regal, Measurement-based entanglement of noninteracting bosonic atoms, Phys. Rev. Lett. 120, 193602 (2018).
  94. J. P. Ronzheimer, M. Schreiber, S. Braun, S. S. Hodgman, S. Langer, I. P. McCulloch, F. Heidrich-Meisner, I. Bloch, and U. Schneider, Expansion dynamics of interacting bosons in homogeneous lattices in one and two dimensions, Phys. Rev. Lett. 110, 205301 (2013).
  95. N. Karjanto, Peregrine soliton as a limiting behavior of the Kuznetsov-Ma and Akhmediev breathers, Front. Phys. 9, 599767 (2021).
  96. J. Satsuma and N. Yajima, Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media, Prog. Theor. Phys. Suppl. 55, 284 (1974).
  97. B. I. Suleimanov, Effect of a small dispersion on self-focusing in a spatially one-dimensional case, JETP Lett. 106, 400 (2017).
  98. A. Romero-Ros, G. C. Katsimiga, S. I. Mistakidis, B. Prinari, G. Biondini, P. Schmelcher, and P. G. Kevrekidis, Theoretical and numerical evidence for the potential realization of the Peregrine soliton in repulsive two-component Bose-Einstein condensates, Phys. Rev. A 105, 053306 (2022).

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Phys. Rev. Research 8, 023355– Published 29 June, 2026
  • Received 23 December 2025
  • Accepted 3 June 2026
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