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arXiv:2603.25908

Extreme (Rogue) Waves: From Theory to Experiments in Ultracold Gases and Beyond

A. Chabchoub, P. Engels, P. G. Kevrekidis, S. I. Mistakidis, G. C. Katsimiga, M. E. Mossman, S. Mossman

cond-mat.quant-gasnlin.PSquant-phSubmitted Mar 26, 2026• Announced Mar 30, 2026• 0 citations
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Abstract

In this Chapter, we review key theoretical and experimental advances in the study of extreme nonlinear wave events, called rogue waves (RWs), in both single-component attractively interacting and two-component repulsive mixtures of ultracold quantum gases. Starting from the exact rational solutions of the integrable focusing nonlinear Schroedinger model, the hierarchy of RW solutions is exemplified. These range from the Peregrine soliton (PS) and, related to it, the destabilization into a multi-peak cascade of PSs dubbed "Christmas-tree", to the Akhmediev breather, and Kuznetsov-Ma soliton as well as higher-order RWs. Emphasis is placed on their controllable dynamical emergence and characteristics in non-integrable quantum many-body systems described by Gross-Pitaevskii models and extensions thereof through different protocols such as modulational instability, gradient catastrophe, and dam-break flows. We further discuss how immiscible particle-imbalanced repulsive mixtures can be cast into effective attractive single-component environments capable of hosting RWs. Next, state-of-the-art experimental techniques are summarized within the ultracold realm that can be utilized to realize solitary waves, modulational instability, dispersive shock waves and RWs including the very recent first experimental observation of the PS, enabled through engineered effective focusing interactions and precise dynamical triggering. Observations of these extreme events in water waves, nonlinear optics and beyond are also outlined, highlighting their broader relevance and potential of emergence in disparate physical settings. Our exposition aims at showcasing ultracold atomic gases as versatile platforms for controllably generating and probing extreme nonlinear events, among others, in the quantum realm across integrable and non-integrable settings.

Comments
25 pages, 13 figures

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In this Chapter, we review key theoretical and experimental advances in the study of extreme nonlinear wave events, called rogue waves (RWs), in both single-component attractively interacting and two-component repulsive mixtures of ultracold quantum gases. Starting from the exact rational solutions of the integrable focusing nonlinear Schroedinger model, the hierarchy of RW solutions is exemplified. These range from the Peregrine soliton (PS) and, related to it, the destabilization into a multi-peak cascade of PSs dubbed "Christmas-tree", to the Akhmediev breather, and Kuznetsov-Ma soliton as well as higher-order RWs. Emphasis is placed on their controllable dynamical emergence and characteristics in non-integrable quantum many-body systems described by Gross-Pitaevskii models and extensions thereof through different protocols such as modulational instability, gradient catastrophe, and dam-break flows. We further discuss how immiscible particle-imbalanced repulsive mixtures can be cast into effective attractive single-component environments capable of hosting RWs. Next, state-of-the-art experimental techniques are summarized within the ultracold realm that can be utilized to realize solitary waves, modulational instability, dispersive shock waves and RWs including the very recent first experimental observation of the PS, enabled through engineered effective focusing interactions and precise dynamical triggering. Observations of these extreme events in water waves, nonlinear optics and beyond are also outlined, highlighting their broader relevance and potential of emergence in disparate physical settings. Our exposition aims at showcasing ultracold atomic gases as versatile platforms for controllably generating and probing extreme nonlinear events, among others, in the quantum realm across integrable and non-integrable settings.
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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 semi-classical initial conditions and the associated gradient catastrophe scenario facilitating the emergence of a high-density, doubly localized waveform. The ensuing multi-orbital 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.
We investigate the quantum Zeno dynamics of the rogue waves that are encountered in optics and quantum mechanics. Considering their usage in modeling rogue wave dynamics, we analyze the quantum Zeno dynamics of the Akhmediev breathers, Peregrine and Akhmediev-Peregrine soliton solutions of the nonlinear Schrodinger equation. We show that frequent measurements of the wave inhibits its movement in the observation domain for each of these solutions. We analyze the spectra of the rogue waves under Zeno dynamics. We also analyze the effect of observation frequency on the rogue wave profile and on the probability of lingering of the wave in the observation domain.
In recent years, bright soliton-like structures composed of gaseous Bose-Einstein condensates have been generated at ultracold temperature. The experimental capacity to precisely engineer the nonlinearity and potential landscape experienced by these solitary waves offers an attractive platform for fundamental study of solitonic structures. The presence of three spatial dimensions and trapping implies that these are strictly distinct objects to the true soliton solutions. Working within the zero-temperature mean-field description, we explore the solutions and stability of bright solitary waves, as well as their interactions. Emphasis is placed on elucidating their similarities and differences to the true bright soliton. The rich behaviour introduced in the bright solitary waves includes the collapse instability and symmetry-breaking collisions. We review the experimental formation and observation of bright solitary matter waves to date, and compare to theoretical predictions. Finally we discuss the current state-of-the-art of this area, including beyond-mean-field descriptions, exotic bright solitary waves, and proposals to exploit bright solitary waves in interferometry and as surface probes.
We experimentally realize the Peregrine soliton in a highly particle-imbalanced two-component repulsive Bose-Einstein condensate in the immiscible regime. The effective focusing dynamics and resulting modulational instability of the minority component provide the opportunity to dynamically create a Peregrine soliton with the aid of an attractive potential well that seeds the initial dynamics. The Peregrine soliton formation is highly reproducible, and our experiments allow us to separately monitor the minority and majority components, and to compare with the single component dynamics in the absence or presence of the well with varying depths. We showcase the centrality of each of the ingredients leveraged herein. Numerical corroborations and a theoretical basis for our findings are provided through three-dimensional simulations emulating the experimental setting and via a one-dimensional analysis further exploring its evolution dynamics.