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Register a new userCoherent soliton states hidden in phase-space and stabilized by gravitational incoherent structures
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We consider the problem of the formation of soliton states from a modulationally unstable initial condition in the framework of the Schrodinger-Poisson (or Newton-Schrodinger) equation accounting for gravitational interactions. We unveil a previously unrecognized regime: By increasing the nonlinearity, the system self-organizes into an incoherent localized structure that contains hidden coherent soliton states. The solitons are hidden in the sense that they are fully immersed in random wave fluctuations: The radius of the soliton is much larger than the correlation radius of the incoherent fluctuations while its peak amplitude is of the same order of such fluctuations. Accordingly, the solitons can hardly be identified in the usual spatial or spectral domains, while their existence is clearly unveiled in the phase-space representation. Our multi-scale theory based on coupled coherent-incoherent wave turbulence formalisms reveals that the hidden solitons are stabilized and trapped by the incoherent localized structure. Furthermore, hidden binary soliton systems are identified numerically and described theoretically. The regime of hidden solitons is of potential interest for self-gravitating Boson models of fuzzy dark matter. It also sheds new light on the quantum-to-classical correspondence with gravitational interactions. The hidden solitons can be observed in nonlocal nonlinear optics experiments through the measurement of the spatial spectrogram.
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The long-term behavior of a modulationally unstable conservative nonintegrable system is known to be characterized by the soliton turbulence self-organization process. We consider this problem in the presence of a long-range interaction in the framework of the Schrodinger-Poisson (or Newton-Schrodinger) equation accounting for the gravitational interaction. By increasing the amount of nonlinearity, the system self-organizes into a large-scale incoherent localized structure that contains hidden coherent soliton states: The solitons can hardly be identified in the usual spatial or spectral domains, while their existence is unveiled in the phase-space representation (spectrogram). We develop a theoretical approach that provides the coupled description of the coherent soliton component (governed by an effective Schrodinger-Poisson equation) and of the incoherent component (governed by a wave turbulence Vlasov-Poisson equation). The theory shows that the incoherent structure introduces an effective trapping potential that stabilizes the hidden coherent soliton, a mechanism that we verify by direct numerical simulations. The theory characterizes the properties of the localized incoherent structure, such as its compactly supported spectral shape. It also clarifies the quantum-to-classical correspondence in the presence of gravitational interactions. This study is of potential interest for self-gravitating Boson models of fuzzy dark matter. Although we focus our paper on the Schrodinger-Poisson equation, we show that our results are general for long-range wave systems characterized by an algebraic decay of the interacting potential. This work should stimulate nonlinear optics experiments in highly nonlocal nonlinear (thermal) media that mimic the long-range nature of gravitational interactions.
The generation of high-intensity optical fields from harmonic-wave photons, interacting via a cross-phase modulation with dark solitons both propagating in a Kerr nonlinear medium, is examined. The focus is on a pump consisting of time-entangled dark-soliton patterns, forming a periodic waveguide along the path of the harmonic-wave probe. It is shown that an increase of the strength of cross-phase modulation respective to the self-phase modulation, favors soliton-mode proliferation in the bound-state spectrum of the trapped harmonic-wave probe. The induced soliton modes, which display the structures of periodic soliton lattices, are not just rich in numbers, they also form a great diversity of population of soliton crystals with a high degree of degeneracy.
We investigate the interaction between a light beam and a two-dimensional photonic lattice that is photo-induced in a photorefractive crystal using partially coherent light. We demonstrate that this interaction process is associated with a host of new phenomena including lattice dislocation, lattice deformation, and creation of structures akin to optical polarons. In addition, two-dimensional discrete solitons are realized in such partially coherent photonic lattices.
The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals, a type of nonlinear metamaterial, exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures --- which include traveling solitary waves, dispersive shock waves, and discrete breathers --- have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.
We report the numerical realization and demonstration of robustness of certain 2-component structures in Bose-Einstein Condensates in 2 and 3 spatial dimensions with non-trivial topological charge in one of the components. In particular, we identify a stable symbiotic state in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, as a result of the effective potential created by a stable vortex in the other component. The resulting vortex-bright solitary waves, which naturally generalize the recently experimentally observed dark-bright solitons, are examined both in the homogeneous medium and in the presence of parabolic and periodic external confinement and are found to be very robust.
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