Incoherent soliton turbulence in nonlocal nonlinear media

Coexistence of Gaussian and non-Gaussian statistics in vector integrable turbulence

Integrable turbulence studies the complex dynamics of random waves for the nonlinear integrable systems, and it has become an important element in exploring the sophisticated turbulent phenomena. In the present work, based on the coupled nonlinear Schrödinger models, we have shown the coexistence of Gaussian and non-Gaussian single-point statistics in multiple wave components, which might be viewed as an exclusive feature for the vector integrable turbulence. This coexistent statistic can relate to different distributions of the vector solitonic excitations depending on the time-invariant nonlinear spectra. Our results are expected to shed light on a deeper understanding of the turbulent behaviors of vector waves and may motivate relevant experiments in the coupled optical or atomic systems.

Axion dark matter: What is it and why now?

The axion has emerged in recent years as a leading particle candidate to provide the mysterious dark matter in the cosmos, as we review here for a general scientific audience. We describe first the historical roots of the axion in the Standard Model of particle physics and the problem of charge-parity invariance of the strong nuclear force. We then discuss how the axion emerges as a dark matter candidate and how it is produced in the early universe. The symmetry properties of the axion dictate the form of its interactions with ordinary matter. Astrophysical considerations restrict the particle mass and interaction strengths to a limited range, which facilitates the planning of experiments to detect the axion. A companion review discusses the exciting prospect that the axion could be detected in the near term in the laboratory.

Incoherent localized structures and hidden coherent solitons from the gravitational instability of the Schrödinger-Poisson equation

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 Schrödinger-Poisson (or Newton-Schrödinger) 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, but their existence can be unveiled in the phase-space representation (spectrogram). We develop a theoretical approach that provides the coupled description of the coherent soliton component [governed by the Schrödinger-Poisson equation (SPE)] and of the incoherent structure [governed by a wave turbulence Vlasov-Poisson equation (WT-VPE)]. We demonstrate theoretically and numerically that the incoherent structure introduces an effective trapping potential that stabilizes the hidden coherent soliton and we show that the incoherent structure belongs to a family of stationary solutions of the WT-VPE. The analysis reveals that the incoherent structure evolves in the strongly nonlinear regime and that it is characterized by a compactly supported spectral shape. By relating the analytical properties of the hidden soliton to those of the stationary incoherent structure, we clarify the quantum-to-classical (i.e., SPE-to-VPE) correspondence in the limit ℏ/m→0: The hidden soliton appears as the latest residual quantum correction preceding the classical limit described by the VPE. This study is of potential interest for self-gravitating Boson models of fuzzy dark matter. Although we focus our paper on the Schrödinger-Poisson equation, we show that the regime of hidden solitons stabilized by an incoherent structure is general for long-range wave systems featured 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.

Coherent Soliton States Hidden in Phase Space and Stabilized by Gravitational Incoherent Structures

We consider the problem of the formation of soliton states from a modulationally unstable initial condition in the framework of the Schrödinger-Poisson (or Newton-Schrödinger) 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 multiscale 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.

Nearly integrable turbulence and rogue waves in disordered nonlinear Schrödinger systems

Integrable nonlinear Schrödinger (NLS) systems provide a platform for exploring the propagation and interaction of nonlinear waves. Extreme events such as rogue waves (RWs) are currently of particular interest. However, the presence of disorder in these systems is sometimes unavoidable, for example, in the forms of turbulent current in the ocean and random fluctuation in optical media, and its influence remains less understood. Here, we report numerical experiments of two nearly-integrable NLS equations with the effect of disorder showing that the probability of RW occurrence can be significantly increased by adding weak system noise. Linear and nonlinear spectral analyses are proposed to qualitatively explain those findings. Our results are expected to shed light on the understanding of the interplay between disorder and nonlinearity, and may motivate new experimental works in hydrodynamics, nonlinear optics, and Bose-Einstein condensates.

Incoherent Shock and Collapse Singularities in Non-Instantaneous Nonlinear Media

We study the dynamics of a partially incoherent optical pulse that propagates in a slowly responding nonlinear Kerr medium. We show that irrespective of the sign of the dispersion (either normal or anomalous), the incoherent pulse as a whole exhibits a global collective behavior characterized by a dramatic narrowing and amplification in the strongly non-linear regime. The theoretical analysis based on the Vlasov formalism and the method of the characteristics applied to a reduced hydrodynamic model reveal that such a strong amplitude-incoherent pulse originates in the existence of a concurrent shock-collapse singularity (CSCS): The envelope of the intensity of the random wave exhibits a collapse singularity, while the momentum exhibits a shock singularity. The dynamic behavior of the system after the shock-collapse singularity is characterized through the analysis of the phase-space dynamics.

Ensemble dynamics and the emergence of correlations in one- and two-dimensional wave turbulence

We investigate statistical properties of wave turbulence by monitoring the dynamics of ensembles of trajectories. The system under investigation is a simplified model for surface gravity waves in one and two dimensions with a square-root dispersion and a four-wave interaction term. The simulations of decaying turbulence confirm the Kolmogorov-Zakharov spectral power distribution of wave turbulence theory. Fourth-order correlations are computed numerically as ensemble averages of trajectories. The shape, scaling, and time evolution of the correlations agree with the predictions of wave turbulence theory.

Chaoticons described by nonlocal nonlinear Schrödinger equation

It is shown that the unstable evolutions of the Hermite-Gauss-type stationary solutions for the nonlocal nonlinear Schrödinger equation with the exponential-decay response function can evolve into chaotic states. This new kind of entities are referred to as chaoticons because they exhibit not only chaotic properties (with positive Lyapunov exponents and spatial decoherence) but also soliton-like properties (with invariant statistic width and interaction of quasi-elastic collisions).

Decoupled polarization dynamics of incoherent waves and bimodal spectral incoherent solitons

We consider the propagation of strongly incoherent waves in optical fibers in the framework of the vector nonlinear Schrödinger equation (VNLSE) accounting for the Raman effect. On the basis of the wave turbulence theory, we derive a kinetic equation that greatly simplifies the VNLSE and provides deep physical insight into incoherent wave dynamics. When applied to the study of polarization effects, the theory unexpectedly reveals that the linear polarization components of the incoherent wave evolve independently from each other, even in the presence of weak fiber birefringence. When applied to light propagation in bimodal fibers, the theory reveals that the incoherent modal components can be strongly coupled. After a complex transient, the modal components self-organize into a vector spectral incoherent soliton: The two solitons self-trap and propagate with a common velocity in frequency space.

Breather turbulence versus soliton turbulence: Rogue waves, probability density functions, and spectral features

Turbulence in integrable systems exhibits a noticeable scientific advantage: it can be expressed in terms of the nonlinear modes of these systems. Whether the majority of the excitations in the system are breathers or solitons defines the properties of the turbulent state. In the two extreme cases we can call such states "breather turbulence" or "soliton turbulence." The number of rogue waves, the probability density functions of the chaotic wave fields, and their physical spectra are all specific for each of these two situations. Understanding these extreme cases also helps in studies of mixed turbulent states when the wave field contains both solitons and breathers, thus revealing intermediate characteristics.

Stimulated Raman scattering threshold for partially coherent light in silica fibers

Stimulated Raman scattering (SRS) is an important limiting factor for achieving high peak power intensity in fiber amplifier systems. It was proposed to use partially coherent light to increase the SRS threshold significantly. In this paper, the SRS threshold of partially coherent light in silica fibers is investigated by both experiments and theoretical analysis, which show that the SRS threshold is independent on light coherency when the bandwidth of the light is much narrower than 30 nm.

From coherent shocklets to giant collective incoherent shock waves in nonlocal turbulent flows

Understanding turbulent flows arising from random dispersive waves that interact strongly through nonlinearities is a challenging issue in physics. Here we report the observation of a characteristic transition: strengthening the nonlocal character of the nonlinear response drives the system from a fully turbulent regime, featuring a sea of coherent small-scale dispersive shock waves (shocklets) towards the unexpected emergence of a giant collective incoherent shock wave. The front of such global incoherent shock carries most of the stochastic fluctuations and is responsible for a peculiar folding of the local spectrum. Nonlinear optics experiments performed in a solution of graphene nano-flakes clearly highlight this remarkable transition. Our observations shed new light on the role of long-range interactions in strongly nonlinear wave systems operating far from thermodynamic equilibrium, which reveals analogies with, for example, gravitational systems, and establishes a new scenario that can be common to many turbulent flows in photonic quantum fluids, hydrodynamics and Bose–Einstein condensates.

Understanding turbulent flows arising from random dispersive waves that interact through nonlinearities is a challenging issue in physics. Here, the authors model and observe experimentally in a nonlinear optics set-up the transition between a sea of small-scale shocklets and a giant collective shock wave.

Transition of weak wave turbulence to wave turbulence with intermittent collapses

We study the dynamics of one-dimensional nonlinear waves with a square-root dispersion. This dispersion allows strong interactions of distant modes in wave-number space, and it leads to a modulational instability of a carrier wave interacting with distant sidebands. Weak wave turbulence is found when the system is damped and weakly driven. A driving force that exceeds a critical strength leads to wave collapses coexisting with weak wave turbulence. We explain this transition behavior with the modulational instability of waves with the highest power: Below the threshold the instability is suppressed by the external long-wave damping force. Above the threshold the instability initiates wave collapses.

Anomalous velocity fluctuation in one-dimensional defect turbulence

In this paper various eccentric hole dynamics are presented in defect turbulence of the one-dimensional complex Ginzburg-Landau equation. Each hole shows coherent particlelike motion with nonconstant velocity. On the other hand, successive hole velocities without discriminating each hole exhibit anomalous intermittent motions being subject to multi-time-scale non-Gaussian statistics. An alternate non-Markov stochastic differential equation is proposed, by which all these observed statistical properties can be described successfully.

Generalized description of spectral incoherent solitons

Spectral incoherent solitons (SIS) refer to an incoherent solitonic structure that only can be identified in the frequency domain and which is sustained by noninstantaneous Raman-like nonlinearities. We provide a generalized formulation of SIS by considering the generalized nonlinear Schrödinger equation. We show that nonlinear dispersive effects (e.g., self-steepening) dramatically affect the structure of SIS, in particular by significantly decelerating their spectral velocity in frequency space. The wave turbulence description of the problem reveals an underlying self-organization process: the soliton trajectory in frequency space is selected in such a way that it allows the system to self-organize into a stationary SIS state.

Spectral long-range interaction of temporal incoherent solitons

We study the interaction of temporal incoherent solitons sustained by a highly noninstantaneous (Raman-like) nonlinear response. The incoherent solitons exhibit a nonmutual interaction, which can be either attractive or repulsive depending on their relative initial distance. The analysis reveals that incoherent solitons exhibit a long-range interaction in frequency space, which is in contrast with the expected spectral short-range interaction described by the usual approach based on the Raman-like spectral gain curve. Both phenomena of anomalous interaction and spectral long-range behavior of incoherent solitons are described in detail by a long-range Vlasov equation.

Incoherent dispersive shocks in the spectral evolution of random waves

We predict theoretically and numerically the existence of incoherent dispersive shock waves. They manifest themselves as an unstable singular behavior of the spectrum of incoherent waves that evolve in a noninstantaneous nonlinear environment. This phenomenon of "spectral wave breaking" develops in the weakly nonlinear regime of the random wave. We elaborate a general theoretical formulation of these incoherent objects on the basis of a weakly nonlinear statistical approach: a family of singular integro-differential kinetic equations is derived, which provides a detailed deterministic description of the incoherent dispersive shock wave phenomenon.

Spectral dynamics of incoherent waves with a noninstantaneous nonlinear response

We study the influence of a constant background noise on the dynamics of spectral incoherent solitons, which are incoherent structures sustained by a noninstantaneous (Raman-like) nonlinearity. As the level of the noise background increases, the incoherent wave enters a novel nonlinear regime characterized by oscillatory dynamics of the incoherent spectrum, which develop within a spectral cone during the propagation. In contrast to the conventional Raman-like spectral red shift, such incoherent spectral dynamics can be characterized by a significant spectral blue shift. On the basis of the kinetic wave theory, we derive explicit analytical expressions of these incoherent oscillatory spectral dynamics.

Cascaded phase matching and nonlinear symmetry breaking in fiber frequency combs

We report theoretical, numerical, and experimental studies of cascaded phase matching in fiber frequency combs and show how this mechanism is directly connected to the dynamics of supercontinuum generation. In particular, linking cascaded four-wave mixing with direct higher-order nonlinear processes allows us to derive a simple phase matching condition that governs nonlinear symmetry breaking in the presence of higher-order dispersion. We discuss how this mechanism provides a physical interpretation of soliton-induced Cherenkov radiation and associated spectral recoil in terms of phase-matched frequency mixing pumped by bichromatic pump pairs in the soliton spectrum. Theoretical and numerical predictions are confirmed via experiments using both quasicontinuous wave and picosecond pulse excitation.

Temporal dynamics of incoherent waves in noninstantaneous response nonlinear Kerr media

We consider the temporal evolution of an incoherent optical wave that propagates in a noninstantaneous response nonlinear medium, such as single mode optical fibers. In contrast with the expected Raman-like spectral redshift due to a delayed nonlinear response, we show that a highly noninstantaneous response leads to a genuine modulational instability of the incoherent optical wave. We derive a Vlasov-like kinetic equation that provides a detailed description of this process of incoherent modulational instability in the temporal domain.

Spontaneous breaking of the spatial homogeneity symmetry in wave turbulence

We report a surprising new result for wave turbulence which may have broader ramifications for general turbulence theories. Spatial homogeneity, the symmetry property that all statistical moments are functions only of the relative geometry of any configuration of points, can be spontaneously broken by the instability of the finite flux Kolmogorov-Zakharov spectrum in certain (usually one dimensional) situations. As a result, the nature of the statistical attractor changes dramatically, from a sea of resonantly interacting dispersive waves to an ensemble of coherent radiating pulses.