Soliton States Research Articles

Bound state of asymmetric pure-quartic solitons in motion

Bound state of asymmetric pure-quartic solitons in motion

Three-component soliton states in spinor F = 1 Bose-Einstein condensates with PT-symmetric generalized Scarf-II potentials

Abstract Introducing PT-symmetric generalized Scarf-II potentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seeking stable soliton states in quasi-one-dimensional spin-1 Bose-Einstein condensates. In scenarios where the spin-independent parameter c_0 and the spin-dependent parameter c_2 vary, we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross-Pitaevskii equations with PT-symmetric generalized Scarf-II potentials. We obtain analytical soliton states and find that simply modulating c_2 may change the analytical soliton states from unstable to stable. Additionally, we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations, exhibiting distinct behavior in energy exchange. For further investigation, we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components. These findings may contribute to a deeper understanding of solitons in Bose-Einstein condensates with PT-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.

Standing Solitons Tuned by Impurities in Damped Nonlinear Lattices under External Excitation.

Periodic chains of nonlinear oscillators are known to support solitonic solutions within a specific range of physical parameters when damping effect is considered. This Letter investigates the dynamics of stationary solitons in damped nonlinear lattices under external excitation, focusing on the influence of impurities related to the natural frequency of the oscillators. We demonstrate experimentally and numerically that incorporating impurities into externally driven periodic lattices can expand the solitonic stability diagram under high-damping areas and near the Hopf bifurcation of periodic structures. A mathematical description that closely aligns with experimental realities is presented through the disordered damped nonlinear Schrödinger equation. Specifically, we prove how impurities along the chain can spontaneously nucleate the lattice solitons. The obtained results open the way toward the functionalization of disorder to control nonlinear energy localization in damped nonperiodic structures.

Solitonic ground state in supersymmetric theory in background

A solitonic ground state called a chiral soliton lattice (CSL) is realized in a supersymmetric theory with background magnetic field and finite chemical potential. To this end, we construct, in the superfield formalism, a supersymmetric chiral sine-Gordon model as a neutral pion sector of a supersymmetric two-flavor chiral Lagrangian with a Wess-Zumino-Witten term. The CSL ground state appears in the presence of either a strong magnetic field and/or large chemical potential, or a background fermionic condensate in the form of a fermion bilinear consisting of the gaugino and a superpartner of a baryon gauge field.

Topological parametric gain and two-color edge states in equidistant lithium niobate waveguide arrays.

We analyze parametric χ2 processes in equidistant finite-size arrays of thin-film lithium niobate waveguides, where the fundamental harmonic (FH) field supports topological edge states due to the specific interplay between inter- and intra-modal couplings of two families of guided modes, while the second-harmonic (SH) field only supports bulk modes. Regimes of topological parametric gain are identified, where the gain only occurs in the edge states of the FH field, regardless of the spatial distribution of the pump SH field. The topological gain of the FH component generally triggers localization of the SH field near an edge of the array in the optical parametric oscillation dynamics. In small-size arrays, parametric gain at both edges can be observed even when pumped at one side. This process can lead to an anomalous "tunneling" of the SH field to the opposite edge. We also analyze the existence and stability of two-color nonlinear edge states (solitons), in which both FH and SH fields are localized at an edge of the array. Depending on the phase-matching condition, such solitons either emerge from the linear FH edge state without a power threshold or exist above a certain power threshold dictated by the coupling strength in the SH field.

Excitation and manipulation of super cavity solitons in multi-stable passive Kerr resonators

We report on the theoretical analysis as well as the numerical simulations about the nonlinear dynamics of cavity solitons in a passive Kerr resonator operating in the multistable regime under the condition of a sufficiently strong pump. In this regime, the adjacent tilted cavity resonances might overlap, thus leading to the co-existence of combinatory states of temporal cavity solitons and the extended modulation instability patterns. The cavity in the regime of multistablity may sustain distinct families of cavity solitons, vividly termed as super cavity solitons with much higher intensity and broader spectra if compared with those in the conventional bi-stable regime. The description of such complex cavity dynamics in the multstable regime requires either the infinite-dimensional Ikeda map, or the derived mean-field coupled Lugiato-Lefever equations by involving multiple contributing cavity resonances. With the latter model, we revealed the existence of different orders of super cavity solitons, whose stationary solutions were obtained by using the Newton-Raphson algorithm. Along this line, with the continuation calculation, we have plotted the Hopf / saddle-node bifurcation curves, thus identifying the existing map of the stable and breathing (super) cavity solitons. With this defined parameter space, we have proposed an efficient method to excite and switch the super cavity solitons by adding an appropriate intensity (or phase) perturbation on the pump. Such deterministic cavity soliton manipulation technique is demonstrated to underpin the multi-level coding, which may enable the large capacity all-optical buffering based on the passive fiber ring cavities.

Correlation between soliton state and power in erbium-doped fiber lasers based on PtS2 saturable absorbers

Over the past few years, there has been a significant amount of interest in transition metal dichalcogenides (TMDs) materials within the fiber laser area. PtS2 as a typical TMD family material, has a tunable and narrow bandgap, and the material is stable and easy to exfoliate. This material is an excellent option for a saturable absorber (SA) in fiber lasers. In this work, PtS2-SA was obtained by liquid phase exfoliation (LPE) and using tapered fibers. A multi-soliton erbium-doped fiber laser based on PtS2-SA is realized. Experiments were performed by improving the pump power to sequentially realize three soliton phenomena. They were conventional soliton (CS), 120th order harmonic mode-locking (HML) and dissipative soliton resonance (DSR). This work demonstrates that PtS2 has good saturable absorption properties. The potential of PtS2 in the field of fiber lasers is demonstrated. It is valuable for the study of soliton evolution.

Spontaneous symmetry breaking and vortices in a tri-core nonlinear fractional waveguide

We introduce a waveguiding system composed of three linearly-coupled fractional waveguides, with a triangular (prismatic) transverse structure. It may be realized as a tri-core nonlinear optical fiber with fractional group-velocity dispersion (GVD), or, possibly, as a system of coupled Gross–Pitaevskii equations for a set of three tunnel-coupled cigar-shaped traps filled by a Bose–Einstein condensate of particles moving by Lévy flights. The analysis is focused on the phenomenon of spontaneous symmetry breaking (SSB) between components of triple solitons, and the formation and stability of vortex modes. In the self-focusing regime, we identify symmetric and asymmetric soliton states, whose structure and stability are determined by the Lévy index of the fractional GVD, the inter-core coupling strength, and the total energy, which determines the system’s nonlinearity. Bifurcation diagrams (of the supercritical type) reveal regions where SSB occurs, identifying the respective symmetric and asymmetric ground-state soliton modes. In agreement with the general principle of the SSB theory, the solitons with broken inter-component symmetry prevail with the increase of the energy in the weakly-coupled system. Three-components vortex solitons (which do not feature SSB) are studied too. Because the fractional GVD breaks the system’s Galilean invariance, we also address mobility of the vortex solitons, by applying a boost to them.

Pulse-state switchable mode-locked Tm-doped fiber laser based on linear-cavity nonlinear polarization rotation

We present an experimental demonstration of a pulse-state switchable Tm-doped fiber laser, mode-locked using linear-cavity nonlinear polarization rotation (LNPR). Compared to previous LNPR lasers with free-space structures, our laser cavity employs an all-fiber design, which enhances the laser flexibility. The laser operates in three states within a large anomalous dispersion, including conventional soliton, multi-pulse, and noise-like pulse states. This research provides an effective solution for realizing a multifunctional Tm-doped fiber laser with a simple and stable configuration, making it both appealing and promising for various practical applications.

Generation of Soliton Frequency Combs in NEMS.

In this study, we present an innovative approach leveraging combination internal resonances within a NEMS platform to generate mechanical soliton frequency combs (FCs) spanning a broad spectrum. In the time domain, the FCs take the form of a periodic train of narrow pulses, a highly coveted phenomenon within the realm of nonlinear wave-matter interactions. Our method relies on an intricate interaction among multiple vibration modes of a bracket-nanocantilever enabled by the strong nonlinearity of the electrostatic field. Through numerical simulation and experimental validation, we demonstrate that by amplifying the motions of the NEMS with the external electrostatic forcing tuned to excite the superharmonic resonance of order-n of the fundamental mode and exploiting combination internal resonances, we can generate multiple stable localized mechanical wave packets with different lobe sizes embodying soliton states I and II. This represents a significant breakthrough with profound implications for quantum computing and metrology.

Polarization‐Induced Buildup and Switching Mechanisms for Soliton Molecules Composed of Noise‐Like‐Pulse Transition States

AbstractBuildup and switching mechanisms of solitons in complex nonlinear systems are fundamentally important dynamical regimes. Using a novel strongly nonlinear optical system, including saturable absorber metal‐organic framework (MOF)‐253@Au and a polarization controller (PC), the work reveals a new buildup scenario for “soliton molecules (SMs)”, which includes a long‐duration stage dominated by the emergence of transient noise‐like pulses (NLPs) modes to withstand strong disturbances arising from “turbulence” and extreme nonlinearity in the optical cavity. The switching between SMs and NLPs is controlled by the cavity polarization state. The switching involves the spectral collapse, following spectral oscillations with a variable period, and self‐organization of NLPs, following energy overshoot. This switching mechanism applies to various patterns with single, paired, and clustered pulses. In the multi‐pulses stage, XPM (cross‐phase‐modulation)‐induced interactions between solitons facilitate a specific mode of energy exchange between them, proportional to interaction duration, ensuring pulse stability during and after state transitions. Systematic simulations reveal the effects of the PC's rotation angle and intra‐cavity nonlinearity on the periodic phase transitions between the different soliton states and accurately reproduce the experimentally observed buildup and switching mechanisms. These findings can enhance the fundamental study and points to potential uses in designing information encoding systems.

Polarization-diverse soliton transitions and deterministic switching dynamics in strongly-coupled and self-stabilized microresonator frequency combs

Dissipative Kerr soliton microcombs in microresonators have enabled fundamental advances in chip-scale precision metrology, communication, spectroscopy, and parallel signal processing. Here we demonstrate polarization-diverse soliton transitions and deterministic switching dynamics of a self-stabilized microcomb in a strongly-coupled dispersion-managed microresonator driven with a single pump laser. The switching dynamics are induced by the differential thermorefractivity between coupled transverse-magnetic and transverse-electric supermodes during the forward-backward pump detunings. The achieved large soliton existence range and deterministic transitions benefit from the switching dynamics, leading to the cross-polarized soliton microcomb formation when driven in the transverse-magnetic supermode of the single resonator. Secondly, we demonstrate two distinct polarization-diverse soliton formation routes – arising from chaotic or periodically-modulated waveforms via pump power selection. Thirdly, to observe the cross-polarized supermode transition dynamics, we develop a parametric temporal magnifier with picosecond resolution, MHz frame rate and sub-ns temporal windows. We construct picosecond temporal transition portraits in 100-ns recording length of the strongly-coupled solitons, mapping the transitions from multiple soliton molecular states to singlet solitons. This study underpins polarization-diverse soliton microcombs for chip-scale ultrashort pulse generation, supporting applications in frequency and precision metrology, communications, spectroscopy and information processing.

Pure-quartic soliton attracted state and multi-soliton molecules in mode-locked fiber lasers

This article explores the dynamic model of pure-quartic solitons (PQSs) in mode-locked fiber lasers. Firstly, the formation and dynamic behavior of the PQS attracted state in fiber lasers are investigated to demonstrate their exceptional stability, robustness, and predictability. Next, the transmission characteristics of single PQS in mode-locked fiber lasers is subsequently analyzed and compared to those of solitons generated while considering the effect of second-order dispersion. Finally, the evolution of multi-PQS molecules is explored, and a stability analysis method for these soliton molecules is proposed. The findings of this research are not only significant for a deeper understanding of nonlinear interaction mechanisms but also contribute to the development of ultrafast optical devices and offer new insights into the understanding and application of complex nonlinear systems.

Bifurcation analysis and solitary wave solution of fractional longitudinal wave equation in magneto-electro-elastic (MEE) circular rod

In this study, we investigate the longitudinal wave equation (LWE) with the M−fractional derivative, which describes the propagation of longitudinal waves along a rod while incorporating interactions between mechanical, electrical, and magnetic fields within the material. Initially, we apply bifurcation analysis to examine the critical points or phase portraits where the system transitions to new behaviors, such as stability shifts or the emergence of chaos, and observe the mechanism of static soliton formation through a saddle-node bifurcation. Subsequently, we utilize a modified simple equation (MSE) technique to find solitary wave solutions. Depending on the relationships between free parameters, the solutions are expressed as hyperbolic, trigonometric, and exponential functions. The numerical form of the obtained solutions reveals complex phenomena, including dark and bright bell waves, kink periodic lump waves, kink periodic waves, periodic lump waves, interaction waves between kink and periodic waves, linked lump waves, and interactions of periodic and lump waves. Additionally, we compare our results with previously published work, demonstrating that the discussed methods are valuable tools for providing distinct, accurate soliton solutions relevant to nonlinear science and technology applications.

Dynamic of stationary soliton to soliton pulsation transition in spatiotemporal mode-locked fiber lasers

This paper presents the experimental observation of the transition from stationary spatiotemporal soliton (STS) to spatiotemporal soliton pulsation (STSP) in spatiotemporal mode-locked fiber lasers for the first time. Three STSs maintain an asynchronous pulsating state with the same period, while another STS remains in a stationary mode-locked state. Through numerical analysis, the dynamic transition process of STS to STSP is studied. Numerical analysis reveals that STSP occurs under specific cavity parameters when the energy is comparatively high. As pulse energy increases, a stationary STS gradually transitions to a pulsation state. The modes have undergone distinct evolutionary trajectories, and the pivotal role of the saturable absorption effect as well as the interaction among modes has been demonstrated to be crucial for STSP. Our study contributes to understanding the formation mechanism of STSP.

Generalized N-rotor problems, synchronized subsystems, and associated solitons.

We consider systems of N particles interacting on the unit circle through 2π-periodic potentials. An example is the N-rotor problem that arises as the classical limit of coupled Josephson junctions and for various energies is known to have a wide range of behaviors such as global chaos and ergodicity, together with families of periodic solutions and transitions from order to chaos. We focus here on selected initial values for generalized systems in which the second order Euler-Lagrange equations reduce to first order equations, which we show by example can describe an ensemble of oscillators with associated emergent phenomena such as synchronization. A specific case is that of the Kuramoto model with well-known synchronization properties. We further demonstrate the relation of these models to field theories in 1+1 dimensions that allow static kink solitons satisfying first order Bogomolny equations, well-known in soliton physics, which correspond to the first order equations of the generalized N-rotor models. For the nonlinear pendulum, for example, the first order equations define the separatrix in the phase portrait of the system and correspond to kink solitons in the sine-Gordon equation.

Soliton sheets of Bose–Einstein condensates in optical lattices

Soliton sheets are observed in Bose–Einstein condensates in optical lattice which are formed by superposition of condensates occupying different single-particle states. These structures consist of one-dimensional stationary solitons distributed in the x-direction arranged continuously along the peaks of the optical lattice in the y-direction. Notably, the phase difference across the soliton sheets is periodic and varies linearly with y within each period. So, we refer to this configuration as a ‘soliton sheet’. A velocity difference in the y-component is observed between the two sides of the soliton sheets. Similar velocity distributions can be achieved by aligning an infinite number of isotropic vortices along the peaks of the optical lattice. And the soliton sheets are distinguished by their lack of dependence on phase singularities. This independence enables the formation of soliton sheets even in the absence of phase singularities, highlighting a unique aspect of this structure.

Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

Based on the Hirota bilinear method, we systematically investigate the (3+1)-dimensional Boiti-Leon-Manana-Pempinelli (BLMP) equation in incompressible fluids and main results include: (1) the formulas of N-kink-soliton solutions and the bound states of multi solitons are all presented, (2) the lump solution is derived by the positive quadratic function method, (3) the interactional solutions are given, i.e., one lump interacts with one- and two-kink-soliton, (4) some special periodic solutions are discussed, i.e., lump-periodic solutions and homoclinic breather solutions.

Exploring Conformal Soliton Structures in Tangent Bundles with Ricci-Quarter Symmetric Metric Connections

In this study, we investigate the tangent bundle TM of an n-dimensional (pseudo-)Riemannian manifold M equipped with a Ricci-quarter symmetric metric connection ∇˜. Our primary goal is to establish the necessary and sufficient conditions for TM to exhibit characteristics of various solitons, specifically conformal Yamabe solitons, gradient conformal Yamabe solitons, conformal Ricci solitons, and gradient conformal Ricci solitons. We determine that for TM to be a conformal Yamabe soliton, the potential vector field must satisfy certain conditions when lifted vertically, horizontally, or completely from M to TM, alongside specific constraints on the conformal factor λ and the geometric properties of M. For gradient conformal Yamabe solitons, the conditions involve λ and the Hessian of the potential function. Similarly, for TM to be a conformal Ricci soliton, we identify conditions involving the lift of the potential vector field, the value of λ, and the curvature properties of M. For gradient conformal Ricci solitons, the criteria include the Hessian of the potential function and the Ricci curvature of M. These results enhance the understanding of the geometric properties of tangent bundles under Ricci-quarter symmetric metric connections and provide insights into their transition into various soliton states, contributing significantly to the field of differential geometry.

Saturation and absorption effects on the transmission properties of Kerr-type nonlinear layers

The effects of absorption and saturation on soliton states in Kerr-type nonlinear layers are theoretically investigated. In addition to the usual gray and bright soliton structures observed in nonlinear slabs, a flat soliton, i.e., a particular soliton excitation with electric field amplitude independent of the position within the layer, is researched in cases of self-defocusing and self-focusing nonlinearities. Effects caused by the combination of absorption and saturation, such as the shift and extinction of the flat soliton peak, the decrease in the amplitude of the electric field within the nonlinear layer, and the suppression of the multistable behavior of the transmission coefficient in the vicinity of the soliton peaks, are discussed. The present theoretical results are compared and found in good quantitative agreement with previous experimental measurements.Graphical