Feshbach resonance management of vector solitons in two-component Bose—Einstein condensates

We consider two coupled Gross-Pitaevskii equations describing a two-component Bose-Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential,and investigate the dynamics of vector solitons.By using a direct method,we construct a novel family of vector soliton solutions,which are the linear combination between dark and bright solitons in each component.Our results show that due to the superposition between dark and bright solitons,such vector solitons possess many novel and interesting properties.The dynamics of vector solitons can be controlled by the Feshbach resonance technique,and the vector solitons can keep the dynamic stability against the variation of the scattering length.     

Short Vector Envelope Solitons

We find a class of short vector soliton solutions of the coupled third-order nonlinear Schrödinger equation (CNSE-3) and analyze the stability of such solitons in the adiabatic approximation. The analytical results are confirmed by numerical simulations of the dynamics of perturbed short vector solitons corresponding to the CNSE-3.     

Fractal structure in the collision of vector solitons

We study the collision of two orthogonally polarized and equal-amplitude vector solitons in the nonintegrable coupled nonlinear Schrodinger equations. We show that the separation velocity versus collision velocity graph has a fractal structure. When we zoom into this graph, we get a structure qualitatively identical to the original one. In addition, collision dynamics in the zoomed-in windows is intimately related to that in the original graph. We explain this fractal dependence of the collision by a resonance mechanism between the translational motion of vector solitons and internal oscillations inside a vector soliton.     

Multicomponent dipole-mode spatial solitons

We study (2+1) -dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents and demonstrate that these solitary waves exhibit a symmetry-breaking instability, provided their total topological charge is nonzero. We describe a novel type of stable multicomponent dipole-mode solitons with intriguing swinging dynamics.     

Splitting of coupled bright solitons in two-component Bose-Einstein condensates under parametric perturbation

We analyze the dynamics of bright-bright solitons in two-component Bose-Einstein condensates (BECs) subject to parametric perturbations using the variational approach and direct numerical simulations. The system is described by a vector nonlinear Schrödinger equation (NLSE) appropriate to coupled multi-component BECs. A periodic variation of the inter-component coupling coefficient is used to explore nonlinear resonances and splitting of the coupled bright solitons. The analytical predictions are confirmed by direct numerical simulations of the vector NLSE.     

Dynamics of vector solitons in two-component Bose--Einstein condensates with time-dependent interactions and harmonic potential

We present two kinds of exact vector-soliton solutions for coupled nonlinear Schr?dinger equations with time-varying interactions and time-varying harmonic potential. Using the variational approach, we investigate the dynamics of the vector solitons. It is found that the two bright solitons oscillate about slightly and pass through each other around the equilibration state which means that they are stable under our model. At the same time, we obtain the opposite situation for dark--dark solitons.     

One-dimensional spatial solitons in AlGaAs waveguides

We present experimental results on one-dimensional (1-D) spatial solitons in AlGaAs waveguides. Three distinct types of spatial solitons have been observed: namely the fundamental soliton, the Manakov soliton, and the vector soliton. The fundamental soliton is the simplest form of 1-D soliton which consists of a single polarization. The properties of waveguiding and ‘robustness’ are experimentally studied. Vector solitons which result from the complex interplay between the two orthogonally polarized beams due to self-phase modulation, cross-phase modulation, and four-wave mixing effects are studied. The complex beam dynamics and polarization behaviour of the vector solitons are experimentally studied. Manakov solitons which are a special case of the vector soliton exist when the ratio between the self-to-cross-phase modulation is one and the four-wave mixing effects becomes zero are demonstrated experimentally and the basic properties discussed. Finally, some soliton interactions such as trapping and dragging are reported and possible applications of soliton interactions are discussed.     

Collision between scalar and vector spatial solitons in Kerr media

Experimental observation and numerical results concerning collisions between scalar and vector spatial solitons in a Kerr planar waveguide are presented. It is shown that this configuration allows for the full control of spatial and polarization dynamics of the interacting vector solitons. On the one hand, the ability to achieve polarization control of a single-hump vector soliton is demonstrated. On the other hand, the effect of collision on the spatial symmetry-breaking dynamics of multimode vector solitons is investigated.     

Dynamics of the Manakov-typed bound vector solitons with random initial perturbations

Dynamics of the bound vector solitons with random initial perturbations is investigated for the Manakov model, which describes the propagation of the multimode soliton pulses in nonlinear fiber optics and two-component matter-wave solitons in the quasi-one-dimensional Bose–Einstein condensates (BECs) without confining potential. We review the analytic two-bound-vector-soliton solutions and give the three-bound-vector-soliton solutions. Breakup of the typical bound state is presented numerically when the symmetry and asymmetry random perturbations are added to the initial conditions. Relationship between the lifetime of the bound state and amplitude of the random perturbation is discussed. Meanwhile, existence of the symmetry-recovering is illustrated for the bound vector solitons with the asymmetry random perturbations. Discussions of this paper could be expected to be helpful in interpreting the dynamics of the Manakov-typed bound vector solitons when the random initial noises in nonlinear optical fibers or stochastic quantum fluctuations in the BECs are considered.     

Multipole spatial vector solitons

We introduce the concept of multipole spatial optical vector solitons associated with higher-order guided modes trapped by a soliton-induced waveguide in a bulk medium. Such stationary localized waves include previously predicted vortex- and dipole-mode vector solitons and also describe new higher-order vector solitons and necklace-type beams. We present the theoretical and experimental results of the structure, formation, and instability development of the quadrupole vector solitons.     

共振光子晶体中Laue孤子传播的动力学行为

从理论上研究了Laue孤子传播的动力学行为，并通过数值模拟验证了这些行为.结果表明，由于非线性衍射，入射脉冲会分裂产生四种模式，其中产生的Laue孤子的传播行为与一般共振介质中孤子的传播行为相似.     

Soliton switching in nonlinear couplers

We present a theoretical overview of soliton switching phenomena in two-mode nonlinear couplers. By complementing numerical studies with perturbative or exact solitary wave solutions, one finds that nonlinear Schrödinger or sine-Gordon solitons tend to maintain their identity in the coupled systems. Moreover, the coupling itself may originate novel vector solitary waves, such as gap solitons in periodic media. The switching dynamics in the presence of dissipative perturbations such as linear gain or intrapulse Raman scattering is also discussed.     

Parametric vector solitons in tetragonal crystals

We introduce novel types of spatial vector soliton that can be generated in anisotropic optical media, such as tetragonal crystals with third-order nonlinear susceptibility. We demonstrate that these vector solitons provide a nontrivial generalization to both conventional vector solitons of birefringent cubic media and parametric solitons supported by third-order cascaded nonlinearities.     

Soliton interaction in the coupled mixed derivative nonlinear Schrödinger equations

The bright one- and two-soliton solutions of the coupled mixed derivative nonlinear Schrödinger equations in birefringent optical fibers are obtained by using the Hirota's bilinear method. The investigation on the collision dynamics of the bright vector solitons shows that there exists complete or partial energy switching in this coupled model. Such parametric energy exchanges can be effectively controlled and quantificationally measured by analyzing the collision dynamics of the bright vector solitons. The influence of two types of nonlinear coefficient parameters on the energy of each vector soliton, is also discussed. Based on the significant energy transfer between the two components of each vector soliton, it is feasible to exploit the future applications in the design of logical gates, fiber directional couplers and quantum information processors.     

Propagation of vector solitons in a quasi-resonant medium with stark deformation of quantum states

The nonlinear dynamics of a vector two-component optical pulse propagating in quasi-resonance conditions in a medium of nonsymmetric quantum objects is investigated for Stark splitting of quantum energy levels by an external electric field. We consider the case when the ordinary component of the optical pulse induces ?? transitions, while the extraordinary component induces the ?? transition and shifts the frequencies of the allowed transitions due to the dynamic Stark effect. It is found that under Zakharov-Benney resonance conditions, the propagation of the optical pulse is accompanied by generation of an electromagnetic pulse in the terahertz band and is described by the vector generalization of the nonlinear Yajima-Oikawa system. It is shown that this system (as well as its formal generalization with an arbitrary number of optical components) is integrable by the inverse scattering transformation method. The corresponding Darboux transformations are found for obtaining multisoliton solutions. The influence of transverse effects on the propagation of vector solitons is investigated. The conditions under which transverse dynamics leads to self-focusing (defocusing) of solitons are determined.     

Low-amplitude vector screening solitons

We show self-coupled and cross-coupled vector beam evolution equations in the low-amplitude regime for screening solitons,which can exhibit the analytical solutions of bright-bright and dark-dark vector solitons.Our analysis indicates that these self-coupled vector solitons are obtained irrespective of the intensities of the two optical beams,whereas these cross-coupled vector solitons can be established when the intensities of the two optical beams are equal.Relevant examples are provided where the photorefractive crystal is lithium niobate(LiNbO3).The stability properties of these vector solitons have been investigated numerically and it has been found that they are stable.     

Steady-state bright-dark vector spatial solitons in biased two-photon photorefractive crystals

We show that bright-dark vector solitons are possible in biased two-photon photorefractive crystals under steady-state conditions. The analytical solutions of these vector solitons can be obtained if the intensities of the two vector components are approximately equal. When the intensities of the two vector components differ, the vector soliton pair solutions can be determined using simple numerical integration procedures. The stability of the bright-dark vector solitons has been investigated numerically.     

Ultra-short scalar and vector solitons in self-inductively transparent media

The analytical form of the one-soliton solutions to the Maxwell–Bloch equations is found without the slowly-varying envelope approximation with application to the ultra-short (few-cycle or sub-cycle) light pulses propagating in media of two-level atoms as well as to fluxons in the long Josephson junctions. Also, we discuss the dynamics of the ultra-short vector solitons propagating in specific three-level media and magnetic-flux transmission lines (of two long Josephson junctions sharing a common superconducting plate). Studies of the (ultra-short) pulse collisions lead to the prediction of pulse stability against the collisions. In particular, the collisions of the ultra-short vector solitons are investigated in detail. Their collision-induced polarization transform is found to be similar to the polarization transform of the vector (Manakov) solitons propagating in self-focusing media.     

Switching and Self-trapping Dynamics of Dark Solitons in a Two-Component Bose-Einstein Condensate

Two coupled dark solitons are considered in a two-component Bose-Einstein condensate, and their dynamics are investigated by the variational approach based the renormalized integrals of motion. The stationary states as physical solutions to the describing equations are obtained, and the dynamic mechanism is demonstrated by performing a coordinate of a classical particle moving in an effective potential field. The switching and selftrapping dynamics of the coupled dark vector solitons are discussed by the evolution of the atom population transferring ratio.     

Vector soliton fission by reflection at nonlinear interfaces

We address the reflection of vector solitons, comprising several components that exhibit multiple field oscillations, at the interface between two nonlinear media. We reveal that reflection causes fission of the input signal into sets of solitons propagating at different angles. We find that the maximum number of solitons that arises upon fission is given by the number of field oscillations in the highest-order input vector soliton.