Vector Dark Solitons Research Articles

Dynamics of Bose-Einstein condensates near Feshbach resonance in external potential

We review our recent theoretical advances in the dynamics of Bose-Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross-Pitaevskii equations are developed to study the nonlinear dynamics of Bose-Einstein condensates. Analytically, we present the integrable conditions for the Gross-Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose-Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose-Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose-Einstein condensates.

Dark and anti-dark vector solitons of the coupled modified nonlinear Schrödinger equations from the birefringent optical fibers

Coupled modified nonlinear Schrodinger (CMNLS) equations describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. A new type of the Lax pair and another hierarchy of the infinitely many conservation laws are derived based on the Wadati-Konno-Ichikawa system. By means of the Hirota method, soliton solutions in the normal dispersion regime are obtained. Parametric regions for the existence of dark and anti-dark vector soliton solutions are given. Asymptotic analysis shows that the collision between two solitons (two anti-dark solitons, two dark solitons, or dark and anti-dark solitons) in each polarization direction is elastic. Moreover, there is no energy transfer between two polarization components of each vector soliton, whether dark or anti-dark vector soliton. In addition, dark and anti-dark solitons can coexist on the same background seen from the collision between the dark and anti-dark solitons in one polarization direction. Our graphical analysis shows that the parameters in the CMNLS equations not only determine the regions for the existence of dark and anti-dark soliton solutions but also control the phase and direction of the propagation of the solitons. Finally, through the linear stability analysis, the modulational instability condition is given.

Bright–dark self-coupled vector spatial solitons in biased two-photon photovoltaic photorefractive crystals

This paper predicts that bright–dark self-coupled vector solitons are possible in biased two-photon photovoltaic photorefractive crystals under steady-state conditions. The solutions of these vector solitons can be determined by use of simple numerical integration procedures. When the photovoltaic effect is neglectable, these vector solitons are bright–dark vector screening solitons. When the external bias field is absent, these vector solitons degenerate the bright–dark vector photovoltaic solitons.

Vector dark domain wall solitons in a fiber ring laser

We observe a novel type of vector dark soliton in a fiber ring laser. The vector dark soliton consists of stable localized structures separating the two orthogonal linear polarization eigenstates of the laser emission and is visible only when the total laser emission is measured. Numerical simulations based on the coupled complex Ginzburg-Landau equations have well reproduced the results of the experimental observation.

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.

Ultraslow temporal vector optical solitons in a cold five-state atomic medium under Raman excitation

We theoretically investigate the formation of ultraslow temporal vector optical solitons in a lifetime-broadened five-state atomic system under Raman excitation. By analysing the interaction between the atomic system and two strong, linear-polarized continuous wave control fields and a weak, linear-polarized pulsed signal field, having two orthogonally polarized components, we find that the Maxwell equations of describing the propagation of two orthogonal polarization components can evolve into two coupled nonlinear Schrödinger equations, which admit solutions describing vector solitons, including bright–bright, bright–dark, dark–bright and dark–dark vector solitons with ultraslow group velocity. More importantly, the Manakov temporal vector solitons can be easily realized in our system by adjusting the corresponding parameters such as the Rabi frequencies of the control fields, one- and two-photon detunings. The unique features of the two coupled nonlinear Schrödinger equations are also discussed.

Comment on “Stable and unstable vector dark solitons of coupled nonlinear Schrödinger equation: Application to two-component Bose-Einstein condensates

In a recent paper, V. A. Brazhnyi and V. V. Konoto [Phys. Rev. E 72, 026616 (2005)] investigated the dynamics of vector dark solitons in two-component Bose-Einstein condensates. In the small amplitude limit, they deduced a coupled Korteweg-de Vries equation from the coupled Gross-Pitaevskii equations. They found that two branches of (slow and fast) dark solitons corresponding to the two branches of the sound waves exist. The slow solitons, corresponding to the lower branch of the acoustic wave, appear to be unstable and transform during the evolution into the stable fast solitons (corresponding to the upper branch of the dispersion law). However, our discussion shows that these results are incorrect.

Stable and unstable vector dark solitons of coupled nonlinear Schrödinger equations: Application to two-component Bose-Einstein condensates

The dynamics of vector dark solitons in two-component Bose-Einstein condensates is studied within the framework of coupled one-dimensional nonlinear Schrödinger (NLS) equations. We consider the small-amplitude limit in which the coupled NLS equations are reduced to coupled Korteweg-de Vries (KdV) equations. For a specific choice of the parameters the obtained coupled KdV equations are exactly integrable. We find that there exist two branches of (slow and fast) dark solitons corresponding to the two branches of the sound waves. Slow solitons, corresponding to the lower branch of the acoustic wave, appear to be unstable and transform during the evolution into stable fast solitons (corresponding to the upper branch of the dispersion law). Vector dark solitons of arbitrary depths are studied numerically. It is shown that effectively different parabolic traps, to which the two components are subjected, cause an instability of the solitons, leading to a splitting of their components and subsequent decay. A simple phenomenological theory, describing the oscillations of vector dark solitons in a magnetic trap, is proposed.

Steady-state bright–dark vector spatial solitons in biased photorefractive–photovoltaic crystals

We show that bright–dark vector solitons are possible in biased photorefractive–photovoltaic crystals under steady-state conditions, which result from both the bulk photovoltaic effect and the spatially nonuniform screening of the external bias field. The analytical solutions of these vector solitons can be obtained in the case of | σ|≪1, where σ is the parameter controlling the intensities of the two optical beams. In the limit of −1< σ⩽1, these vector solitons can also be determined by use of simple numerical integration procedures. When the bulk photovoltaic effect is neglectable, these vector solitons are bright–dark vector screening solitons studied previously in the | σ|≪1 regime, and predict bright–dark vector screening solitons in the −1< σ⩽1 regime. When the external bias field is absent, these vector solitons predict bright–dark vector photovoltaic solitons in closed and open circuits.

Systematic construction of vector solitons

We present a simple but powerful method for constructing multisolitons; of the integrable Manakov (coupled nonlinear Schrodinger) equation. Our method is essentially equivalent to the inverse scattering method (ISM) with the full strength generality but without the mathematical rigor of the ISM. This makes our method appropriate for practical purposes. A closed form of matrix determinant for the N-soliton solution in a nonvanishing background is found in this way. We work out explicitly the two dark vector soliton and the three bright vector soliton cases and demonstrate their novel behaviors.

Bright–Dark Vector Solitons in Chiral Media

We study wave propagation in nonlinear chiral media. In the weak dispersion, low chirality limit the dynamics of the waves are reduced to the dynamics of a set of coupled partial differential equations of the NLS type. Using reductive perturbation theory we show the existence of bright–dark chiral vector solitons.

Modulational Instability and Stimulated Raman Scattering in Normally Dispersive Highly Birefringent Fibers

The nonlinear interaction of two laser beams in normally dispersive highly birefringent optical fibers leads to a large set of fascinating physical effects such as modulational instability (MI) and stimulated Raman scattering (SRS). These two nonlinear phenomena have a positive role as a mechanism for the generation of short optical pulses and represent a drawback in fiber-optics transmissions. Indeed, we will show that an induced process of modulational instability may be exploited for the generation of THz train of vector dark solitons. The technique of frequency-resolved optical gating is used to completely characterize the intensity and phase of the dark soliton trains. On the other hand, we shall discuss control processes for MI and SRS in birefringent optical fibers. In particular, we analyze experiments showing that with dual-frequency, orthogonal polarization pumping one may achieve the simultaneous suppression of modulational instability and substantial reduction of stimulated Raman scattering.

Dark optical solitons: physics and applications

We present a detailed overview of the physics and applications of optical dark solitons: localized nonlinear waves (or `holes') existing on a stable continuous wave (or extended finite-width) background. Together with the traditional problems involving properties of dark solitons of the defocusing cubic nonlinear Schrödinger equation, we also describe recent theoretical results on optical vortex solitons; ring dark solitons; polarization domain walls; parametric dark solitons in a dispersive χ (2) medium; vector dark solitons; coupled dark–bright soliton pairs, and we discuss the instability-induced dynamics of dark solitons in the models of generalized (i.e., non-Kerr) optical nonlinearities. Special attention is paid to the experimental demonstrations of temporal dark solitons in optical fibres and spatial dark solitons, especially dark-soliton stripes and vortex solitons, in a defocusing bulk medium.

Multimode structure of bright and dark vector solitons in photorefractive media

We study coupled solitary waves in a photorefractive medium. For a special orientation of a cubic photorefractive crystal, stationary wave propagation in the form of coupled dark and bright solitons is possible. We classify these solutions and study their stability, using numerical simulations.

Vector soliton associated with polarization modulational instability in the normal-dispersion regime.

We investigate the dynamics of the coupled nonlinear Schr\"odinger equations which describe light propagation in isotropic Kerr media including polarization effects. It is shown that the phenomenon of polarization modulational instability in the normal-dispersion regime is associated with the existence of a novel type of dark vector soliton. This soliton constitutes a localized structure separating adjacent domains of orthogonal polarization eigenstates of the Kerr medium and can be viewed as a polarization domain wall.

Vector dark solitons

It is shown that a novel class of optical soliton is possible in the form of vector dark solitons. These nonlinear waves describe bound states of two gray solitons with different background intensities in each mode that are strongly coupled through cross-phase modulation.

Dark spatial solitons in non-Kerr-law media.

Two-dimensional light trapping of TM and TE patterns in saturable self-defocusing nonlinear media is examined. The vector dark spatial soliton of TM type is found to exist only within a certain range of the beam effective index, which can be wider or narrower compared with the corresponding one in the Kerr-law nonlinearity, depending on the nonlinear saturation index. This contrasts with the scalar dark spatial soliton of TE type, the guidable region of which in saturable nonlinear media is equal to or narrower than that in the Kerr-law nonlinear medium. The physical origin leading to such a distinct contrast is also explored.