Modulating the amplitude of dark soliton by scattering-length management in Bose-Einstein condensates

We present a family of soliton solutions of the quasi-one-dimensional Bose-Einstein condensates with time-dependent scattering length, by developing multiple-scale method combined with truncated Painlevé expansion. Then, by numerical calculating the solutions, it is shown that there exhibit two types of dark solitons—black soliton (the zero minimum amplitude at its center) and gray soliton (the minimum density does not drop to zero) in a repulsive condensate. Furthermore, we propose experimental protocols to realize the exchange between black and gray solitons by varying the scattering length via the Feshbach resonance in currently experimental conditions.     

Emission of supersonic soliton wave beams—generators of restructuring of nanocrystals under atom bombardment,and the self-organization of a dynamic superlattice of complexes of soliton atomic vibrations

It has been shown that the dynamic superlattice of pulsed complexes of soliton vibrations or, actually, a “soliton crystal” is self-organized in crystalline materials at high levels of thermal and dynamic excitations of atomic vibrations. The results obtained have been adapted to the alpha uranium crystal system. It has been demonstrated that the atom bombardment of crystalline materials leads to the generation of beams of nonlinear subsonic and supersonic soliton and breather waves. The breathers and solitons initiate threshold kinetic processes of defect formation, such as surface vibrations and evaporation of surface atoms, multiple reflection of bombarding atoms, and restructuring of nanocrystals. The results obtained can be used in experimental investigations of microdynamics of materials under high dynamic and temperature loads by the neutron and ion scattering methods.     

Controlling the amplitude of soliton in agrowing Bose--Einstein condensate by means of Feshbach resonance

By using Darboux transformation, this paper studies analytically the nonlinear dynamics of a one-dimensional growing Bose-Einstein condensate （BEC）. It is shown that the growing model has an important effect on the amplitude of the soliton in the condensates. In the absence of the growing model, there exhibits the stable alternate bright solitons in the condensates. In the presence of the growing model, the obtained results show that the amplitude of the bright soliton decreases （increases） for the BEC growing coefficient Ω 〈 0 （Ω 〉 0）. Furthermore, we propose experimental protocols to manipulate the amplitude of the bright soliton by varying the scattering length via the Feshbach resonance in the future experiment.     

Analyzing Dynamics of a Bright Soliton in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length

We analyze the dynamics of a bright soliton in Bose-Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential. Under a safe range of parameters in which the Gross-Pitaevskii (GP) equation is effective in one dimension, our results show that, the dynamics of the bright soliton can be classed into two phases, depending on the value of the scattering length. Meanwhile, there exists a critical value of the absolute value of the atomicscattering length, below which, the dynamics of the bright soliton is very regular. Those phenomena can be useful for developing concrete applications of the nonlinear matter waves. We also obtain the orbital equation of the bright soliton and get some interesting data which may be useful for the experimental observation of the bright soliton and the application of the atom laser with manipulated intensity.     

Ultrashort pulse propagation under manipulated resonance conditions

The propagation of a polarized ultrashort laser pulse is analyzed by the inverse scattering method under initial conditions including a spatial pulse profile, a state of the medium, and a “switched-on” resonant atom-field interaction. Magnetic degeneracy of atomic levels is taken into account. The Maxwell-Bloch equations are rewritten in Hamiltonian form without redefining the spatial and temporal variables. The inverse scattering method is based on an analysis of a new spectral problem. Gelfand-Levitan-Marchenko-type equations are derived, a soliton solution is obtained, and the changes in parameters of two solitons after their collision are calculated. A possible experimental setup for implementing the system under analysis is discussed.     

Compton散射下多信道平面光波导的空间光孤子开关

应用量子微扰理论和多光子非线性Compton散射模型,对Compton散射下多信道平面光波导的空间光孤子开关进行了研究.结果表明:在横向具有正弦形周期折射率调制的非线性平面光波导的多信道系统中,原先束缚在一个信道中的孤子可以靠由入射和散射光形成的耦合控制光点,通过交叉相位调制横向吸引孤子波束,使孤子从原信道切换到邻近信道,从而实现光孤子开关的功能.控制光点可由耦合光在势谷之间的横向聚焦来实现.散射既能使控制光点的有效强度的阈值和孤子的辐射损耗增大,势垒增高,幅度下降较小,有利于孤子开关的形成;又能使波束展宽较宽,并存在开关被破坏的危险.由此可见,Compton散射下恰当控制入射激光强度是实现孤子开关的关键.     

Dynamics of a bright soliton in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential

We present a family of exact solutions of the one-dimensional nonlinear Schro dinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background.     

Resonant and non-resonant soliton scattering by impurities

The NLSE soliton scattering by impurities is considered in the framework of the one-dimensional model. The scattering intensity is characterized by the reflection coefficient of the soliton is calculated in the Born approximation of the perturbation theory for the following cases: (i) and isolated impurity, (ii) two point impurities, and (iii) a regular or random system of point impurities. An analytical comparison with the scattering of linear waves is carried out. In particular, we analytically describe the nonlinear resonant scattering by two point impurities, and the non-resonant soliton scattering by a random system of point impurities.     

Soliton splitting in a dispersion-oscillating fiber

A single-mode fiber with a sinusoidal variation of the core diameter was fabricated. The soliton splitting due to the longitudinal oscillation of the fiber dispersion is demonstrated experimentally. The experimental observations are confirmed through numerical simulations. The periodical modulation of the fiber dispersion can be used for controlling the soliton splitting even under the strong effect of the Raman scattering.     

脉冲内拉曼散射影响下的孤子之间的相互作用及其控制

研究了脉冲内拉曼散射效应影响下的同相和反相相邻孤子脉冲之间的相互作用,分析了孤子之间的相互作用对定时抖动的影响和脉冲内拉曼散射效应对孤子频移的影响。研究结果表明:在脉冲内,在拉曼散射效应的影响下,同相基态孤子脉冲的周期性离合被破坏了,两孤子脉冲一次碰撞后一直处于排斥状态,并且在碰撞后自频移现象十分明显;反相孤子脉冲的影响则较弱,两孤子脉冲都向下降沿发生偏移。引入非线性增益可以有效地控制孤子之间的相互作用,抑制自频移效应和稳定孤子传输。     

Spatio-temporal dynamics of multicolor spatial Kerr solitons

We present numerical and experimental results showing the rich and complex spatio-temporal dynamics of multicolor spatial vector soliton generated by stimulated Raman scattering in a Kerr planar waveguide. By taking into account their temporal dimension, we found the precise domain of existence of multicolor soliton whose components are mutually guided and spatio-temporally superimposed. In addition, we observe the Raman Stokes component in the trailing edge of the pump pulse and show that it is associated with the slow-light process induced by the sharp resonance of the Raman gain medium.     

Amplifying optical signals with discrete solitons in waveguide arrays

We present a design and protocol to achieve an essential feature of an optical transistor, namely the amplification of input signal with the use of discrete solitons in waveguide arrays. We consider the scattering of a discrete soliton by a reflectionless potential in the presence of a control soliton. We show that at the sharp transition region between full reflectance and full transmittance, the intensity of the reflected or transmitted soliton is highly sensitive to the intensity of the control soliton. This suggests a setup of signal amplifier. For realistic purposes, we modulate the parameters of the reflectionless potential well to achieve a performance of amplifier with a controllable amplification. To facilitate the experimental realization, we calculate the amplification factor in terms of the parameters of the potential well and the input power of the control soliton. The suggested signal amplifier device will be an important component in the all-optical data processing.     

Solitary wave dynamics in shallow water over periodic topography

The problem of long-wave scattering by piecewise-constant periodic topography is studied both for a linear solitary-like wave pulse, and for a weakly nonlinear solitary wave [Korteweg-de Vries (KdV) soliton]. If the characteristic length of the topographic irregularities is larger than the pulse length, the solution of the scattering problem is obtained analytically for a leading wave in the framework of linear shallow-water theory. The wave decrement in the case of the small height of the topographic irregularities is proportional to delta2, where delta is the relative height of the topographic obstacles. An analytical approximate solution is also obtained for the weakly nonlinear problem when the length of the irregularities is larger than the characteristic nonlinear length scale. In this case, the Korteweg-de Vries equation is solved for each piece of constant depth by using the inverse scattering technique; the solutions are matched at each step by using linear shallow-water theory. The weakly nonlinear solitary wave decays more significantly than the linear solitary pulse. Solitary wave dynamics above a random seabed is also discussed, and the results obtained for random topography (including experimental data) are in reasonable agreement with the calculations for piecewise topography.     

Suppression of stimulated Brillouin scattering with phase modulator in soliton pulse compression

A phase modulator is employed in the scheme of soliton pulse compression with dispersion shifted fiber （DSF）. Stimulated Brillouin scattering （SBS） effect, as a negative influence here, can be dramatically suppressed after optical phase modulation. The experimental result shows that the launched power required for high-order soliton pulse compression has been significantly increased by 11 dB under the condition of 100-MHz phase modulation. Accordingly, the experiment of picosecond pulse compression generated from electro-absorption sampling window （EASW） has also been implemented.     

内脉冲拉曼散射效应对暗孤子传输系统的影响及其抑制

利用守恒量扰动法，研究了内脉冲拉曼散射效应对暗孤子脉冲到达检测窗口时间抖到、传输系统误码率的影响。结果表明，内脉冲拉曼散身效应对暗孤子速度产生了影响，引起了暗孤子传输系统的平衡点漂移，并与放大器噪声联合作用增大了暗孤子脉冲到达时间的抖动，恶化了系统的误码率，限制了系统的传输距离。引入非线性增益可以有效３内脉冲拉曼散身效应对暗孤子传输系统的不良影响。     

Observation of the bright photovoltaic spatial soliton in fiber-like photorefractive crystal

We have observed two-dimensional bright photorefractive spatial soliton for the first time in a Ce:KNSBN fiber-like crystal at wave-length of 514.5 nm with the intensity range between 2.83 × 10³ W/cm² and 4.71 × 10³ W/cm², then compared it with the one formed in a bulk sample. By comparison we have found that the intensity of forming a soliton in a fiber-like crystal is 7 9 times that in a bulk crystal due to stronger scattering light and complicated multi-wave interaction. By comparison we have also found that the transverse dimensions of a soliton formed in a fiber-like crystal are about 4% smaller than the ones in a bulk crystal when the experimental geometry remains the same, then we have exploited the theory including the contribution of scattering field to interpret the experimental phenomenon.     

Optical solitons in resonant and nonresonant nonlinear media in the presence of perturbations

We studied the optical solitons in nonlinear resonant and nonresonant media in the presence of perturbations, assuming that the transient effects are stimulated by the light scanning beam. We treated a slight deviation from the exact necessary condition for the soliton existence (2betanu=1), as a small perturbation for the integrable system, studying its influence upon the soliton propagation conditions. The approximation is constructed by the help of an algebraic version of the soliton perturbation theory using a Riemann boundary problem in connection with the inverse scattering method. We have obtained the soliton equation and we have solved it in the presence of a small perturbation in the adiabatic approximation. In this case we have demonstrated that for a Lorentz profile line the amplitude of the soliton remains unchanged, the only effect of the perturbation results in a phase shift.     

Stimulated Brillouin scattering in dispersion-decreasing fiber with ultrahigh-speed femtosecond soliton pulse compression

We report that stimulated Brillouin scattering (SBS) in a dispersion-decreasing fiber (DDF) is particularly disadvantageous with ultrahigh-speed femtosecond soliton compression that exceeds 40 GHz. It is important to note that the increase in the longitudinal mode power of a soliton is proportional to the square of the repetition rate. The SBS threshold is determined by the dispersion-decreasing rate of the DDF, rather than its fiber loss. We suppressed the SBS by applying 30-MHz frequency modulation to a mode-locked fiber laser and successfully obtained a stable 40-GHz, 100-fs pulse train.     

Stabilization of the Soliton Transported Bio-energy in Protein Molecules in the Improved Model

We study the stabilization of the soliton transported bio-energy by the dynamic equations in the improved Davydov theory from four aspects containing the feature of free motion and states of the soliton at the long-time motion and at biological temperature 300 K and behaviors of collision of the solitons by Runge-Kutta method and physical parameter values appropriate to the $\alpha$-helix protein molecules. We prove that the new solitons can move without dispersion at a constant speed retaining its shape and energy in free and long-time motions and can go through each other without scattering. If considering further influence of the temperature effect of heat bath on the soliton, it is still thermally stable at biological temperature 300 K and in a time as long as 300 ps and amino acid spacings as large as 400, which shows that the lifetime of the new soliton is at least 300 ps, which is consistent with analytic result obtained by quantum perturbation theory. These results exhibit that the new soliton is a possible carrier of bio-energy transport and the improved model is possibly a candidate for the mechanism of this transport.     

Inverse Scattering Method and Soliton Solution Family for String Effective Action

A modified Hauser-Ernst-type linear system is established and used to develop an inverse scattering method for solving the motion equations of the string effective action describing the coupled gravity, dilaton and KalbRamond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the proposed inverse scattering method applied fine and effective. As an application, a concrete family of soliton solutions for the considered theory is obtained.