Dark soliton in one-dimensional Bose–Einstein condensate under a periodic perturbation of trap

The perturbation of a confining trap leads to the collective oscillation of a Bose--Einstein condensate, thereby the propagation of a dark soliton in the condensate is affected. In this study, periodic perturbation is employed to match the soliton oscillation. We find that the soliton dynamics depends sensitively on the coupling between the moving direction of the trap and that of the soliton. The soliton energy/depth evolves periodically, and a relevant shift in the soliton trajectory occurs as compared with the unperturbed case. Overall, the soliton oscillation frequency changes little even if the perturbation amplitude and frequency vary.     

Effects of localized impurity on a dark soliton in a Bose--Einstein condensate with an external magnetic trap

The dynamics of a dark soliton has been investigated in a Bose--Einstein condensate with an external magnetic trap, and the effects of localized impurity on the dynamics are discussed by the variational approach based on the renormalized integrals of motion. The reciprocal movement of the dark soliton is discussed by performing a standard linear analysis, and it is found that the effects of the localized impurity depend strictly on the positive or negative value of the impurity strength corresponding to the repulsive or attractive impurity. The numerical results confirm the theoretical analysis, and show that the effects also depend on the effective nonlinear coefficient and the harmonic frequency.     

Collision induced splitting of bright soliton in Bose--Einstein condensate

This paper studies the collision dynamics of bright soliton in Bose--Einstein condensate with trapezoid potential. It is found that besides the total reflection and total transmission, one bright soliton can be divided into two bright solitons with different amplitudes in a controllable manner.     

Dark Soliton of a Growing Bose--Einstein Condensate in an External Trap

The dynamics of dark soliton in a growing Bose-Einstein condensate with an external magnetic trap are investigated by the variational approach based on the renormalized integrals of motion. The stationary states as physical solutions to the describing equation are obtained, and the evolution of the dark soliton is numerically simulated. The numerical results confirm the theoretical analysis and show that the dynamics depend strictly on the initial condition, the gain coefficient and the external potential.     

Effects of periodic optical lattice potential on dark solitons in a Bose Einstein condensate

This paper investigates the dynamics of dark solitons in a Bose--Einstein condensate with a magnetic trap and an optical lattice (OL) trap, and analyses the effects of the periodic OL potential on the dynamics by applying the variational approach based on the renormalized integrals of motion. The results show that the dark soliton becomes only a standing-wave and free propagation of the dark soliton is not possible when the periodic length of the OL potential is approximately equal to the effective width of the dark soliton. When the periodic length is very small or very large, the effects of the OL potential on the dark soliton will be sharply reduced. Finally, the numerical results confirm these theoretical findings.     

Formation of combined solitons in two-component Bose—Einstein condensates

<正>We investigate the combined soliton solutions of two-component Bose—Einstein condensates with external potential. The "phase diagram" is obtained for the formation regions of different combined solitons.Our results show that the intraspecies(interspecies) interaction strengths and the external trapped potential clearly affect the formation of dark-dark, bright-bright,and dark-bright soliton solutions in different regions.Especially,we find that the bright-bright (dark-dark) soliton can exist in the case of both repulsive(attractive) intraspecies interaction strengths in the presence of external potential.This novel phenomenon is completely different from the formation of soliton solution of one-component Bose-Einstein condensates without external potential,and it will be useful for the study of two-component Bose-Einstein condensates.     

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.     

Nonlinear Wave in a Disc-Shaped Bose-Einstein Condensate

We discuss the possible nonlinear waves of atomic matter wave in a Bose-Einstein condensate. One and two of two-dimensional （2D） dark solitons in the Bose-Einstein condensed system are investigated. A rich dynamics is studied for the interactions between two solitons. The interaction profiles of two solitons are greatly different if the angle between them are different. If the angle is small enough, the maximum amplitude during the interaction between two solitons is even less than that of a single soliton. However, if the angle is large enough, the maximum amplitude of two solitons can gradually attend to the sum of two soliton amplitudes.     

准二维凝聚体中暗孤子环的动力学演化

发展多重尺度方法,解析研究了准二维凝聚体中孤子的动力学行为.当原子间为相互排斥作用时,凝聚体中可观察到暗孤子.计算表明,该暗孤子不稳定,将随时间演化成幅度较小的暗孤子环.特别是,所形成的暗孤子环被表明具有动力学稳定性. 关键词： 玻色-爱因斯坦凝聚 多重尺度方法 暗孤子环     

Effect of a localized impurity on soliton dynamics in the Bose-Einstein condensates

By using a multiple-scale method,we analytically study the effect of a localized impurity on the soliton dynamics in the Bose-Einstein condensates.It is shown that a dark soliton can be transmitted through a repulsive (or attractive) impurity,while at the position of the localized impurity the soliton can be quasitrapped by the impurity.Additionally,we find that the strength of the localized impurity has an important effect on the dark soliton dynamics.With increasing strength of the localized impurity,the amplitude of the dark soliton becomes bigger,while its width is narrower,and the soliton propagates slower.     

Dissipative dynamics of dark solitons in elongated Bose--Einstein condensates

The dissipative dynamic stability is investigated of dark solitons in elongated Bose--Einstein condensates that can be described by the Gross--Pitaevskii equation including an additional term. Based on the direct perturbation theory for the nonlinear Schr?dinger equation, the dependence of the soliton velocity on time is explicitly given, and the shape of dark solitons remaining unchanged under the dissipative condition is confirmed theoretically for the first time. It is found that the dynamically stable dark solitons turn out to be thermodynamically unstable.     

Dark lump excitations in superfluid Fermi gases

We study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases.A Kadomtsev-Petviashvili I(KPI) solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen-Cooper-Schrieffer(BCS) regime,Bose-Einstein condensate(BEC) regime,and unitarity regime.Onelump solution as well as one-line soliton solutions for the KPI equation are obtained,and two-line soliton solutions with the same amplitude are also studied in the limited cases.The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.     

The dynamics of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates

This paper investigates the dynamical properties of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates.It gives three kinds of stationary solutions to this model and develops a general method of constructing nonstationary solutions.It obtains the unique features about general evolution and soliton evolution of nonstationary solutions in this model.     

Effect of a barrier potential on soliton dynamical characteristics in condensates

By using the multiple-scale method, this paper analytically studies the effect of a barrier potential on the dynamical characteristics of the soliton in Bose--Einstein condensates. It is shown that a stable soliton is exhibited at the top of the barrier potential and the region of the absence of the barrier potential. Meanwhile, it is found that the height of the barrier potential has an important effect on the dark soliton dynamical characteristics in the condensates. With the increase of height of the barrier potential, the amplitude of the dark soliton becomes smaller, its width is narrower, and the soliton propagates more slowly.     

Generation of maximally entangled states in a two-component Bose-Einstein condensate

We study analytically the generation of maximally entangled states （MESs） formed by a two-component Bose-Einstein condensate （BEC） trapped in an adiabatically driven single potential well. Under the condition of the linear interaction controlled by a driven field being much stronger than the effective nonlinear interaction between the components, MESs, as some particular cases of superpositions of spin coherent states （SSCS）, may emerge periodically along with not only time evolution but also the equidifferent change of the linear coupling strength at a particular time.     

凝聚体中亮孤子和暗孤子的交替演化

利用Darboux变换法，解析地研究了局限于恒定不变外部势阱中的玻色-爱因斯坦凝聚体的非线性动力学性质.结果发现凝聚体中的粒子之间的相互作用强度对其非线性动力学特征有重要的影响.当玻色子之间的相互排斥作用相当强时，凝聚体中只会存在亮孤子；而玻色子之间的相互排斥作用相当弱(小于临界值)时，凝聚体中会出现亮孤子和暗孤子交替演化. 关键词： 玻色-爱因斯坦凝聚 Darboux变换 孤子     

Dynamical Stability of Gap Soliton of One-Dimensional Condensate in Optical Lattices with Strong Interatomic Interaction

By developing the multiple scales method, we analytically study the dynamics properties of gap soliton of Bose- Einstein condensate in optical lattices. It is shown that the gap soliton will appear at Brillouin zone edge of linear band spectrum of the condensates when the interatomic interaction strength is larger than the lattice depth. Moreover, the density of gap soliton starts to be relatively small, while it increases with time and becomes stable.     

Chaos in a Bose-Einstein condensate

It is demonstrated that Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose-Einstein condensate driven by time-periodic harmonic or inverted-harmonic potential.A formally exact solution of the time-dependent Gross-Pitaevskii equation is constructed,which describes the matter shock waves with chaotic or periodic amplitudes and phases.     

Precisely controllable bright nonautonomous solitons in Bose-Einstein condensate

We study on bright nonautonomous solitons of Bose-Einstein condensate analytically in a time-dependent harmonic trap with an arbitrary time-dependent linear potential and complex potential. The explicit ways to control dynamics of soliton are presented through observing the evolution of its width, peak, and the motion of its center analytically. Furthermore, we present two-solitons solution in generalized form to observe the collision of solitons conveniently.     

Controlled Manipulation with a Bose--Einstein Condensates N-Soliton Train under the Influence of Harmonic and Tilted Periodic Potentials

A model of the perturbed complex Toda chain （PCTC） to describe the dynamics of a Bose-Einstein condensate （BEC） N-soliton train trapped in an applied combined external potential consisting of both a weak harmonic and tilted periodic component is first developed. Using the developed theory, the BEC N-soliton train dynamics is shown to be well approximated by 4N coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude, velocity, centre-of-mass position, and phase. The simplified analytic theory allows for an efficient and convenient method for characterizing the BEC N-soliton train behaviour. It further gives the critical values of the strength of the potential for which one or more localized states can be extracted from a soliton train and demonstrates that the BEC N-soliton train can move selectively from one lattice site to another by simply manipulating the strength of the potential.