Effect of interaction strength on gap solitons of Bose--Einstein condensates in optical lattices

We have developed a systematic analytical approach to the study on the dynamic properties of the linear and the nonlinear excitations for quasi-one-dimensional Bose-Einstein condensate trapped in optical lattices. A novel linear dispersion relation and an algebraic soliton solution of the condensate are derived analytically under consideration of Bose-Einstein condensate with a periodic potential. By analysing the soliton solution, we find that the interatomic interaction strength has an important effect on soliton dynamic properties of Bose-Einstein condensate.     

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     

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.     

具有三体作用的玻色-爱因斯坦凝聚暗孤子的演化

运用变分法研究了具有三体作用的玻色-爱因斯坦凝聚暗孤子的演化特性,分析了调谐囚禁电势对暗孤子运动的影响.结果表明,囚禁在调谐势阱中的暗孤子将振动,势阱强度和三体作用的符号影响了暗孤子的演化,并改变了BEC系统的振动特性.     

Parametric driving of dark solitons in atomic Bose-Einstein condensates

A dark soliton oscillating in an elongated harmonically confined atomic Bose-Einstein condensate continuously exchanges energy with the sound field. Periodic optical paddles are employed to controllably enhance the sound density and transfer energy to the soliton, analogous to parametric driving. In the absence of damping, the amplitude of the soliton oscillations can be dramatically reduced, whereas with damping, a driven soliton equilibrates as a stable soliton with lower energy, thereby extending the soliton lifetime up to the lifetime of the condensate.     

Quantum frequency standards based on the soliton state of a Bose-Einstein condensate

A method for stabilizing frequency based on using the soliton state of the Bose-Einstein condensate of alkali metal atoms as an atomic source was suggested. The critical total number of lithium condensate particles at which the existence of a quasi-one-dimensional soliton in the condensate was possible and the lifetime of such a soliton were estimated. The attainable accuracy of measuring reference transition frequencies in the suggested standard was shown to be substantially higher than with the known quantum frequency standards.     

Watching dark solitons decay into vortex rings in a Bose-Einstein condensate

We have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings. We have imaged the resulting vortex rings.     

Fermi–Pasta–Ulam recurrence and modulation instability

We give a qualitative conceptual explanation of the Fermi–Pasta–Ulam (FPU) like recurrence in the onedimensional focusing nonlinear Schrodinger equation (NLSE). The recurrence can be considered as a result of the nonlinear development of the modulation instability. All known exact localized solitary wave solutions describing propagation on the background of the modulationally unstable condensate show the recurrence to the condensate state after its interaction with solitons. The condensate state locally recovers its original form with the same amplitude but a different phase after soliton leave its initial region. Based on the integrability of the NLSE, we demonstrate that the FPU recurrence takes place not only for condensate, but also for a more general solution in the form of the cnoidal wave. This solution is periodic in space and can be represented as a solitonic lattice. That lattice reduces to isolated soliton solution in the limit of large distance between solitons. The lattice transforms into the condensate in the opposite limit of dense soliton packing. The cnoidal wave is also modulationally unstable due to soliton overlapping. The recurrence happens at the nonlinear stage of the modulation instability. Due to generic nature of the underlying mathematical model, the proposed concept can be applied across disciplines and nonlinear systems, ranging from optical communications to hydrodynamics.     

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     

Soliton excitations in a polariton condensate with defects

To study soliton excitations in a polariton condensate with defects, we use the Gross-Pitaevskii equation and its hydrodynamic form. An extra term is added to take into account the non-equilibrium nature of the polariton condensate and the presence of defects. The reductive perturbation method transforms these hydrodynamic equations into a modified Korteweg-de Vries equation in the long wavelength limit. We linearize this equation and study the soliton linear excitations.We give an analytic expression of traveling excitations using the variation of constants method. In the more general form,we show numerically that the excitations are oscillations, i.e., the amplitude and the width of the dark soliton oscillate simultaneously but in an opposite way.     

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.     

The soliton in the asymmetric scalar field theory

A new soliton solution for the asymmetric scalar field theory is obtained. The soliton is interpreted as the boson condensate drop. The phase transition is examined.     

Dilatons in the topological soliton model for the hyperons

We show that the predicted hyperon masses in the topological soliton model are very sensitive to the value to the gluon condensate parameter that appears when the scale invariance and trace anomaly of QCD are taken into account by introduction of a dilaton field. This contrasts with the insensitivity of the soliton properties to the dilaton coupling. In order that the predicted strange and charmed hyperon spectra agree with the empirical ones the gluon condensate parameter has to be about (400 MeV)⁴, which agrees with the result obtained from QCD sum rules. Within the framework of the present model this implies that the bag formed by the scalar field must be very shallow.     

Matter wave solitons in coupled system with external potentials

We present Lax-pair corresponding to the coupled Gross-Pitaevskii equation (CGPE) which governs the evolution of the macroscopic wave function of two components Bose-Einstein condensates trapped in time-dependent harmonic potential. Kinds of soliton solutions can be derived from the Lax-pair through Darboux transformation conveniently. Furthermore, soliton management in two-component Bose-Einstein condensate would be realized base on that the shape and motion of soliton in both components are investigated analytically. Moreover, it is found that there is a transformation existed between the nonautonomous coupled system and Manakov model.     

Motion of a Bose-Einstein Condensate Bright Soliton Incident on a Step-Like Potential

The motion characteristics of a Bose-Einstein condensate bright soliton incident on a local step-like potential barrier are investigated analytically by means of the variational approach. The dynamics of the soliton-potential interaction is studied as well. Then the results are verified by direct numerical simulations of the Gross-Pitaevskii equation. It is found that a moving bright soliton can be reflected from or pass over a step-like potentiaI in a controllable fashion, the critical velocity depends on the width of the soliton and the parameters of the step, and the motion trajectory of the soliton does not depend on its phase. The atom density envelope of the soliton is changed as the result of the interaction between the soliton and the step-like potential.     

Two-Dimensional Soliton Interaction for Multi-component Bose-Einstein Condensates

For two-component disk-shaped Bose-Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a Kadomtsev-Petviashvili-Ⅰ equation at the lowest order from the originai coupled Gross-Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev- Petviashvili-1 equation are given, therefore, the wave functions of both atomic gases are obtained as well. The instability of a soliton under higher-order long wavelength disturbance has been investigated. It is found that the instability depends on the angle between two directions of both soliton and disturbance.     

Dynamics of matter-wave solitons in a ratchet potential

We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory.     

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.     

Motion of dark solitons in trapped bose-einstein condensates

We use a multiple time scale boundary layer theory to derive the equation of motion for a dark (or grey) soliton propagating through an effectively one-dimensional cloud of Bose-Einstein condensate, assuming only that the background density and velocity vary slowly on the soliton scale. We show that solitons can exhibit viscous or radiative acceleration (antidamping), which we estimate as slow but observable on experimental time scales.     

Bright soliton trains of trapped Bose-Einstein condensates

We variationally determine the dynamics of bright soliton trains composed of harmonically trapped Bose-Einstein condensates with attractive interatomic interactions. In particular, we obtain the interaction potential between two solitons. We also discuss the formation of soliton trains due to the quantum mechanical phase fluctuations of a one-dimensional condensate.