Solitons in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in a Harmonic Trap

We obtain the integrable relation for the one-dimensional nonlinear Schrodinger equations which describes the dynamics of a Bos-Einstein Condensates with time-dependent scattering length in a harmonic potential. The exact one- and two-soliton solutions are constructed analytically by using the Hirota method. Then we further discuss the dynamics of the one soliton and the interactions between two solitons in currently experimental conditions.     

Dynamics of Analytical Matter-Wave Solutions in Three-Dimensional Bose–Einstein Condensates with Two- and Three-Body Interactions

Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s~udied in details.     

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 atomic scattering length in an expulsive parabolic potential. Bose-Einstein condensates （BECs） with time-dependent Under a safe ravage 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 atomic scattering 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.     

装载于外势场中的玻色-爱因斯坦凝聚N-孤子间的相互作用

首先建立起玻色-爱因斯坦凝聚孤子链的微扰复数Toda链理论,然后深入研究玻色-爱因斯坦凝聚N-孤子间的绝热相互作用,分别通过对二次外势场、周期性外势场和二者叠加的复合外势场所引起的三类微扰,利用微扰的复数Toda链理论给出了解析处理, 并和基于分步傅里叶变换的直接数值方法进行比较,发现微扰的复数Toda链方程能够充分揭示上述三类外势场中的N-孤子链的动力学行为和特征.同时还给出了从孤子链中提取一个或多个局域态的倾斜势场或周期性势场的强度临界值,这可为玻色-爱因斯坦凝聚的实验研究关键词：玻色-爱因斯坦凝聚Gross-Pitaevskii方程物质波孤子相互作用     

Spatial Chaos of Bose-Einstein Condensates in a Cigar-Shaped Trap

The spatial chaos of Bose-Einstein condensates in a cigar-shaped trap is studied. For a system with a steady current, we construct the general solution of the 1st-order equation. From the boundedness condition of the general solution, we obtain the Melnikov function predicting the onset of chaos. The unpredictability of the system's distribution of atom density is also theoretically analyzed. For a 23Na system meeting the perturbation condition, numerical simulations show the existence of chaos, which is in accordance with our analytical results. Numerical simulations of a 87 Rb system dissatisfying the perturbation condition also demonstrate that there exists chaos in the system. The case without a current is also investigated.     

Reflection-Transmission Transition of Bright-Bright Solitons Collision in Two Species Condensates with Repulsive Interspecies Interactions

Considering repulsive interspecies interactions,we study the dynamical properties of bright-bright solitons in two species Bose-Einstein condensates by using a variational approach combined with numerical simulation.It is shown that the interactions between bright-bright solitons vary from repulsive to attractive interactions with the increasing their separating distances,and at equilibrium position the bright-bright solitons are localized.Interestingly,a transition from reflection-to transmission-collision is firstly observed,different from previous results of only reflection collision appearing there.These results will be helpful for the experimental manipulating such solitons.     

Solitons of two-component Bose-Einstein condensates modulated in space and time

In this Letter we present soliton solutions of two coupled nonlinear Schrödinger equations modulated in space and time. The approach allows us to obtain solitons for a large variety of solutions depending on the nonlinearity and potential profiles. As examples we show three cases with soliton solutions: a solution for the case of a potential changing from repulsive to attractive behavior, and the other two solutions corresponding to localized and delocalized nonlinearity terms, respectively.     

Rabi Oscillations in Two-Component Bose-Einstein Condensates with a Coupling Drive

The Rabi oscillations in two-component Bose-Einstein condensates with a coupling drive are studiedby means of a pair of bosonic operators. The coupling drive and initial phase difference will affect the amplitudeand the period of the Rabi oscillations. The Rabi oscillations will vanish in the evolution of the condensate densityfor some special initial phase differences (ψ = 0 or π). Our theory provides not only an analytical framework forquantitative predictions for two-component condensates, but also gives an intuitive understanding of some mysteriousfeatures observed in experiments and numerical. simulations.     

Interference of Two-Component Bose-Einstein Condensates with a Coupling Drive in Presence of Dissipation

The interference of the two-component Bose-Einstein condensates with a coupling drive in the presence of the dissipation is studied. We find that when the two-component Bose-Einstein condensates are initially in the coherent states, for the smaller dissipation parameters compared with that of the rf frequency ωrf, the interference intensity exhibits damply oscillation behavior, whereas when the dissipation parameters are larger than that of the ωrf, the interference intensity exhibits a fast attenuation behavior. As a comparison, the interference intensity in the absence of the dissipation is also studied. We conclude that the dissipation of the system can be evaluated by selecting the ωrf experimentally.     

外势场作用下的玻色-爱因斯坦凝聚啁啾孤子的演化与操控

提出了一种处理玻色-爱因斯坦凝聚啁啾孤子动力学的拓展变分方法,深入研究了玻色-爱因斯坦凝聚孤子在周期势与抛物势联合作用下的动力学演化,利用拓展变分法给出了解析处理,并和基于分步傅里叶变换的直接数值法进行比较,发现这种拓展变分方法能够充分揭示上述外势场中的玻色-爱因斯坦凝聚啁啾孤子的动力学行为和特征．同时给出了能支持多稳定晶格囚禁玻色-爱因斯坦凝聚啁啾孤子的周期势与抛物势强度比值的临界值和一种通过控制外势场可有选择地移动玻色-爱因斯坦凝聚啁啾孤子的操控方法,这为玻色-爱因斯坦凝聚的实验和应用研究提供了理论参关键词：玻色-爱因斯坦凝聚Gross-Pitaevskii方程啁啾孤子操控     

Compression of Bright Bound Solitons in the Bose-Einstein Condensates with Exponentially Time-Dependent Atomic Scattering Length by the Feshbach Resonance

We investigate compression of the bright bound solitons in the Bose-Einstein condensates (BECs) by exponentially increasing the absolute value of the atomic scattering length. Similarity transformation and Hirota bilinear method are used to symbolically solve the one-dimensional nonlinear Schrödinger equation with the time-dependent coefficients. We present types of the bright bound solitons in compression through manipulating their initial coherence. Results show that the improved quantity of the atomic density peaks can be observed before the collapse of the solitons when their coherence is increased. Furthermore, we discuss how those compressed bound solitons are influenced by the adjacent solitons. The bound structures in our study are illustrated to exist with the parameters within the current experimental capacity (the spatial and temporal ranges of the bound solitons are less than 56 μm and 50 ms in our investigation), which suggests a future observation in the BECs experiments.     

Bright and dark solitons in a quasi-1D Bose-Einstein condensates modelled by 1D Gross-Pitaevskii equation with time-dependent parameters

We investigate the exact bright and dark solitary wave solutions of an effective 1D Bose-Einstein condensate (BEC) by assuming that the interaction energy is much less than the kinetic energy in the transverse direction. In particular, following the earlier works in the literature Pérez-García et al. (2004) [50], Serkin et al. (2007) [51], Gurses (2007) [52] and Kundu (2009) [53], we point out that the effective 1D equation resulting from the Gross-Pitaevskii (GP) equation can be transformed into the standard soliton (bright/dark) possessing, completely integrable 1D nonlinear Schrödinger (NLS) equation by effecting a change of variables of the coordinates and the wave function. We consider both confining and expulsive harmonic trap potentials separately and treat the atomic scattering length, gain/loss term and trap frequency as the experimental control parameters by modulating them as a function of time. In the case when the trap frequency is kept constant, we show the existence of different kinds of soliton solutions, such as the periodic oscillating solitons, collapse and revival of condensate, snake-like solitons, stable solitons, soliton growth and decay and formation of two-soliton bound state, as the atomic scattering length and gain/loss term are varied. However, when the trap frequency is also modulated, we show the phenomena of collapse and revival of two-soliton like bound state formation of the condensate for double modulated periodic potential and bright and dark solitons for step-wise modulated potentials.     

Three-dimensional solitons in two-component Bose-Einstein condensates

We investigate a kind of solitons in the two-component Bose-Einstein condensates with axisymmetric configurations in the R2 × S1 space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional （3D） skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross-Pitaevskii equations in imaginary time.     

Statistical Entropy of an Acoustic Black Hole in Bose–Einstein Condensates

The entanglement entropy of an acoustic black hole in a Bose-Einstein condensates （BEC） is derived, which is associated with the phonons generated via the Hawking mechanism in a sonic hole. Considering the dispersion relation of a BEC, we recalculate the entanglement entropy of the acoustic black hole by means of statistical method in two limits. We find that the entropy is still proportional to the area of event horizon, but with a coefficient dependent on the infrared cutoff.