二元凝聚体中亮-亮孤子的振荡-局域转变行为

考虑时间相关的种间相互吸引作用,研究了局限于谐振外部势阱中的二元玻色-爱因斯坦凝聚体中亮-亮孤子的传播特性.结果表明,当种内和种间相互吸引作用都不变时,亮-亮孤子呈现出周期性的振荡;如果种内相互吸引作用仍保持不变,而种间相互吸引作用随时间指数增加时,发现凝聚体中产生振荡-局域转变行为,且这种振荡-局域的转变行为可通过调节谐振势阱的横向囚禁频率来控制.此外,还设计了实验方案来观察孤子的这种振荡-局域转变行为.     

光晶格势阱中二元凝聚体的矢量孤子的振荡和分裂

考虑外部囚禁势阱为光晶格势阱,研究了二元玻色-爱因斯坦凝聚体中亮-亮孤子的动力学行为.结果表明,亮-亮孤子的运动方向和振荡行为可以分别通过调节光晶格势阱的晶格常数和势阱深度来控制.进一步地,亮-亮孤子还可以被局域在光晶格势阱中,并且随着势阱深度的增加,局域孤子会产生分裂行为.     

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     

方势阱中凝聚体的孤子动力学行为

利用多重尺度法, 解析地研究了方势阱中玻色-爱因斯坦凝聚体的孤子动力学行为. 结果表明, 方势阱对凝聚体中的孤子动力学有重要的影响. 进入方势阱时孤子作加速运动, 逃逸出势阱时孤子作减速运动; 且随着势阱深度的增加, 孤子的速度增加、幅度增加、宽度减小. 这为实验操控孤子的动力学行为提供一定的参考价值. 关键词： 玻色-爱因斯坦凝聚体 孤子 方势阱     

玻色-爱因斯坦凝聚体中的双孤子相互作用操控

考虑周期性驱动线性势, 利用Darboux变换法解析地研究了玻色-爱因斯坦凝聚体(BEC)中的双孤子相互作用, 得到了S-波散射长度的临界值. 结果表明: 当S-波散射长度高于临界值时, BEC中的两个亮孤子相互吸引并融合; 而当S-波散射长度低于临界值时, 两个亮孤子保持局域稳定. 此外, 在外部势阱的驱动下, 两个稳定的亮孤子产生周期性振荡行为.     

非谐势阱中二维G-P方程的数值计算

通过能量泛函的方法得到描述囚禁在非谐势阱中玻色-爱因斯坦凝聚体的二维G-P方程数值解,讨论原子间相互作用和非谐振势能项对玻色-爱因斯坦凝聚体的分布、能量和化学势的影响.     

线性塞曼劈裂对自旋-轨道耦合玻色-爱因斯坦凝聚体中亮孤子动力学的影响

利用变分近似及基于Gross-Pitaevskii方程的直接数值模拟方法,研究了自旋-轨道耦合玻色-爱因斯坦凝聚体中线性塞曼劈裂对亮孤子动力学的影响,发现线性塞曼劈裂将导致体系具有两个携带有限动量的静态孤子,以及它们在微扰下存在一个零能的Goldstone激发模和一个频率与线性塞曼劈裂有关的谐振激发模.同时给出了描述孤子运动的质心坐标表达式,发现线性塞曼劈裂明显影响孤子的运动速度和振荡周期.     

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.     

异核两组分玻色-爱因斯坦凝聚体中暗孤子的形成及其性质

数值模拟准一维异核两组分玻色-爱因斯坦凝聚体在谐振子势阱中的运动,研究调制不稳定性条件(MI条件)下暗孤子的形成及其性质.在调制不稳定性条件下,凝聚体基态形成后,瞬间使组分间的相互排斥力变为相互吸引力,实时演化可以形成暗孤子.对各组分自身相互作用系数分析发现,它们之间满足一定关系时暗孤子在不同的组分内形成,而且形成的暗孤子在谐振子势阱中呈现周期性的往返对穿运动.讨论了形成暗孤子数目与两种粒子的质量比率和粒子数比率存在的关系.     

计及两体和三体作用下的二维凝聚体中的孤子特性

使用多重尺度法,解析地研究计及粒子间两体和三体同时作用下二维凝聚体中孤子的特性. 结果发现,当凝聚体粒子间两体作用为排斥、三体作用为吸引时,凝聚体内会产生暗孤子环,且随着三体吸引作用的减弱,暗孤子环中心峰的高度逐渐降低,并当三体吸引作用消失时暗孤子环演化为一个完美的二维暗孤子. 当两体和三体作用均为排斥时,凝聚体中的暗孤子的宽度和幅度随着三体排斥作用的加强而减小,且当三体作用强度增加到与两体作用同一数量级时,凝聚体产生坍塌现象. 关键词： 玻色-爱因斯坦凝聚体 两体和三体作用 暗孤子     

Enhanced soliton transport in quasiperiodic lattices with introduced aperiodicity

We study linear transmission and nonlinear soliton transport through quasiperiodic structures, where the lattice profiles are described by multiple modulation frequencies. We show that resonant scattering at mixed-frequency resonances limits transmission efficiency of localized wave packets, leading to radiation and possible trapping of solitons. We obtain an explicit analytical expression for optimal quasiperiodic lattice profiles, where additional aperiodic modulations suppress mixed-frequency resonances, resulting in dramatic enhancement of soliton mobility. Our results can be applied to the design of photonic waveguide structures, and arrays of magnetic micro-traps for atomic Bose-Einstein condensates.     

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.     

Quantum coherent tunneling between two atomic-molecular Bose-Einstein condensates

We study the quantum coherent tunneling dynamics of two weakly coupled atomic-molecular Bose-Einstein condensates (AMBEC). A weak link is supposed to be provided by a double-well trap. The regions of parameters where the macroscopic quantum localization of the relative atomic population occurs are revealed. The different dynamical regimes are found depending on the value of nonlinearity, namely, coupled oscillations of population imbalance of atomic and molecular condensate, including irregular oscillations regions, and macroscopic quantum self trapping regimes. Quantum means and quadrature variances are calculated for population of atomic and molecular condensates and the possibility of quadrature squeezing is shown via stochastic simulations within P-positive phase space representation method. Linear tunnel coupling between two AMBEC leads to correlations in quantum statistics.Received: 22 May 2004, Published online: 10 August 2004PACS: 03.75.-b Matter waves - 03.75.Gg Entanglement and decoherence in Bose-Einstein condensates - 03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations - 05.30.Jp Boson systems     

Dynamics of matter-wave solitons in Bose-Einstein condensates with time-dependent scattering length and complex potentials

We investigate the dynamics of matter-wave solitons in the one-dimensional (1-D)Gross-Pitaevskii (GP) equation describing Bose-Einstein condensates (BECs) withtime-dependent scattering length in varying trapping potentials with feeding/loss term. Byperforming a modified lens-type transformation, we reduce the GP equation into a classicalnonlinear Schrödinger (NLS) equation with distributed coefficients and find its integrablecondition. Under the integrable condition, we apply the generalized Jacobian ellipticfunction method (GJEFM) and present exact analytical solutions which describe thepropagation of a bright and dark solitons in BECs. Their stability is examined usinganalytic method. The obtained exact solutions show that the amplitude of bright and darksolitons depends on the scattering length, while their motion and the total number of BECatoms depend on the external trapping potential. Our results also shown that the loss ofatoms can dominate the aggregation of atoms by the attractive interaction, and thus thepeak density can decrease in time despite that the strength of the attractive interactionis increased.     

Domain wall solitons in binary mixtures of Bose-Einstein condensates

The structure and dynamics of the domain walls separating segregated condensates in trapped mixtures of repulsive Bose-Einstein condensates are studied. Our work reveals that, under fairly general conditions, these domain walls behave as independent dynamical entities, which allows us to identify them as constituting a novel class of multicomponent solitons in Bose-Einstein condensates.     

Collision dynamics of two Bose–Einstein condensates in the presence of Raman coupling

A collision of two-component Bose-Einstein condensates in the presence of Raman coupling is proposed and studied by numerical simulations. Raman transitions are found to be able to reduce collision-produced irregular excitations by forming a time-averaged attractive optical potential. Raman transitions also support a kind of dark soliton pair in two-component Bose-Einstein condensates. Soliton pairs and their remnant single solitons are shown to be controllable by adjusting the initial relative phase between the two colliding condensates or the two-photon detuning of Raman transitions. Received: 5 February 2001 / Published online: 27 April 2001     

Dynamic stability and manipulation of bright matter-wave solitons by optical lattices in Bose-Einstein condensates

An extended variation approach to describing the dynamic evolution of self-attractive Bose-Einstein condensates is developed. We consider bright matter-wave solitons in the presence of a parabolic magnetic potential and a time-space periodic optical lattice. The dynamics of condensates is shown to be well approximated by four coupled nonlinear differential equations. A noteworthy feature is that the extended variation approach gives a critical strength ratio to support multiple stable lattice sites for the condensate. We further examine the existence of the solitons and their stabilities at the multiple stable lattice sites. In this case, the analytical predictions of Bose-Einstein condensates variational dynamics are found to be in good agreement with numerical simulations. We then find a stable region for successful manipulating matter-wave solitons without collapse, which are dragged from an initial stationary to a prescribed position by a moving periodic optical lattice.     

Compression of bright bound soliton trains in the Bose-Einstein condensates with exponentially time-dependent atomic scattering length in an expulsive parabolic potential

Three types of two bright bound solitons with increasing coherence are investigated in the Bose-Einstein condensates (BECs) with the exponentially time-dependent interparticle interaction in an expulsive parabolic potential. Two methods are provided with symbolic computation to improve the number of matter density peaks within the given temporal range before the collapse of the solitons under the one-dimensional approximation: (i) enhancing the axial harmonic oscillator frequency; (ii) increasing the initial coherence of the bound solitons. Compression of the three- and four-bright-bound-soliton trains is presented. Estimation of the net binding forces among the bound solitons gives an explanation for the interaction patterns if the coherence of the bound state is limited. Our investigation theoretically reveals the existence of the bright bound solitons in the BECs and analyzes their complex interactions.     

Collision of bright vector solitons in two-component Bose-Einstein condensates

We investigate the coupled Gross-Pitaevskii equation describing the dynamics of two hyperfine states of Bose-Einstein condensates and deduce the integrability condition for the propagation of bright vector solitons. We show how the transient trap and scattering length can be suitably tailored to bring about fascinating collisional dynamics of vector solitons.