Bose-Einstein Condensates in Optical Lattices with Higher-Order Interactions

The higher-order interactions of Bose-Einstein condensate in multi-dimensional optical lattices are discussed both analytically and numerically.It is demonstrated that the effects of the higher-order atomic interactions on the sound speed and the stabilities of Bloch waves strongly depend on the lattice strength.In the presence of higher-order effects,tighter and high-dimensional lattices are confirmed to be two positive factors for maintaining the system's energetic stability,and the dynamical instability of Bloch waves can take place simultaneously with the energetic instability.In addition,we find that the higher-order interactions exhibit a long-range behavior and the long-lived coherent Bloch oscillations in a tilted optical lattice exist.Our results provide an effective way to probe the higher-order interactions in optical lattices.     

光晶格中双组分偶极玻色-爱因斯坦凝聚体的调制不稳定性

利用线性稳定性分析的方法,对光晶格中双组分偶极玻色-爱因斯坦凝聚体(Bose-Einstein condensates,简称BECs)的调制不稳定性进行了研究.得到了光晶格中双组分偶极BECs原子系统调制不稳定性区域的分布与在位相互作用和由偶极-偶极相互作用所导致的格点间BECs相互作用之间的关系.结果显示,格点间BECs的相互作用对光晶格中双组分偶极BECs的调制不稳定性有较大的影响,这可为实际应用中如何操控双组分偶极BECs提供有用的信息. 关键词： 光晶格 双组分玻色-爱因斯坦凝聚体 调制不稳定性 偶极-偶极相互作用     

光晶格中双组分玻色-爱因斯坦凝聚系统的调制不稳定性

利用线性稳定分析的方法,在不满足原子流相等的条件下,对光晶格中双组分玻色-爱因斯坦凝聚原子(BEC)系统的调制不稳定性区域与不同BEC组分的波长和不同的调制波长,以及两组分BEC间相互作用大小之间的关系进行了研究.结果显示,光晶格中双组分BEC系统的调制稳定性的区域在不满足原子流相等的条件下,随不同的波长,不同的调制和相互作用之间的大小会出现了较大的变化.相应结果可为实际应用中如何操控双组分BEC提供有用的信息.     

Tunable ground-state solitons in spin–orbit coupling Bose–Einstein condensates in the presence of optical lattices

Properties of the ground-state solitons, which exist in the spin–orbit coupling(SOC) Bose–Einstein condensates(BEC) in the presence of optical lattices, are presented. Results show that several system parameters, such as SOC strength,lattice depth, and lattice frequency, have important influences on properties of ground state solitons in SOC BEC. By controlling these parameters, structure and spin polarization of the ground-state solitons can be effectively tuned, so manipulation of atoms may be realized.     

双色光晶格势阱中玻色-爱因斯坦凝聚体的Landau-Zener隧穿行为

考虑玻色-爱因斯坦凝聚体局限于周期性的双色光晶格势阱中,研究其中的Bloch能带结构、第一能隙和第二能隙的Landau-Zener隧穿行为.结果表明,随着双色光晶格势阱的主、次晶格相位差从0增加到π,Bloch能带中第一能隙宽度逐渐增加,而第二能隙宽度逐渐减小.同时发现,双色光晶格势阱的主、次晶格深度及其相位差对第一能隙和第二能隙的Landau-Zener隧穿性质有重要的影响.     

Bessel型光晶格中双组分玻色-爱因斯坦凝聚体的基态解

研究了平面Bessel型光晶格(BL)中双组分玻色-爱因斯坦凝聚(BECs)体系的基态解.从描述三维(3D)BECs体系的动力学方程Gross-Pitaevskii方程(GPE)出发,当垂直方向囚禁频率远大于平面上囚禁频率时,得到了描述2D-BECs体系的动力学方程.利用双组分BECs体系中原子之间相互作用与BL强度相互平衡的条件,得到了平面BL光晶格中2D-GPE的一组基态精确解,给出了基态的原子数分布,总原子数和能量与原子之间相互作用强度及BL势的关系.相对于单组分BEC体系,由于不同组分原子相互作用的存在,使得BL光晶格中双组分BECs基态具有更丰富的结构.当不存在不同组分原子之间的相互作用时,模型简化到单组分体系,并给出了相应的基态解,原子数分布和能量. 关键词： Bessel型光晶格 基态解 双组分玻色-爱因斯坦凝聚     

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     

深光晶格势阱中凝聚体的扭结包络隙孤子

发展准离散多尺度法结合紧束缚近似,解析地研究了局陷于光晶格势阱中凝聚体的非线性动力学性质.结果发现,系统中出现稳定的对称包络孤子外,还可观察到一种新的非线性元激发:扭结包络隙孤子.有趣的是,该隙孤子并不传播且局域在初始位置,其幅度可通过光晶格势阱的晶格常数和势阱深度来调控.相应的实验方案是:通过改变形成光晶格势阱的两交叉耦合激光束之间的夹角和(或)激光光强来调控扭结包络隙孤子的幅度.     

光格中玻色-爱因斯坦凝聚的自旋磁子和自旋波

研究了一维光格中旋量玻色—爱因斯坦凝聚体的自旋磁子和自旋波。求出了自旋磁子和自发磁化强度。用经典方法求得了均匀体系的自旋波和能级以及激光调制下的自旋波和能级。特别是在连续极限近似下,求得了马丢函数波及其能级。     

光格中玻色-爱因斯坦凝聚的自旋磁子和自旋波

研究了一维光格中旋量玻色—爱因斯坦凝聚体的自旋磁子和自旋波。求出了自旋磁子和自发磁化强度。用经典方法求得了均匀体系的自旋波和能级以及激光调制下的自旋波和能级。特别是在连续极限近似下,求得了马丢函数波及其能级。     

一维双组分玻色-爱因斯坦凝聚体系的量子隧穿特性

利用双模近似方法研究了一维双组分玻色-爱因斯坦凝聚体(Bose-Einstein condensates,BECs)的量子隧穿特性.从描述三维双组分BECs系统的Gross-Pitaevskii方程(GPE)出发,得到了描述一维体系的GP方程.把体系波函数写成原子数和相位指数的乘积,得到描述体系隧穿特性的费曼方程.数值求解费曼方程,研究了原子之间相互作用(双组分BECs体系原子之间的相互作用包括组分内部原子之间的相互作用和不同组分原子之间的相互作用)对隧穿特性的影响.结果显示,当原子之间的相互作用较弱时,体系发生量子隧穿现象,表现为原子数在平衡位置附近作周期振荡;随着原子之间相互作用增强,体系经历一个临界状态,进入自俘获状态,即由于原子之间相互作用的存在,在对称双势阱中演化的BECs可以呈现出原子数高度的不对称分布,好像绝大数原子被其中一个势阱俘获.从隧穿到自俘获原子之间的相互作用存在一个临界值,从而体系的能量也对应一个临界值,根据体系的哈密顿函数,就能求出相互作用临界值的表达式.     

磁偶极相互作用下玻色-爱因斯坦凝聚体中出现的奇特涡旋晶格结构

文章简要地介绍了玻色-爱因斯坦凝聚体中出现的涡旋和铬原子玻色-爱因斯坦凝聚体的实验研究进展,还介绍了文章作者的一项最新的理论工作.研究指出,由于铬原子磁偶极相互作用的影响,凝聚体中将出现奇特的各向异性的涡旋晶格结构     

Band structure and dynamic behaviors of Bose-Einstein condensates in Fourier-Synthesized optical lattices

By employing a nonlinear three-mode model, we study the band structure of Bose-Einstein condensates in Fourier-Synthesized optical lattices, where the nonlinearity comes from the mean field treatment of interaction between atoms. In linear case, we present the band structure of the system. It is demonstrated that the energy band structure is strongly dependent on the value of relative phase of the two lattice harmonics. In the nonlinear case, we show that the eigenenergies as the functions of the quasi-momentum have a novel bowl structure in the middle energy level. It is found that there exist four critical values of interaction strength at which the band structure will undergo interesting changes. Furthermore, the stability of the eigenstate is also investigated.     

Interactions between bright solitons in different species of Bose—Einstein condensates

The dynamics of a bright-bright vector soliton in a cigar-shaped Bose-Einstein condensate trapping in a harmonic potential is studied.The interaction between bright solitons in different species with small separation is derived.Unlike the interaction between solitons of the same species,it is independent of the phase difference between solitons.It may be of attraction or repulsion.In the former case,each soliton will oscillate about and pass through each other around the mass-center of the system,which will also oscillate harmonically due to the harmonic trapping potential.     

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.     

Mode-locked matter waves in Bose-Einstein condensates

A new method is proposed for the spontaneous generation of mode-locked, atomic bright matter waves. The nonlinear mode-coupling dynamics induced by a three-well, cigar shaped potential, generates the intensity discrimination (saturable absorption) necessary to begin the pulse shaping necessary for mode-locking. When combined with proven BEC gain technologies and output coupling, the three critical physical components are shown to allow for the generation of a soliton-like bright matter wave from an incoherent (white-noise) initial state. The mode-locked bright matter wave can be generated in both attractive and repulsive condensates. Further, when a Feshbach resonance is used to periodically and rapidly alternate the condensate between attractive and repulsive states, parabolic similarity solutions can be created.     

Landau-Zener Tunnelling of Two-Component Bose-Einstein Condensates inOptical Lattices

We investigate the Landau--Zener tunnelling of two-componentBose-Einstein condensates (BECs) in optical lattices. In the neighborhood of the Brillouin zone edge, the system can be reduced to two coupled nonlinear two-level models. From the models, we calculate the change of the tunnelling probability for each component with the linear sweeping rate. It is found that the probability for each component exhibits regular oscillating behavior for the larger sweeping rate, but for smaller rate the oscillation is irregular. Moreover, the asymmetry of the tunnelling between the two components can be induced by the unbalanced initial populations or the inequality of the twoself-interactions when the cross-interaction between the components exists. The result can not be found in the single component BECs.     

玻色-爱因斯坦凝聚体中的怪波操控

利用Darboux变换法,解析地研究了玻色-爱因斯坦凝聚体(BEC)中的怪波.结果表明:当谱参数等于非线性系数时,BEC中形成一种新型的单洞怪波;而当谱参数小于非线性系数时,BEC中出现双洞怪波.进一步地,怪波的出现位置可通过调节周期性势阱的驱动频率和强度来控制.此外,随着原子间相互作用的减小,怪波的最高幅度也随之降低.相关结果可为预防怪波的危害提供帮助.     

玻色-爱因斯坦凝聚体中的怪波操控

利用Darboux变换法, 解析地研究了玻色-爱因斯坦凝聚体(BEC)中的怪波. 结果表明: 当谱参数等于非线性系数时, BEC中形成一种新型的单洞怪波; 而当谱参数小于非线性系数时, BEC中出现双洞怪波. 进一步地, 怪波的出现位置可通过调节周期性势阱的驱动频率和强度来控制. 此外, 随着原子间相互作用的减小, 怪波的最高幅度也随之降低. 相关结果可为预防怪波的危害提供帮助.