Entanglement and localization of a two-mode Bose-Einstein condensate

A simple second quantization model is used to describe a two-mode Bose-Einstein condensate (BEC), which can be written in terms of the generators of a SU(2) algebra with three parameters. We study the behavior of the entanglement entropy and localization of the system in the parameter space of the model. The phase transitions in the parameter space are determined by means of the coherent state formalism and the catastrophe theory, which besides let us get the best variational state that reproduces the ground state energy. This semiclassical method let us organize the energy spectrum in regions where there are crossings and anticrossings. The ground state of the two-mode BEC, depending on the values of the interaction strengths, is dominated by a single Dicke state, a spin collective coherent state, or a superposition of two spin collective coherent states. The entanglement entropy is determined for two recently proposed partitions of the two-mode BEC that are called separation by boxes and separation by modes of the atoms. The entanglement entropy in the boxes partition is strongly correlated to the properties of localization in phase space of the model, which is given by the evaluation of the second moment of the Husimi function. To compare the fitness of the trial wavefunction its overlap with the exact quantum solution is evaluated. The entanglement entropy for both partitions, the overlap and localization properties of the system get singular values along the separatrix of the two-mode BEC, which indicates the phase transitions which remain in the thermodynamical limit, in the parameter space.     

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.     

非线性系统的非对角Berry相

研究了非线性系统中非对角情况的Berry相位, 给出了非线性非对角Berry相位的计算公式. 结果表明, 在非线性非对角情况下, 总相位包含有动力学相位, 通常意义的Berry相位, 以及非线性引起的附加相位. 此外, 还包含有非对角情况时所特有的新的附加项. 这新的一项表示, 当系统哈密顿慢变时产生的Bogoliubov涨落, 与另一个瞬时本征态之间的交叉效应, 进而对总的Berry相位产生影响. 作为应用, 对二能级玻色爱因斯坦凝聚体系, 具体计算了非线性非对角的Berry相位. 关键词： Berry 相位 非对角 绝热演化 玻色爱因斯坦凝聚     

Adiabatic tunneling of Bose–Einstein condensates with modulated atom interaction in a double-well potential

We study the adiabatic tunneling of Bose–Einstein condensates in a symmetric double-well potential when the interaction strength between the atoms is modulated linearly or in a cosine periodic form. It is shown that the system evolves along a nonlinear eigenstate path. In the case of linear modulation under the adiabatic approximation conditions, the tunneling probability of the condensate atoms to the other potential well is half. However, when the system is periodically scanned in the adiabatic process, we find an interesting phenomenon. A small change in the cycle period can lead to the condensate atoms returning to the right well or tunneling to the left well. The system comes from a linear eigenstate back to a nonlinear one, which is completely different from the linear eigenstate evolution. We explain the results by using the energy level and the phase diagram.     

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.     

双势阱中玻色-爱因斯坦凝聚的绝热隧穿

研究了玻色-爱因斯坦凝聚体在双势阱中随着能级差绝热循环变化而发生的绝热隧穿.发现当相互作用较强且初态选择为凝聚体全部置于较浅势阱时,演化过程破坏绝热定理,而演化结果有可能回到初态,也有可能不回到初态,取决于演化周期的选择;另外还发现演化过程表现出对初态选择的依赖,具有不对称的特征.利用能级图和相图,对上述现象给出了解释. 关键词： 玻色-爱因斯坦凝聚 Landau-Zener模型 绝热隧穿     

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     

Vortex chains induced by anisotropic spin-orbit coupling and magnetic field in spin-2 Bose-Einstein condensates

We investigate the anisotropic spin-orbit coupled spin-2 Bose-Einstein condensates with Ioffe-Pritchard magnetic field. With nonzero magnetic field, anisotropic spin-orbit coupling will introduce several vortices and further generate a vortex chain. Inside the vortex chain, the vortices connect to each other, forming a line along the axis. The physical nature of the vortex chain can be explained by the particle current and the momentum distribution. The vortex number inside the vortex chain can be influenced via varying the magnetic field. Through adjusting the anisotropy of the spin-orbit coupling, the direction of the vortex chain is changed, and the vortex lattice can be triggered. Moreover, accompanied by the variation of the atomic interactions, the density and the momentum distribution of the vortex chain are affected. The realization and the detection of the vortex chain are compatible with current experimental techniques.     

二维线性与非线性光晶格中物质波孤立子的稳定性

利用变分法和数值计算方法研究了二维线性和非线性光晶格中二维玻色-爱因斯坦凝聚体系中物质波孤立子的存在及其稳定性. 利用定态变分原理及Vakhitov-Kolokolov判据总结了线性和非线性结合光晶格中几种参数组合下定态定域解的稳定性. 结果表明, 当存在二维非线性光晶格时, 在吸引和排斥相互作用的原子体系中均可以存在稳定的物质波孤立子. 另外, 利用含时变分法研究了线性和非线性光晶格中物质波孤立子随时间的传播特性, 使波包参数对时间的一阶导数等于零, 可以给出稳定状态对应的参数, 结论和定态变分法给出的结果一致. 最后用数值计算方法研究变分结果的正确性, 把变分结果作为初始条件代入Gross-Pitaevskii方程研究其随时间传播特征, 得到了稳定的传播过程, 所得到的结果和变分分析结果一致. 关键词： 线性非线性光晶格 玻色-爱因斯坦凝聚 孤立子 稳定性     

线性与非线性光晶格中偶极孤立子的稳定性

利用变分法研究了线性和非线性交叉光晶格中偶极玻色-爱因斯坦凝聚(BEC)体系中物质波孤立子的稳定性.选用柱对称高斯型试探波函数,得出参数的Euler-Lagrange方程和体系的有效作用势能,根据有效势能是否具有局域最小值判断体系是否具有稳定孤立子解.结果表明,由于存在接触相互作用的空间调制,在排斥和吸引偶极相互作用下,均能形成稳定的孤立子解.给出了参数空间中存在稳定解的区域和物质波波包宽度随时间的变化曲线.     

Coherent manipulation of spin squeezing in atomic Bose-Einstein condensate via electromagnetically induced transparency

We propose a scheme to coherently control spin squeezing of atomic Bose-Einstein condensate (BEC) via the technique of electromagnetically induced transparency (EIT). We study quantum dynamics of the mean spin vector and spin squeezing. It is shown that the mean spin vector and spin squeezing of the BEC can be controlled and manipulated by adjusting the external coupling fields or/and internal nonlinear interactions of the BEC. It is indicated that the spin squeezing can be generated rapidly in the dynamical process and maintained in a long time interval. It is found that a larger effective Rabi coupling between atoms and lasers can produce a stronger spin squeezing, and the squeezing can maintain a longer time interval.     

Adjustable half-skyrmion chains induced by SU(3) spin-orbit coupling in rotating Bose-Einstein condensates

The ground state properties of the rotating Bose-Einstein condensates (BECs) with SU(3) spin-orbit coupling (SOC) in a two-dimensional harmonic trap are studied. The results show that the ferromagnetic and antiferromagnetic systems present three half-skyrmion chains at an angle of 120° to each other along the coupling directions. With the enhancement of isotropic SU(3) SOC strength, the position of the three chains remains unchanged, in which the number of half-skyrmions increases gradually. With the increase of rotation frequency and atomic density-density interaction, the number of half-skyrmions on the three chains and in the regions between two chains increases gradually. The relationships of the total number of half-skyrmions on the three chains with the increase of SU(3) SOC strength, rotation frequency and atomic density-density interaction are also given. In addition, changing the anisotropic SU(3) SOC strength can regulate the number and morphology of the half-skyrmion chains.     

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     

Effective Two-State Model and NOON States for Double-Well Bose-Einstein Condensates in Strong-Interaction Regime

The model of double-well Bose-Einstein condensates in the strong-interaction regime is shown to reduce adiabatically to an effective two-state model describing the Rabi oscillations between the two atomic Fock states ｜N, 0〉 and [0, N〉, and the NOON states of arbitrary ultracold atoms can therefore be generated periodically from the initial state of either one of the Foek states.     

物质的新状态——玻色-爱因斯坦凝聚——2001年诺贝尔物理奖介绍

美国国家标准和技术研究所的Eric A.Cornell教授，美国麻省理工学院的Wolfgang Ketterle教授与美国科罗拉多大学的Car E.Wieman教授由于“在稀薄的碱金属气体中成功地获得玻色－爱因斯坦凝聚，并且对凝聚体特性进行的早期基础性研究”方面的贡献，而荣获2001年诺贝尔物理奖，文章介绍了该研究的背景，三位诺贝尔奖得主的贡献及其意义。     

非线性作用随空间变化的玻色-爱因斯坦凝聚原子的规则与混沌分布

本文研究了非线性作用随空间变化的玻色-爱因斯坦凝聚原子的规则与混沌空间分布.空间变化的凝聚体相位导致系统中存在稳定的原子流.对化学势为正,原子间呈排斥作用的系统,构造了系统的一级微扰通解,该通解的有界性条件包含了著名的Mel'nikov混沌判据.在系统不满足微扰条件的情况下,数值模拟表明无论凝聚原子呈混沌分布还是规则分布,原子流的增大都可以破坏凝聚原子分布的空间对称性.     

Phase separation in the trapped spinor gases with anisotropic spin-spin interaction

We investigate the effect of the anisotropic spin-spin interaction on the ground state density distribution of the one dimensional spin-1 bosonic gases within a modified Gross-Pitaevskii theory both in the weakly interaction regime and in the Tonks-Girardeau (TG) regime. We find that for ferromagnetic spinor gas the phase separation occurs even for weak anisotropy of the spin-spin interaction, which becomes more and more obvious and the component of m_F=0 diminishes as the anisotropy increases. However, no phase separation is found for anti-ferromagnetic spinor gas in both regimes.     

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.     

非线性薛定谔方程的高阶分裂改进光滑粒子动力学算法

为提高传统光滑粒子动力学(SPH)方法求解高维非线性薛定谔(nonlinear Schr?dinger/Gross-Pitaevskii equation, NLS/GP)方程的数值精度和计算效率,本文首先基于高阶时间分裂思想将非线性薛定谔方程分解成线性导数项和非线性项,其次拓展一阶对称SPH方法对复数域上线性导数部分进行显式求解,最后引入MPI并行技术,结合边界施加虚粒子方法给出一种能够准确、高效地求解高维NLS/GP方程的高阶分裂修正并行SPH方法.数值模拟中,首先对带有周期性和Dirichlet边界条件的NLS方程进行求解,并与解析解做对比,准确地得到了周期边界下孤立波的奇异性,且对提出方法的数值精度、收敛速度和计算效率进行了分析;随后,运用给出的高阶分裂粒子方法对复杂二维和三维NLS/GP问题进行了数值预测,并与其他数值结果进行比较,准确地展现了非线性孤立波传播中的奇异现象和玻色-爱因斯坦凝聚态中带外旋转项的量子涡旋变化过程.     

Effects of three-body atomic interaction and optical lattice on solitons in quasi-one-dimensional Bose-Einstein condensate

We make use of a coordinate-free approach to implement Vakhitov-Kolokolov criterion for stability analysis in order to study the effects of three-body atomic recombination and lattice potential on the matter-wave bright solitons formed in Bose-Einstein condensates. We analytically demonstrate that (i) the critical number of atoms in a stable BEC soliton is just half the number of atoms in a marginally stable Townes-like soliton and (ii) an additive optical lattice potential further reduces this number by a factor of √1 − bg ₃ with g ₃ the coupling constant of the lattice potential and b = 0.7301.