Tunneling Dynamics of Two-Species Bose-Einstein Condensates with Feshbach Resonances

We investigate tunneling dynamics of atomic group consisting of three atoms in Bose-Einstein condensates with Feshbach resonance. It is shown that the tunneling of the atom group depends not only on the inter-atomic nonlinear interactions and the initial number of atoms in these condensates, but also on the tunneling coupling between the atomic condensate and the three-atomic molecular condensate. It is found that besides oscillating tunneling current between the atomic condensate and the molecular condensate, the nonlinear atomic group tunneling dynamics sustains a self-maintained population imbalance: a macroscopic quantum self-trapping effect. The influence of de-coherence caused by non-condensate atoms on the tunneling dynamics is studied. It is indicated that de-coherence suppresses the atomic group tunneling.     

Tunneling Dynamics Between Any Two Multi-atomic-molecular Bose-Einstein Condensates

Tunneling dynamics of multi-atomic molecules between any two multi-atomic molecular Bose-Einstein condensates with Feshbach resonance is investigated. It is indicated that the tunneling in the two Bose-Einstein condensates depends not only on the inter-molecular nonlinear interactions and the initial number of molecule in these condensates, but also on the tunneling coupling between them. It is discovered that besides oscillating tunneling current between the multi-atomic molecular condensates, the nonlinear multi-atomic molecular tunneling dynamics sustains a self-locked population imbalance: a macroscopic quantum self-trapping effect. The influence of de-coherence caused by non-condensate molecule on the tunneling dynamics is studied. It is shown that de-coherence suppresses the multi-atomic molecular tunneling.     

Tunneling Dynamics of Two-Species Molecular Bose-Einstein Condensates

We study tunneling dynamics of atomic group in two-species molecular Bose-Einstein condensates. It is shown that the tunneling of the atom group depends on not only the tunneling coupling constant between the atomic pair molecular condensate and the three-atomic group molecular condensate, but also the inter-molecular nonlinear interactions and the initial number of atoms in these condensates. It is discovered that besides oscillating tunneling current between the atomic pair molecular condensate and the three-atomic group molecular condensate, the nonlinear atomic group tunneling dynamics sustains a self-maintained population imbalance: a macroscopic quantum self-trapping effect.     

Tunneling Dynamics Between Atomic and Molecular Bose-Einstein Condensates

Tunneling dynamics of multi-atomic molecules between atomic and multi-atomic molecular Bose-Einstein condensates with Feshbach resonance is investigated.It is indicated that the tunneling in the two Bose-Einstein condensates depends on not only the inter-atomic-molecular nonlinear interactions and the initial number of atoms in these condensates,but also the tunneling coupling between the atomic condensate and the multi-atomic molecular condensate.It is discovered that besides oscillating tunneling current between the atomic condensate and the multi-atomic molecular condensate,the nonlinear multi-atomic molecular tunneling dynamics sustains a self-locked population imbalance:a macroscopic quantum self-trapping effect.The influence of de-coherence caused by non-condensate atoms on the tunneling dynamics is studied.It is shown that de-coherence suppresses the multi-atomic molecular tunneling.Moreover,the conception of the molecular Bose-Einstein condensate,which is different from the conventional single-atomic Bose-Einstein condensate,is specially emphasized in this paper.     

Tunneling Dynamics of Two-Species Bose-Einstein Condensates

We have studied the tunneling dynamics of two-species Bose-Einstein condensates. It is shown that the population difference and the Josephson-like tunneling current between the two condensates exhibit oscillation behaviors and there exists macroscopic quantum self-trapping, which strongly depends on the initial state, interatomic nonlinear self-interaction, interspecies nonlinear interaction, and the total number of atoms in the two condensates.     

The Atomic Tunneling Current in Two—Species Bose—Einstein Condensates

It is shown that the atomic tunneling current and the Shapiro-like steps strongly depend on the initial number of atoms in each condensate and the initial phase difference between the two condensates which are initially in even(odd) coherent states.The nonlinearity of interatomic interactions in the two condensates may lead to the atomic tunneling current and Shapiro-like step between the two condensates.It is found that the interatomic nonlinear interactions can induce the atomic tunneling current and Shapiro-like step between two condensates even though there does not exist the interspecies Josephson-like tunneling coupling.The static atomic tunneling current flows in positive or negative direction,which depends on the phase difference of the two-species condensates.     

Tunneling of Spinor Bose-Einstein Condensates in Optical Lattice

In this letter, we have studied the tunneling effects and fluctuations of spinor Bose-Einstein condensates in optical lattice. It is found that there exist tunneling effects and fluctuations between lattices l and l ＋ 1, l and l - 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices I and l＋ 1, and I and l - 1. In this case the fluctuations are a constant, and the magnetic soliton appears.     

Tunneling of Spinor Bose-Einstein Condensates in Optical Lattice

In this letter, we have studied the tunneling effects and fluctuations of spinor Bose-Einstein condensates in optical lattice. It is found that there exist tunneling effects and fluctuations between lattices l and l 1, l and l - 1,respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices l and l 1, and l and l - 1. In this case the fluctuations are a constant,and the magnetic soliton appears.     

Quantum Statistical Properties in Two—Species Bose—Einstein Condensates

We have studied quantum statistical properties in a zero-temperature two-species Bose-Einstein condensate system in the presence of the nonlinear self-interaction of each species,the interspecies nonlinear interaction,and the Jisephson-like tunneling interaction.It is found that the two condensates may periodically exhibit sub-Poissonian distribution.It is revealed that the correlation between the two condensates can be nonclassical,which means that there exists a violation of Cauchy-Schwartz inequality.The nonclassical effect about the correlation between the two condensates can be realized experimentally by properly preparing the total number of atoms in the two 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.     

玻色-爱因斯坦凝聚领域Feshbach共振现象研究进展

Feshbach共振现象是当前玻色一爱因斯坦凝聚领域中的一个研究热点．目前在大多数低温碱金属原子气体里都已观测到Feshbach共振现象．在实验里利用Feshbach共振可以任意改变这些系统中原子之间的相互作用强度，从强相互排斥作用到强相互吸引作用都可以实现．文章详细介绍Feshbach共振现象以及目前它在原子气体系统里的最重要的两个应用，研究费米子气体里的超流态和有强相互作用的玻色子气体．     

Dynamics of Spin-2 Bose-Einstein Condensates

We numerically simulate the dynamics of a spin-2 Bose-Einstein condensate. We find that the initial phase plays an important role in the spin component oscillations. The spin mixing processes can fully cancel out due to quantum interference when taking some initial special phase. In all the spin mixing processes, the total spin is conversed. When the initial population is mainly occupied by a component with the maximal or minimal magnetic quantum number, the oscillations of spin components cannot happen due to the total spin conversation. The presence of quadratic Zeeman energy terms suppresses some spin mixing processes so that the oscillations of spin components are suppressed in some initial spin configuration. However, the linear Zeeman energy terms have no effects on the spin mixing processes.     

Soliton Solutions in Three-Component Bose-Einstein Condensates

We obtain soliton and plane wave solutions for the coupled nonlinear Schrotinger equations, which describe the dynamics of the three-component Bose-Einstein condensates by using the Hirota method. Meanwhile we find that the system which has attractive atomic interaction will only possess a shape changing （inelastic） collision property due to intensity redistribution in the absence of the spin-exchange interaction. As a discussed example, we investigate the one-soliton, two-soliton solutions and collisional effects between bright two-soliotn solution, which lead to the intensity redistribu tion.     

The Weak-Coupling of Bose-Einstein Condensates

The coherent characteristics of four trapped Bose-Einstein condensates (BEC) conjunct one by one in aring shape which is divided by two far off-resonant lasers, are studied. Four coupled Gross-Pitaevskii equations are usedto describe the dynamics of the system. Two kinds of self-trapping effects are discussed in the coupled BECs, and thephase diagrams for different initial conditions and different coupling strengths are discussed. This study can be used todetermine interaction parameters between atoms in BEC.     

Atomic Tunneling Effect in Two-Component Bose-Einstein Condensates with a Coupling Drive

In this paper, we have studied the atomic population difference and the atomic tunneling current of twocomponent Bose-Einstein condensates with a coupling drive. It is found that when the two-component Bose-Einstein condensates are initially in the coherent states, the atomic population difference may exhibit the step structure, in which the numbers of the step increase with the decrease of the Rabi frequency and with the increment of the initial phase difference. The atomic population difference may exhibit collapses, and revivals, in which their periods are affected dramatically by the Rabi frequency and the initial phase difference. The atomic tunneling current may exhibit damping oscillation behaviors, and exist the step structure for the time range of 10-10 ～ 10-9 second.     

Localized Asymmetric Atomic Matter Waves in Two-Component Bose-Einstein Condensates Coupled with Two-Photon Microwave Field

We investigate localized atomic matter waves in the two-photon microwave field. Interestingly, the oscillations two-component Bose-Einstein condensates coupled by of localized atomic matter waves will gradually decay and finally become non-oscillating behavior even if existing coupling field. In particular, atom numbers occupied in two different hyperfine spin states will appear asymmetric occupations after some time evolution.     

Feshbach共振下BCS-BEC渡越量子分析

考虑一个涵盖分子间相互作用的多体模型,给出一种半解析计算模型中费米原子对转化成玻色分子转化率的有效方法.这种方法主要使用独立交叉近似,并在平均场理论下推导出一个精确计算转化率的解析公式.对比分析证明,该解析公式的计算结果得到多体模型的数值分析的支持,并与Rice小组的⁶Li实验能够很好的吻合.     

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.     

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 original coupled Gross-Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev-Petviashvili-I 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.     

玻色-爱因斯坦凝聚体系中的混沌隧穿行为

研究了双势阱玻色-爱因斯坦凝聚(BEC)系统在外加周期调制下的混沌相变过程,着重讨论了混沌现象对BEC系统隧穿的影响.当外加调制频率与系统固有频率达到共振时,相平面会出现不稳定现象,即混沌现象.在量子情况下,研究了系统的Husimi函数随时间的演化.研究发现：当混沌现象出现时,系统中粒子间相互作用增大,使得混沌区域扩大,进而引起混沌辅助隧穿程度的变化. 关键词： 玻色-爱因斯坦凝聚 混沌 隧穿