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.     

Assessment of interspecies scattering lengths a12 from stability of two-component Bose-Einstein condensates

A stability method is used to assess possible values of interspecies scattering lengths a12 in two-component Bose-Einstein condensates described within the Gross-Pitaevskii approximation. The technique, based on a recent stability analysis of solitonic excitations in two-component Bose-Einstein condensates, is applied to ninety combinations of atomic alkali pairs with given singlet and triplet intraspecies scattering lengths as input parameters. Results obtained for values of a12 are in a reasonable agreement with the few ones available in the literature and with those obtained from a Painlevé analysis of the coupled Gross-Pitaevskii equations.     

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.     

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     

Tunneling of trapped-atom Bose condensates

We obtain the dynamics in number and phase difference, for Bose condensates that tunnel between two wells of a double-well atomic trap, using the (nonlinear) Gross-Pitaevskii equation. The dynamical equations are of the canonical form for the two conjugate variables, and the Hamiltonian corresponds to that of a momentum-shortened pendulum, supporting a richer set of tunneling oscillation modes than for a superconductor Josephson junction, that has a fixed-length pendulum as a mechanical model. Novel modes include ‘inverted pendulum’ oscillations with an average angle of π; and oscillations about a self-maintained population imbalance that we term ‘macroscopic quantum self-trapping’. Other systems with this phase-number nonlinear dynamics include two-component (interconverting) condensates in a single harmonic trap, and He³B superfluids in two containers connected by micropores.     

Binary quantum turbulence arising from countersuperflow instability in two-component Bose-Einstein condensates

We theoretically study the development of quantum turbulence from two counter-propagating superfluids of miscible Bose-Einstein condensates by numerically solving the coupled Gross-Pitaevskii equations. When the relative velocity exceeds a critical value, the countersuperflow becomes unstable and quantized vortices are nucleated, which leads to isotropic quantum turbulence consisting of two superflows. It is shown that the binary turbulence can be realized experimentally in a trapped system.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

Quantum coherent oscillations between two coupled bose-einstein condensates

The theoretical investigation of quantum coherent atomic oscillations between two coupled Bose-Einstein condensates(BECs) is studied. We apply the inseparable wave function of time-space to describe two trapped BECs in a double-well magnetic trap. According to Thomas-Fermi approximation, dynamical equations of the interwell phase difference and population imbalance are obtained. Using numerical method, coherent atomic tunneling and macroscopic quantum self-trapping(MQST) effect are investigated.     

两耦合玻色-爱因斯坦凝聚体间的量子相干振荡

理论上考察了两耦合玻色-爱因斯坦凝聚体间的相干原子振荡,我们用时空不能完全分离的波函数去描述囚禁在双磁阱中的玻色-爱因斯坦凝聚体,根据托马斯-费米近似,得到两凝聚体的相位差和布局数随时间的演化方程,应用数值计算的方法,考察了相干原子遂穿和宏观量子自囚禁效应.这些研究结果和采用双模时空分离波函数近似法得到的结果进行了比较.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schr(o)dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

Effect of quantum fluctuations on bose-einstein condensation of bilayer atomic gases in rapid rotation

We investigate vortex states and quantum fluctuations of bilayer atomic gases in rapid rotation. Among mean-field solutions of the Gross-Pitaevskii equation, we consider two types of vortex configurations: the vortex core positions of the layers are coincident or staggered. It is found that the coincident type is energetically preferred in the practical parameter regime. We also calculate the dispersion relations of collective modes and the filling factor for bosons outside the condensates. In the double layer system, quantum depletion is found to be suppressed due to interlayer tunneling. This means that Bose-Einstein condensation is stabilized compared to the single layer case.     

Bose-Einstein condensate of cavity exciton polaritons in a trap

The properties of traps for exciton polaritons in a semiconductor microcavity with an embedded quantum well have been considered. The behavior of the two-component Bose-Einstein condensate of photons and excitons described by the coupled system of Gross-Pitaevskii equations has been investigated. The analytical solutions for weak-confinement traps have been found in the Thomas-Fermi approximation. In the case of strong confinement, the behavior of the condensate has been investigated and constraints on the possible values of the chemical potential of the system have been obtained. The wavefunctions and generally different spatial profiles of the coupled photon and exciton condensates have been found.     

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.     

Bose condensation of exciton polaritons in an optical microcavity

Two methods are considered for producing traps for exciton polaritons in an optical microcavity with an embedded quantum well. The first method for controlling polaritons consists in producing a polariton trap governed by the longitudinal confinement of photons. Traps of this type can be created using an optical microcavity with a variable width. In traps of the second type, the exciton confinement is ensured by a weak potential that is applied to a quantum well with excitons or when this well is subjected to an inhomogeneous deformation. The behavior of a two-component Bose condensate of photons and excitons is analyzed theoretically. The Bose condensate is described by the coupled system of equations of the Gross-Pitaevskii type. The approximate wave functions and the spatial profiles of coupled photon and exciton condensates are obtained.     

Moving Matter-Wave Solitons in Spin-Orbit Coupled Bose-Einstein Condensates

We investigate the moving matter-wave solitons in spin-orbit coupled Bose-Einstein condensates(BECs) by a perturbation method.Starting with the one-dimensional Gross-Pitaevskii equations,we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spinorbit coupling.The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin-orbit coupled BECs.We find different types of moving solitons:dark-bright,bright-bright and dark-dark solitons.Interestingly,moving dark-dark soliton for attractive intra- and inter-species interactions is found,which depends on the Raman coupling.The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin-orbit coupling.     

Mean-field dynamics of spin-orbit coupled Bose-Einstein condensates

Spin-orbit coupling (SOC), the interaction between the spin and momentum of a quantum particle, is crucial for many important condensed matter phenomena. The recent experimental realization of SOC in neutral bosonic cold atoms provides a new and ideal platform for investigating spin-orbit coupled quantum many-body physics. In this Letter, we derive a generic Gross-Pitaevskii equation as the starting point for the study of many-body dynamics in spin-orbit coupled Bose-Einstein condensates. We show that different laser setups for realizing the same SOC may lead to different mean-field dynamics. Various ground state phases (stripe, phase separation, etc.) of the condensate are found in different parameter regions. A new oscillation period induced by the SOC, similar to the Zitterbewegung oscillation, is found in the center-of-mass motion of the condensate.     

Analytical studies of two-component Bose-Einstein condensates in two-dimensional optical lattices

The two-component Bose-Einstein condensates (BECs) trapped in 2D optical lattice potential is studied analytically. A new family of stationary exact solutions of the coupled Gross-Pitaevskii (GP) equations with 2D periodic potential are obtained. In particular, the phase diagram of the system in the trigonometric limit is determined analytically according to the nontrivial phase macroscopic wave functions of the condensates.     

Rabi flopping induces spatial demixing dynamics

We experimentally investigate the mixing and demixing dynamics of Bose-Einstein condensates in the presence of a linear coupling between two internal states. The observed amplitude reduction of the Rabi oscillations can be understood as a result of demixing dynamics of dressed states as experimentally confirmed by reconstructing the spatial profile of dressed state amplitudes. The observations are in quantitative agreement with numerical integration of coupled Gross-Pitaevskii equations without free parameters, which also reveals the criticality of the dynamics on the symmetry of the system. Our observations demonstrate new possibilities for changing effective atomic interactions and studying critical phenomena.     

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.     

Instabilities and vortex-lattice formation in rotating conventional and dipolar dilute-gas Bose-Einstein condensates

A theoretical study of vortex-lattice formation in atomic Bose-Einstein condensates confined by a rotating elliptical trap is presented. For the conventional case of purely s-wave interatomic interactions, this is done through a consideration of both hydrodynamic equations and time-dependent simulations of the Gross-Pitaevskii equation. We discriminate three distinct, experimentally testable regimes of instability: ripple, interbranch, and catastrophic. Additionally, we generalize the classical hydrodynamical approach to include long-range dipolar interactions, showing how the static solutions and their stability in the rotating frame are significantly altered. This enables us to examine the routes towards unstable dynamics, which, in analogy to conventional condensates, may lead to vortex-lattice formation.