带调和势的超临界非线性Schrdinger方程的最佳门槛

考虑带调和势的超临界非线性Schroedinger方程，解决了该方程整体解和爆破解存在所依赖的初始条件的最佳分界门槛．通过构造两类强制变分问题和建立局部不变半流，运用势井方法和凹方法，获得了该方程在两个不同的空间中的整体解和爆破解的最佳门槛条件．     

Exact solutions for nonlinear Schr?dinger equation in phase space: applications to Bose－Einstein condensate

The stationary-state nonlinear Schr?dinger equation, which models the dilute-gas Bose－Einstein condensate, is introduced within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The exact solutions of equation are obtained in the phase space, by means of the wave-mechanics method. The eigenfunctions in position and momentum spaces are obtained through the ‘Fourier-like' projection transformation from the phase space eigenfunctions. The eigenfunction with a hypersecant part is discussed as an example.     

Microtraps and Atom Chips: Toolboxes for Cold Atom Physics

Magnetic microtraps and Atom Chips are safe, small-scale, reliable and flexible tools to prepare ultra-cold and degenerate atom clouds as sources for various atom-optical experiments. We present an overview of the possibilities of the devices and indicate how a microtrap can be used to prepare and launch a Bose-Einstein condensate for use in an atom clock or an interferometer.     

Interference of Two-Component Bose-Einstein Condensates with a Coupling Drive in Presence of Dissipation

The interference of the two-component Bose-Einstein condensates with a coupling drive in the presence of the dissipation is studied. We find that when the two-component Bose-Einstein condensates are initially in the coherent states, for the smaller dissipation parameters compared with that of the rf frequency ωrf, the interference intensity exhibits damply oscillation behavior, whereas when the dissipation parameters are larger than that of the ωrf, the interference intensity exhibits a fast attenuation behavior. As a comparison, the interference intensity in the absence of the dissipation is also studied. We conclude that the dissipation of the system can be evaluated by selecting the ωrf experimentally.     

简谐势阱中非理想气体玻色-爱因斯坦凝聚转变温度的数值研究

用数值计算的方法研究了简谐势阱中非理想气体的玻色 爱因斯坦凝聚情况.通过计算能级的分布，用图形的方式给出了考虑相互作用时，简谐势阱中体系转变温度相对无相互作用体系转变温度的变化趋势 对于存在排斥作用的体系，转变温度升高；对于存在吸引作用的体系，转变温度降低. 关键词： 玻色－爱因斯坦凝聚 相互作用 能级 转变温度     

Scattering effect of atoms through a Bose-Einstein condensate in an optical Lattice with a single defect

We study the transport of atoms across a localized Bose-Einstein condensate in an onedimensional optical lattice with a single defect. Our analytical and numerical results show that the defect as well as the nonlinear parameter can control the transmission of the atoms beam and the position of total reflection caused by Fano resonance. These interesting features may be a very useful basis for devising tunable atom filters or a button.     

Bose-Einstein condensation in spin-polarized atomic hydrogen: A new superfluid

We find that in the spin-polarized hydrogen, Bose condensation occurs for certain quantized values of the magnetic field. Once the field is fixed, sweeping of the radio-frequency results in nuclear magnetic resonance so that condensation and NMR occur simultaneously. We have found that nuclear self-induced transparency occurs. A new excitation designated by the present author as superboojum, which is a discontinuity in the hydrodynamic equations in spin-polarized hydrogen having finite nuclear as well as electronic spin is discovered.     

Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice

The accessibility of the critical parameters for the superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice is investigated. We determine the hopping matrix element J, the on-site interaction U, and hence the ratio J/U, in the harmonic oscillator wave function approximation. We show that for a range of realistic parameters the critical values of J/U, predicted by different methods for the Bose-Hubbard model in 2D, such as mean field theory and Monte Carlo simulations, are accessible in a 2D permanent magnetic lattice. The calculations are performed for a 2D permanent magnetic lattice created by two crossed arrays of parallel rectangular magnets plus a bias magnetic field.     

Superfluidity and Anderson localisation for a weakly interacting Bose gas in a quasiperiodic potential

Using exact diagonalisation and Density Matrix Renormalisation group (DMRG) approach we analyse the transition to a localised state of a weakly interacting quasi-1D Bose gas subjected to a quasiperiodic potential. The analysis is performed by calculating the superfluid fraction, density profile, momentum distribution and visibility for different periodicities of the second lattice and in the presence (or not) of a weak repulsive interaction. It is shown that the transition is sharper towards the maximally incommensurate ratio between the two lattice periodicities, and shifted to higher values of the second lattice strength by weak repulsive interactions. We also relate our results to recent experiments.     

Metastable state and macroscopic quantum tunneling of binary mixtures

We provide a mixing model to explore the metastable state and the macroscopic quantum tunneling (MQT) of binary mixtures. For , we first observe the two condensates form the symmetry-breaking state (SBS) and then suddenly transfer to the symmetry-preserving state (SPS) through the MQT. The SBS is shown to be the metastable state in our system. We find the MQT does not spontaneously arise. The inducement mechanism is the damping but not the excitations. The damping mechanism can also control the lifetime and the tunneling decay rate of the SBS. Finally, we further present the origin of these phenomena by examining the energy of the system.