Breakdown of time-dependent mean-field theory for a one-dimensional condensate of impenetrable bosons

We show that the time-dependent nonlinear Schrodinger equation of mean-field theory has limited utility for a one-dimensional condensate of impenetrable bosons. Mean-field theory with its associated order parameter predicts interference between split condensates that are recombined, whereas an exact many-body treatment shows minimal interference.     

Generation and dynamics of vortex lattices in coherent exciton-polariton fields

Vortex dynamics in coherent ensembles of exciton polaritons (condensates) is studied in the framework of the polarization-dependent Gross-Pitaevskii equation. Vortex lattices can be resonantly excited in the polariton field by the interference of three or more optical pumps. Vortex-antivortex pairs can also appear in polariton condensates due to scattering with disorder. The nonlinear vortex dynamics is characterized by interactions of vortex cores and vortex-antivortex recombination.     

Solutions of Two Kinds of Non-Isospectral Generalized Nonlinear Schrodinger Equation Related to Bose-Einstein Condensates

Two non-isospectral generalized nonlinear Schrodinger （ONLS） equations, which are two important models of nonlinear excitations of matter waves in Bose-Einstein condensates, are studied. Two novel transformations are constructed such that these two GNLS equations are transformed to the well-known nonlinear Schr6dinger （NLS） equation, which is an isospectral equation. Therefore, once one solution of the NLS equation is provided, we can immediately obtain one solution for two ONLS equations by these transformations. Thus it is unnecessary to solve these two non-isospectral GNLS equations directly. Soliton solutions and periodic solutions are obtained for them by two transformations from the corresponding solutions of the NLS equation, which are generated by Darboux transformation.     

Generating periodic interference in Bose–Einstein condensates

The interference between two condensates with repulsive interaction is investigated numerically by solving the onedimensional time-dependent Gross–Pitaevskii equation.The periodic interference pattern forms in two condensates,which are prepared in a double-well potential consisting of two truncated harmonic wells centered at different positions.Dark solitons are observed when two condensates overlap.Due to the existence of atom–atom interactions,atoms are transferred among the ground state and the excited states,which coincides with the condensate energy change.     

Localization in physical systems described by discrete nonlinear Schrodinger-type equations

Following a short introduction on localized modes in a model system, namely the discrete nonlinear Schrodinger equation, we present explicit results pertaining to three different physical systems described by similar equations. The applications range from the Raman scattering spectra of a complex electronic material through intrinsic localized vibrational modes, to the manifestation of an abrupt and irreversible delocalizing transition of Bose-Einstein condensates trapped in two-dimensional optical lattices, and to the instabilities of localized modes in coupled arrays of optical waveguides.     

Matter wave interference pattern in the collision of bright solitons

We investigate the dynamics of Bose–Einstein condensates in a quasi one-dimensional regime in a time-dependent trap and show analytically that it is possible to observe matter wave interference patterns in the intra-trap collision of two bright solitons by selectively tuning the trap frequency and scattering length.     

Averaging of nonlinearity-managed pulses

We consider the nonlinear Schrodinger equation with the nonlinearity management which describes Bose-Einstein condensates under Feshbach resonance. By using an averaging theory, we derive the Hamiltonian averaged equation and compare it with other averaging methods developed for this problem. The averaged equation is used for analytical approximations of nonlinearity-managed solitons.     

Dynamics of a bright soliton in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential

We present a family of exact solutions of the one-dimensional nonlinear Schro dinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background.     

Dynamics of Bright Solitons in Bose-Einstein Condensates with Complicated Potential

We present analytical solutions of the one-dimensional nonlinear Schrodinger equations of Bose-Einstein condensates in an expulsive parabolic background with a complex potential and gravitational field, by performing the Darboux transformation from a trivial seed solution. It is shown that under a safe range of parameter, the shape of bright soliton can be controlled well by adjusting the experimental parameter of the ratio of axial oscillation to radial oscillation and feeding condensates from a thermal cloud. The gravitational field can change the contrail of the bright soliton trains without changing their peak and width.     

Path integral approach to electron scattering in classical electromagnetic potential

As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential.     

强激光场中原子的束缚态和连续态对高次谐波的影响

利用基函数展开结合线性最小二乘法方法求解含时薛定谔方程,研究了一维原子在强激光场中产生高次谐波过程中,束缚态和连续态以及它们的干涉效应对高次谐波的影响.结果表明,低能的高次谐波是由束缚态束缚态之间的相互作用产生的,高能的高次谐波是由束缚态连续态之间的相互作用产生的,而截断频率后消失的高次谐波是由于束缚态束缚态与束缚态连续态之间存在干涉效应的结果 关键词： 线性最小二乘法 强激光场 高次谐波的产生     

Interference of Bose-Einstein condensates and entangled single-atom state in a spin-dependent optical lattice

We present a theoretical model to investigate the interference of an array of Bose-Einstein condensates loaded in a one-dimensional spin-dependent optical lattice, which is based on an assumption that for the atoms in the entangled single-atom state between the internal and the external degrees of freedom each atom interferes only with itself. Our theoretical results agree well with the interference patterns observed in a recent experiment by Mandel et al. [Phys. Rev. Lett. 91, 010407 (2003)]. In addition, an experimental suggestion of nonuniform phase distribution is proposed to test further our theoretical model and prediction. The present work shows that the entanglement of a single atom is sufficient for the interference of the condensates confined in a spin-dependent optical lattice and this interference is irrelevant with the phases of individual condensates, i.e., this interference arises only between each condensate and itself and there is no interference effect between two arbitrary different condensates.     

Dynamics of Bright/Dark Solitons in Bose--Einstein Condensates with Time-Dependent Scattering Length and External Potential

We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton＇s parameters （amplitude, width, and period） can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.     

Interference of an array of independent Bose-Einstein condensates

We have observed high-contrast matter wave interference between 30 Bose-Einstein condensates with uncorrelated phases. Interferences were observed after the independent condensates were released from a one-dimensional optical lattice and allowed to overlap. This phenomenon is explained with a simple theoretical model, which generalizes the analysis of the interference of two condensates.     

Bose-Einstein Condensates in a One-Dimensional Optical Lattice: from Superfluidity to Number-Squeezed States

We study the phase coherence property of Bose-Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza-Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.     

Absence of Localization in One-Dimensional Lattice with Off-Diagonal Nonlinearity Disorder

The time evolution of an initially localized mode in a one-dimensional lattice with off-diagonal nonlinearity disorder is studied by solving a modified nonlinear Schrodinger equation. Absence of localization is found when the nonlinearity parameter is beyond the selftrapping region for corresponding periodic httice. The propagation of electrons shows ballistic behavior even in the presence of disorder. When self-trapping occurs, the untrapped portion still escapes ballistically.     

Application of the homotopy analysis method for the Gross-Pitaevskii equation with a harmonic trap

<正>The Homotopy analysis method(HAM) is adopted to find the approximate analytical solutions of the GrossPitaevskii equation,a nonlinear Schrodinger equation is used in simulation of Bose-Einstein condensates trapped in a harmonic potential.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they fit very well with each other when the atomic interaction is weak.     

玻色爱因斯坦凝聚体一维轴向干涉中的非线性现象

利用含时的Ｇｒｏｓｓ－Ｐｉｔａｅｖｓｋｉｉ方程,研究了轴对称的高密度玻色爱因斯坦凝聚体在干涉过程中因原子间相互人用而产生的非线性现象。发现玻色爱因斯坦凝聚体的一维轴向干涉条纹的密度分布是一种驻波状结构。通过原子波之间非线性耦合相互作用,这种结构可以表现为物质波光栅,对其周期的原子波产生衍射现象。     

改进打靶法求解Gross-Pitaevskii方程及三个凝聚体的干涉

用改进的打靶法求解零温简谐势阱中中性原子玻色-爱因斯坦凝聚的一维Gross-Pitaevskii方程,给出不同非线性参数时凝聚体基态的本征值.用辛算法研究三个凝聚体在撤掉陷俘势后产生的干涉,和三个凝聚体处于同-陷俘势中的干涉及周期性演化,讨论不同的相对相位对凝聚体干涉的影响.     

玻色-爱因斯坦凝聚体间相互作用的动力学性质研究

采用辛算法数值求解一维含时Gross-Pitaevskii方程.数值模拟玻色爱因斯坦凝聚体的"Breathing"特征,研究撤掉简谐势阱时两个凝聚体相互作用产生的干涉现象及两个凝聚体相位差发生变化时凝聚体的动力学性质.