Anderson localization of a spin-orbit coupled Bose-Einstein condensate in disorder potential

We present numerical results of a one-dimensional spin-orbit coupled Bose-Einstein condensate expanding in a speckle disorder potential by employing the Gross-Pitaevskii equation. Localization properties of a spin-orbit coupled Bose-Einstein condensate in zero-momentum phase, magnetic phase and stripe phase are studied. It is found that the localizing behavior in the zero-momentum phase is similar to the normal Bose-Einstein condensate. Moreover, in both magnetic phase and stripe phase, the localization length changes non-monotonically as the fitting interval increases. In magnetic phases, the Bose-Einstein condensate will experience spin relaxation in disorder potential.     

Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide

We investigate the one-dimensional expansion of a Bose-Einstein condensate in an optical guide in the presence of a random potential created with optical speckles. With the speckle the expansion of the condensate is strongly inhibited. A detailed investigation has been carried out varying the experimental conditions and checking the expansion when a single optical defect is present. The experimental results are in good agreement with numerical calculations based on the Gross-Pitaevskii equation.     

Internal modes of solitons in a Bose-Einstein condensate

A modified Gross-Pitaevskii equation for a Bose-Einstein condensate with nonlocal interaction between atoms is used to analyze and calculate the characteristics of internal modes of bright solitons (eigen-modes of small perturbations of the condensate). The spectra of even and odd internal modes are found for one-and two-dimensional solitons, and the rate constant characterizing nonlinear internal-mode damping is determined. The possibility of experimental verification of the results is discussed.     

Spatially periodic structures of an atomic Bose-Einstein condensate

The conditions providing the formation of periodic vortex lattices of an interference nature in an atomic Bose-Einstein condensate (i.e., in the absence of rotation of the condensate) are determined. Spatially periodic exact solutions of the nonlocal nonlinear Schrödinger equation (the generalized Gross-Pitaevskii equation) that describes the Bose-Einstein condensate of a dilute gas of alkali metal atoms with due regard for the nonlocality of interatomic interactions are obtained in the form of a set of two or three plane waves. It is shown that periodic vortex lattices can be produced in interference experiments with a Bose-Einstein condensate of a dilute gas of alkali metal atoms.     

Oscillations of a Bose-Einstein condensate in a rapidly contracting circular box

A Bose-Einstein condensate will evolve almost adiabatically if the number of atoms is large enough, even though the trap parameters may be changing rapidly. We demonstrate this by examining a Bose-Einstein condensate in a two-dimensional rapidly contracting circular box. We show that as a result of the contraction the condensate will oscillate about the instantaneous ground state. These oscillations will be small though when the number of atoms is large. Approximate analytic expressions are found for the evolving condensate wavefunction, both before and after the contraction has begun.     

Structure of vortex shedding past potential barriers moving in a Bose-Einstein condensate

The problem of excitation of a homogeneous Bose-Einstein condensate by axially symmetric potential barriers moving with respect to the condensate with both supersonic and subsonic velocities is considered in terms of the Gross-Pitaevskii equation. The specific features of the structure of the vortex shedding past the barriers are analyzed for both regimes of motion.     

Bragg spectroscopy of a strongly interacting 85Rb Bose-Einstein condensate

We report on measurements of the excitation spectrum of a strongly interacting Bose-Einstein condensate. A magnetic-field Feshbach resonance is used to tune atom-atom interactions in the condensate and to reach a regime where quantum depletion and beyond mean-field corrections to the condensate chemical potential are significant. We use two-photon Bragg spectroscopy to probe the condensate excitation spectrum; our results demonstrate the onset of beyond mean-field effects in a gaseous Bose-Einstein condensate.     

Excitations in a nonequilibrium Bose-Einstein condensate of exciton polaritons

We develop a mean-field theory of the dynamics of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity. The spectrum of elementary excitations around the stationary state is analytically studied by means of a generalized Gross-Pitaevskii equation. A diffusive behavior of the Goldstone mode is found in the spatially homogeneous case and new features are predicted for the Josephson effect in a two-well geometry.     

Dynamical properties of a rotating Bose-Einstein condensate

Within a variational approach to solving the Gross-Pitaevskii equation we investigate dynamical properties of a rotating Bose-Einstein condensate confined in an anharmonic trap. In particular, we calculate the eigenfrequencies of low-energy excitations out of the equilibrium state and the aspect ratio of the condensate widths during the free expansion.     

Theory of Bose-Einstein condensation of light in a microcavity

A theory of Bose-Einstein condensation (BEC) of light in a dye microcavity is developed. The photon polarization degeneracy and the interaction between dye molecules and photons in all of the cavity modes are taken into account. The theory goes beyond the grand canonical approximation and allows one to determine the statistical properties of the photon gas for all numbers of dye molecules and photons at all temperatures, thus describing the microscopic, mesoscopic, and macroscopic light BEC from a general perspective. A universal relation between the degrees of second-order coherence for the photon condensate and the polarized photon condensate is obtained. The photon Bose-Einstein condensate can be used as a new source of nonclassical light.     

偶极相互作用对自旋轨道耦合自旋-1凝聚体中磁畴分布的影响

研究准一维简谐势阱中存在自旋轨道耦合（SOC）的自旋-1偶极玻色-爱因斯坦凝聚体,数值求解旋量Gross-Pitaevskii方程,给出磁畴的分布。计算结果表明：磁畴结构与偶极-偶极相互作用（DDIs）密切相关,随着自旋轨道耦合强度和磁化强度的增强,原来的空间对称分布被破坏,随之出现新的分布模式。     

Semiclassical theory of superradiant scattering from a Bose-Einstein condensate

A semiclassical theory of superradiant scattering of light from a Bose-Einstein condensate of a dilute atomic gas is proposed. Choosing atomic states with definite values of the momenta as a basis, we derive a nonlinear Schrödinger equation. Its solutions describe the evolution of the scattered light intensity and of the populations of the coherent atomic states with different recoil momenta.     

Oblique dark solitons in supersonic flow of a Bose-Einstein condensate

In the framework of the Gross-Pitaevskii mean field approach, it is shown that the supersonic flow of a Bose-Einstein condensate can support a new type of pattern--an oblique dark soliton. The corresponding exact solution of the Gross-Pitaevskii equation is obtained. It is demonstrated by numerical simulations that oblique solitons can be generated by an obstacle inserted into the flow.     

Vortex formation in a slowly rotating Bose-Einstein condensate confined in a harmonic-plus-Gaussian laser trap

Motivated by the recent experiment at ENS [V. Bretin, S. Stock, Y. Seurin and, J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004)], we study a rotating (non-)interacting atomic Bose-Einstein condensate confined in a harmonic-plus-Gaussian laser trap potential. By adjusting the amplitude of the Gaussian laser potential, one can make quadratic-plus-quartic potential, purely quartic potential, and quartic-minus-quadratic potential. We show that an interacting Bose-Einstein condensate confined in a harmonic-plus-Gaussian laser trap breaks the rotational symmetry of the Hamiltonian when rotational frequency is greater than one-half of the lowest energy surface mode frequency. We also show that by increasing the amplitude of the Gaussian laser trap, a vortex appears in a slowly rotating Bose-Einstein condensate. Moreover, one can also create a vortex in a slowly rotating non-interacting Bose-Einstein condensate confined in harmonic-plus-Gaussian laser potential.Received: 24 June 2004, Published online: 24 August 2004PACS: 03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations - 05.30.Jp Boson systems     

二维玻色-爱因斯坦凝聚中孤立波的调制不稳定性

研究了盘状势阱中二维玻色-爱因斯坦凝聚(BEC)的孤立波. 在平均场理论下, 由BEC所满足的Gross-Pitaevkii方程出发导出了二维BEC所满足的非线性Schrödinger方程. 从该方程出发, 研究单组分常振幅二维BEC(单组分常振幅 BEC)的调制不稳定性, 得到了该系统相应的增长率. 关键词： 孤子 不稳定性 玻色-爱因斯坦凝聚     

Complex chemical potential: signature of decay in a bose-einstein condensate

We explore the zero-temperature statics of an atomic Bose-Einstein condensate in which a Feshbach resonance creates a coupling to a second condensate component of quasibound molecules. Using a variational procedure to find the equation of state, the appearance of this binding is manifest in a collapsing ground state, where only the molecular condensate is present up to some critical density. Further, an excited state is seen to reproduce the usual low-density atomic condensate behavior in this system, but the molecular component is found to produce a coherent, many-body decay, quantified by the imaginary part of the chemical potential. Most importantly, the unique decay rate dependencies on density (approximately rho (3/2)) and on scattering length (approximately (5/2)) can be measured in experimental tests of this result.     

玻色-爱因斯坦凝聚体干涉现象的数值模拟

采用含时非线性薛定谔方程的数值解法模拟了两种情况下玻色-爱因斯坦凝聚体的演化.一种是在初始状态中有两个包含粒子数差别很大、在空间上可区分的玻色-爱因斯坦凝聚体的情况;另一种是一个玻色-爱因斯坦凝聚体被外力一分为二后在自由空间及约束势阱中继续演化的情况. 关键词：     

THE GROWTH RATE AND STATISTICAL FLUCTUATION OF BOSE-EINSTEIN CONDENSATE FORMATION

Using the generating function method to solve the master equation of Bose-Einstein condensate and to evaluate the growth rate, statistical fluctuation of condensate atoms, we find out that there is a plateau in the growth rate curve and a super-Poisson distribution observed.