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.     

Vortex-antivortex pair in a Bose-Einstein condensate

Presented is a type-II quantum algorithm for superfluid dynamics, used to numerically predict solutions of the GP equation for a complex scalar field (spinless bosons) in φ⁴ theory. The GP equation is a long wavelength effective field theory of a microscopic quantum lattice gas with nonlinear state reduction. The quantum lattice gas algorithm for modeling the dynamics of the one-body BEC state in 3+1 dimensions is presented. To demonstrate the method's strength as a computational physics tool, a difficult situation of filamentary singularities is simulated, the dynamics of solitary vortex-antivortex pairs, which are a basic building block of morphologies of quantum turbulence.     

Controlling chaos in a Bose-Einstein condensate loaded into a moving optical lattice potential

The spatial structure of a Bose-Einstein condensate loaded into an optical lattice potential is investigated, and spatially chaotic distributions of the condensates are revealed. By means of changing of the s-wave scattering length with a Feshbach resonance, the chaotic behavior can be well controlled to enter into periodicity. Numerical simulation shows that there are different periodic orbits according to different s-wave scattering lengths only if the maximal Lyapunov exponent of the system is negative. The text was submitted by the authors in English.     

Bose-Einstein condensate in a random potential

An optical speckle potential is used to investigate the static and dynamic properties of a Bose-Einstein condensate in the presence of disorder. With small levels of disorder, stripes are observed in the expanded density profile and strong damping of dipole and quadrupole oscillations is seen. Uncorrelated frequency shifts of the two modes are measured and are explained using a sum-rules approach and by the numerical solution of the Gross-Pitaevskii equation.     

Vortex rings and lieb modes in a cylindrical Bose-Einstein condensate

We present a calculation of a solitary wave propagating along a cylindrical Bose-Einstein trap. For sufficiently strong couplings of experimental interest, it is found to be a hybrid of a one-dimensional (1D) soliton and a three-dimensional vortex ring. The calculated energy-momentum dispersion exhibits characteristics similar to those of a mode proposed sometime ago by Lieb within a 1D model, as well as some rotonlike features.     

Vortex lattice of a Bose-Einstein condensate as a photonic band gap material

Photonic crystal behavior of a rotating Bose-Einstein condensate with a triangular vortex lattice is reviewed and a scheme for getting much wider band gaps is proposed. It is shown that photonic band gaps can be widened an order of magnitude more by using a Raman scheme of index enhancement, in comparison to previously considered upper level microwave scheme.     

Phase diagram for a Bose-Einstein condensate moving in an optical lattice

The stability of superfluid currents in a system of ultracold bosons was studied using a moving optical lattice. Superfluid currents in a very weak lattice become unstable when their momentum exceeds 0.5 recoil momentum. Superfluidity vanishes already for zero momentum as the lattice deep reaches the Mott insulator (MI) phase transition. We study the phase diagram for the disappearance of superfluidity as a function of momentum and lattice depth between these two limits. Our phase boundary extrapolates to the critical lattice depth for the superfluid-to-MI transition with 2% precision. When a one-dimensional gas was loaded into a moving optical lattice a sudden broadening of the transition between stable and unstable phases was observed.     

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     

Optically induced lensing effect on a Bose-Einstein condensate expanding in a moving lattice

We report the experimental observation of a lensing effect on a Bose-Einstein condensate expanding in a moving 1D optical lattice. The effect of the periodic potential can be described by an effective mass dependent on the condensate quasimomentum. By changing the velocity of the atoms in the frame of the optical lattice, we induce a focusing of the condensate along the lattice direction. The experimental results are compared with the numerical predictions of an effective 1D theoretical model. In addition, a precise band spectroscopy of the system is carried out by looking at the real-space propagation of the atomic wave packet in the optical lattice.     

Nonlinear dynamics of a spinor Bose-Einstein condensate in a double-well potential

We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.     

Dynamics of an interacting Bose-Einstein condensate in a three-well potential

We study the dynamics of an ultracold interacting Bose-Einstein gas confined in a one-dimensional potential composed of three symmetrical wells. We numerically solve the time-dependent Schrödinger equation of the N-particle Hamiltonian for N = 50, 150, 500, 1000. We demonstrate that the quantum phase transition from a superfluid (SF) to a Mott insulator (MI) phase in the three-well potential depends on the strength of the interactions among the particles, the total number of particles, and the confining potential in which the particles move. We discuss the appearance of population revivals as a function of time and find that, even in the case when the interaction strength among the particles is very small, its effect has the consequence that the system never returns to the initial condition. A stationary state for long times is observed in the SF phase, while the particle population in each well remains almost equal to the initial condition in the MI phase.     

双势阱中玻色-爱因斯坦凝聚的绝热隧穿

研究了玻色-爱因斯坦凝聚体在双势阱中随着能级差绝热循环变化而发生的绝热隧穿.发现当相互作用较强且初态选择为凝聚体全部置于较浅势阱时,演化过程破坏绝热定理,而演化结果有可能回到初态,也有可能不回到初态,取决于演化周期的选择;另外还发现演化过程表现出对初态选择的依赖,具有不对称的特征.利用能级图和相图,对上述现象给出了解释. 关键词： 玻色-爱因斯坦凝聚 Landau-Zener模型 绝热隧穿     

Chaos in a Bose-Einstein condensate

It is demonstrated that Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose-Einstein condensate driven by time-periodic harmonic or inverted-harmonic potential.A formally exact solution of the time-dependent Gross-Pitaevskii equation is constructed,which describes the matter shock waves with chaotic or periodic amplitudes and phases.     

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.     

Casimir-like force arising from quantum fluctuations in a slowly moving dilute Bose-Einstein condensate

We calculate a force due to zero-temperature quantum fluctuations on a stationary object in a moving superfluid flow. We model the object by a localized potential varying only in the flow direction and model the flow by a three-dimensional weakly interacting Bose-Einstein condensate at zero temperature. We show that this force exists for any arbitrarily small flow velocity and discuss the implications for the stability of superfluid flow.     

Bose-Einstein condensate in a harmonic trap with an eccentric dimple potential

We investigate Bose-Einstein condensation of noninteracting gases in a harmonic trap with an offcenter dimple potential. We specifically consider the case of a tight and deep dimple potential, which is modeled by a point interaction. This point interaction is represented by a Dirac delta function. The atomic density, chemical potential, critical temperature and condensate fraction, and the role of the relative depth and the position of the dimple potential are analyzed by performing numerical calculations.     

自旋轨道耦合的23Na自旋-1玻色-爱因斯坦凝聚体中的涡旋斑图的研究

利用阻尼映射Gross-Pitaevkii方程, 研究了二维体系中自旋轨道耦合的 ²³Na自旋-1 玻色-爱因斯坦凝聚体中的涡旋斑图, 探索自旋轨道耦合强度对涡旋斑图的影响. 研究发现, 较弱的自旋轨道耦合就可以完全破坏不考虑自旋轨道耦合情况下出现的周期性涡旋晶格; 在自旋轨道耦合较强的情况下, 各自旋态的涡旋易形成涡旋组, 它们绕凝聚体中心形成花瓣状涡旋斑图. 关键词： 玻色-爱因斯坦凝聚体 自旋 涡旋     

Anderson localization of a Bose-Einstein condensate in a 3D random potential

We study the effect of Anderson localization on the expansion of a Bose-Einstein condensate, released from a harmonic trap, in a 3D random potential. We use scaling arguments and the self-consistent theory of localization to show that the long-time behavior of the condensate density is controlled by a single parameter equal to the ratio of the mobility edge and the chemical potential of the condensate. We find that the two critical exponents of the localization transition determine the evolution of the condensate density in time and space.     

Dynamical properties of a condensate in a moving random potential

We study the dynamics of an inhomogeneous Bose-Einstein condensate subject to a one-dimensional harmonic trap and a moving random potential of finite extent. Above the critical velocity, a part of a condensate glues to the moving random potential with a consequent displacement of the condensate center-of-mass along the harmonic trap. We show that the center-of-mass turning point provides a direct measure of the average drag force acting on the condensate.     

Observation of dynamical instability for a Bose-Einstein condensate in a moving 1D optical lattice

We have experimentally studied the unstable dynamics of a harmonically trapped Bose-Einstein condensate loaded into a 1D moving optical lattice. The lifetime of the condensate in such a potential exhibits a dramatic dependence on the quasimomentum state. This is unambiguously attributed to the onset of dynamical instability, after a comparison with the predictions of the Gross-Pitaevskii theory. Deeply in the unstable region we observe the rapid appearance of complex structures in the atomic density profile, as a consequence of the condensate phase uniformity breakdown.