Critical trap aspect ratios for dipolar BEC

We show that there exists critical trap aspect ratios for a trapped Bose-Einstein condensate with dipole-dipole interactions. We discuss the role of critical trap aspect ratios on both the critical angular velocity above which a vortex is energetically favorable and the precession velocity of an off-axis vortex.     

Vortex dynamics in Bose-Einstein condensates: Numerical calculations

We numerically study properties of the dynamics of vortices in nonrotating Bose-Einstein condensates in the Thomas-Fermi regime. On the one hand, we compute the vortex energy as a function of its position and we predict, using the expression of the Magnus force, the vortex precession velocity. On the other hand, we calculate the temporal evolution of the vortex-state and test the accuracy of the previous prediction. We also investigate the validity of analytical formulae of this velocity involving the healing length. In addition, we analyze the velocity field and the angular momentum and we compare them to available analytical expressions.     

Phase separation and vortex states in the binary mixture of Bose-Einstein condensates

The phase separation and vortex states in a two-component Bose-Einstein condensate consisting of |F = 1, m _f = 1〉 and |2, 1〉 internal spin states of ⁸⁷Rb atoms are considered in the framework of the Thomas-Fermi approximation. It is shown that in the nonrotating system, the atoms in the state |1, ?1〉 form a shell around the atoms in the state |2, 1〉. The critical angular velocity for each state is calculated. These velocities depend drastically on the relative concentrations of the components, the critical angular velocity of the outer component being less than the angular velocity of the inner one. It is shown that the atoms in the |1, ?1〉 state can form a rotating ring around the resting core of the atoms in the |2, 1〉 state.     

环形势阱中旋转玻色爱因斯坦凝聚体的基态

应用托马斯-费米近似和虚时演化数值方法研究环形势阱中旋转玻色爱因斯坦凝聚体的基态密度分布.当增加其旋转角频率,或者增加环形势阱的宽度及相应的中心高度,凝聚体基态密度分布均从涡旋晶格相转变为巨涡旋相.当旋转角频率为零时,增加环形势阱的宽度及相应的中心高度,凝聚体基态密度分布从一个圆盘变为圆环.解析结果与数值结果相互吻合.     

Explanation of critical angular velocities of the vortex formation in a stirred Bose-Einstein condensate

The problem of explaining the critical angular velocity Ω_c when the formation of a vortex in the stirred Bose-Einstein condensate becomes energetically possible is considered in the framework of the variational approach. The origin of smallness of the calculated Ω_c in comparison with the measured values, which takes place for a pure quantum state with the unit angular momentum per condensed particle, is uncovered. The agreement with the measured Ω_c is achieved upon admitting a small admixture of the zero angular-momentum state in the wave function of the one-vortex quantum state prepared after stirring. A portion of this admixture amounts to 1–13% of the total condensed atoms. A possible test of this hypothesis is proposed.     

转动冷原子研究的前沿介绍

环流的宏观量子化是超流体最引人瞩目的性质之一．1995年玻色一爱因斯坦凝聚的实现为超流提供了一个新的研究对象，使得人们可以对转动的超流体进行深入的研究．实验上在BEC中产生了涡旋激发，并进一步观测到了涡旋晶格．理论研究表明当冷原子的转速进一步增大，涡旋品格会融解成一种新的强关联系统——量子霍尔液体．文章主要介绍近年在转动冷原子方向上理论和实验的进展．     

Oscillations of a bose-einstein condensate rotating in a harmonic plus quartic trap

We study the normal modes of a two-dimensional rotating Bose-Einstein condensate confined in a quadratic plus quartic trap. Hydrodynamic theory and sum rules are used to derive analytical predictions for the collective frequencies in the limit of high angular velocities Omega where the vortex lattice produced by the rotation exhibits an annular structure. We predict a class of excitations with frequency sqrt[6]Omega in the rotating frame, irrespective of the mode multipolarity m, as well as a class of low energy modes with frequency proportional to |m|/Omega. The predictions are in good agreement with results of numerical simulations based on the 2D Gross-Pitaevskii equation. The same analysis is also carried out at even higher angular velocities, where the system enters the giant vortex regime.     

推广的Gross-Pitaevskii理论中的涡旋问题(英文)

利用推广 Gross- Pitaevskii方程 ,分别研究了 (2 +1 )维时空和 3维空间的 Bose- Einstein凝聚体中涡旋的拓扑结构 .这一推广的方程能够被用于非均匀并且高度非线形的 Bose- Einstein凝聚系统 .利用Φ映射拓扑流理论 ,给出了基于序参数的涡旋速度场,以及该速度场的拓扑结构 .最后 ,仔细地探讨了这两种 Bose- Einstein系统中涡旋的各种分支条件.We studied the topological structure of vortex in the Bose-Einstein condensation with a generalized Gross-Pitaevskii equation in (2+1)-dimensional space-time and 3-dimensional space, respectively. Such equation can be used in discussing Bose-Einstein condensates in heterogeneous and highly nonlinear systems. An explicit expression for the vortex velocity field as a function of the order parameter field is derived in terms of the Φ -mapping theory, and the topological structure of ...     

Dissipative flow and vortex shedding in the Painlevé boundary layer of a Bose-Einstein condensate

This paper addresses the drag force and formation of vortices in the boundary layer of a Bose-Einstein condensate stirred by a laser beam following the experiments of Phys. Rev. Lett. 83, 2502 (1999)]. We make our analysis in the frame moving at constant speed where the beam is fixed. We find that there is always a drag around the laser beam. We also analyze the mechanism of vortex nucleation. At low velocity, there are no vortices and the drag has its origin in a wakelike phenomenon: This is a particularity of trapped systems since the density gets small in an extended region. The shedding of vortices starts only at a threshold velocity and is responsible for a large increase in drag. This critical velocity for vortex nucleation is lower than the critical velocity computed for the corresponding 2D problem at the center of the cloud.     

Effects of Higher Order Interaction on Vortex Formation in Bose-Einstein Condensates

We consider theoretically the formation of vortex in rotating Bose-Einstein condensates (BECs) with higher order interaction (HOI). Our results are obtained from the twodimensional Gross-Pitaevskii equation. As the first step, for the certain number vortices, we discuss the ground state properties and show that the critical rotation frequency for HOI is smaller than those without HOI. As the increasing of HOI strength, the critical rotation frequency decreases. In addition, we verify that the Feynman rule is meet well. Moreover, we study the vortex dynamics.Numerical results indicate that the angular momentum remains almost unchanged irrespective of the HOI strength. The time taken for the nucleation of vortices pays less for strong HOI. These results suggest that the HOI is favorable to rotate the condensate, and this mechanism is useful to control the vortex number in BECs.

     

Subcritical dissipation in three-dimensional superflows

Three-dimensional (3D) superflows past a circular cylinder are studied by numerically integrating the nonlinear Schrodinger equation. 3D initial data are built from the two-dimensional (2D) stationary vortex nucleation solutions. Quasistationary half-ring vortices, pinned at the sides of the cylinder, are generated after a short time. On a longer time scale, either 3D vortex stretching induces dissipation and drag, or the vortex is absorbed by the cylinder. The corresponding 3D critical velocity is found to be well below the 2D one. The implications for experiments in Bose-Einstein condensed gas and low-temperature helium are discussed.     

Vortex pair excitation in a Bose-Einstein condensate by moving potential barriers

The subsonic motion regime of a potential barrier in a Bose-Einstein condensate is considered. It is characterized by a critical velocity above which vortex pairs appear with opposite topological charges (“vortex-antivortex” pairs). The theoretical picture developed is confirmed by the results of numerical simulations within the framework of the Gross-Pitaevskii equation.     

Experimental observation of a superfluid gyroscope in a dilute Bose-Einstein condensate

We have observed a three-dimensional gyroscopic effect associated with a vortex in a dilute Bose-Einstein condensed gas. A condensate with a vortex possesses a single quantum of circulation, and this causes the plane of oscillation of the scissors mode to precess around the vortex line. We have measured the precession rate of the scissors oscillation. From this we deduced the angular momentum associated with the vortex line and found a value close to Planck's over 2pi per particle, as predicted for a superfluid.     

Dark Matter as a Cosmic Bose-Einstein Condensate and Possible Superfluid

Dark matter arising from spontaneous symmetry breaking of a neutral scalar field coupled to gravity comprises ultra low mass bosons with a Bose-Einstein condensation temperature far above the present background temperature. Assuming galactic halos to consist of a Bose-Einstein condensate of astronomical extent, we calculate the condensate coherence length, transition temperatures, mass distribution, and orbital velocity curves, and deduce the particle mass and number density from the observed rotation curves for the Andromeda and Triangulum galaxies. We also consider the possibility of superfluid behaviour in the halos of rotating galaxies, and estimate the critical angular frequency and line density for formation of quantised vortices.     

谐振子势与高斯势联合势阱中玻色爱因斯坦凝聚体的巨涡旋态

研究谐振子势与高斯势联合势阱中玻色爱因斯坦凝聚体的基态。发现凝聚体形成巨涡旋时,其涡旋个数等于平均角动量,且凝聚体密度分布和角动量密度分布相同,进而得到凝聚体形成巨涡旋时所处基态是角动量的本征态。发现势阱从各向同性的环形势阱逐渐变为各向异性的环形势阱的过程中,凝聚体的平均角动量与涡旋个数之比先由1平缓下降,然后迅速下降,最后保持在0.5附近。同时给出凝聚体密度分布和角动量分布的特征,并作出相应解释。     

Dynamics of rotating two-component Bose-Einstein condensates and its efficient computation

In this paper, we investigate the dynamics of rotating two-component Bose-Einstein condensates (BEC) based on the coupled Gross-Pitaevskii equations (CGPEs) with an angular momentum rotation term and an external driving field, and propose an efficient and accurate method for numerical simulations. We prove the conservation of the angular momentum expectation, derive the dynamic laws for the density of each component and condensate widths, and analyze the dynamics of a stationary state with its center shifted from the trap center. By formulating the CGPEs in either 2D (two-dimensional) polar coordinate or 3D cylindrical coordinate system, the angular momentum rotation term becomes a term with constant coefficients. This allows us to develop an efficient time-splitting method which is time reversible, time transverse invariant, unconditionally stable, efficient and accurate for the problem. Moreover, it conserves the total position density in the discretized level. The numerical method is applied to verify our analytical results and study the dynamics of quantized vortex lattices in rotating two-component BEC with/without an external driving field.     

Thermal fluctuations of vortex matter in trapped bose-einstein condensates

We perform Monte Carlo studies of vortices in three dimensions in a cylindrical confinement, with uniform and nonuniform density. The former is relevant to rotating 4He; the latter is relevant to a rotating trapped Bose-Einstein condensate. In the former case, we find dominant angular thermal vortex fluctuations close to the cylinder wall. For the latter case, a novel effect is that at low temperatures the vortex solid close to the center of the trap crosses directly over to a tensionless vortex tangle near the edge of the trap. At higher temperatures an intermediate tensionful vortex liquid located between the vortex solid and the vortex tangle may exist.     

Influence of global features of a Bose-Einstein condensate on the vortex velocity

We study the way in which the geometry of the trapping potential affects the vortex velocity in a Bose-Einstein condensate confined by a toroidal trap. We calculate the vortex precession velocity through a simple relationship between such a velocity and the gradient of the numerically obtained vortex energy. We observe that our results correspond very closely to the velocity calculated through time evolution simulations. However, we find that the estimates derived from available velocity field formulas present appreciable differences. To resolve such discrepancies, we further study the induced velocity field, analyzing the effect of global features of the condensate on such a field and on the precession velocity.     

Quantized rotation of atoms from photons with orbital angular momentum

We demonstrate the coherent transfer of the orbital angular momentum of a photon to an atom in quantized units of variant Planck's over 2pi, using a 2-photon stimulated Raman process with Laguerre-Gaussian beams to generate an atomic vortex state in a Bose-Einstein condensate of sodium atoms. We show that the process is coherent by creating superpositions of different vortex states, where the relative phase between the states is determined by the relative phases of the optical fields. Furthermore, we create vortices of charge 2 by transferring to each atom the orbital angular momentum of two photons.     

Angular dependence of the transverse and vortex modesin magnetic nanotubes

The angular dependence of the transverse and vortex modes in a magnetic nanotube is investigated as a function of the tube geometry, by means of analytical calculations and numerical simulations. A critical radius defining the transition between vortex and transverse reversal modes is determined, leading to low or high coercivity modes just by varying the direction of the external field, in a fixed nanotube.