轴对称谐振势阱中玻色凝聚气体基态和单涡旋态解

对囚禁在轴对称谐振势阱中的玻色凝聚气体，提出一种新的试探波函数，运用Gross-Pitaevskii(G-P)平均场能量泛函和变分的方法，得到玻色凝聚气体基态和单涡旋态波函数的解析表达式，并计算出凝聚原子的平均能量、原子云轴向和径向尺度比，以及产生单涡旋态的临界角速度等重要物理量与凝聚原子数N之间的关系.其结果与Dalfovo等人直接数值求解G-P方程所得到的结果相一致. 关键词： 玻色凝聚气体 G-P泛函 波函数 谐振势阱     

Manifestations of the roton mode in dipolar Bose-Einstein condensates

We investigate the structure of trapped Bose-Einstein condensates (BECs) with long-range anisotropic dipolar interactions. We find that a small perturbation in the trapping potential can lead to dramatic changes in the condensate's density profile for sufficiently large dipolar interaction strengths and trap aspect ratios. By employing perturbation theory, we relate these oscillations to a previously identified "rotonlike" mode in dipolar BECs. The same physics is responsible for radial density oscillations in vortex states of dipolar BECs that have been predicted previously.     

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.     

Vortices in dipolar Bose–Einstein condensates in synthetic magnetic field

We study the formation of vortices in a dipolar Bose–Einstein condensate in a synthetic magnetic field by numerically solving the Gross–Pitaevskii equation. The formation process depends on the dipole strength, the rotating frequency, the potential geometry, and the orientation of the dipoles. We make an extensive comparison with vortices created by a rotating trap, especially focusing on the issues of the critical rotating frequency and the vortex number as a function of the rotating frequency. We observe that a higher rotating frequency is needed to generate a large number of vortices and the anisotropic interaction manifests itself as a perceptible difference in the vortex formation. Furthermore, a large dipole strength or aspect ratio also can increase the number of vortices effectively. In particular, we discuss the validity of the Feynman rule.     

Critical rotation of an anharmonically trapped Bose--Einstein condensate

We consider rotational motion of an interacting atomic Bose-Einstein condensate (BEC) with both two- and three-body interactions in a quadratic-plus-quartic and harmonic-plus-Gaussian trap. By using the variational method, the influence of the three-body interaction and the anharmonicity of the trap on the lowest energy surface mode excitation and the spontaneous shape deformation (responsible for the vortex formation) in a rotating BEC is discussed in detail. It is found that the repulsive three-body interaction helps the formation of the vortex and reduces the lowest energy surface mode frequency and the critical rotational frequency of the system. Moreover, the critical rotational frequency for the vortex formation in the harmonic-plus-Gaussian potential is lower than that in the quadratic-plus-quartic potential.     

幺正极限附近费米气体反常激发模式的涡旋

在幺正极限附近研究了处于旋转外势中费米气体的量子化涡旋动力学. 选取适当的试探波函数并利用含时变分法, 得到了小振幅涡旋运动方程及描述其反常激发模式的解. 详细讨论了在幺正极限附近的反常模式产生的条件. 结果显示系统囚禁外势的临界转动频率在幺正极限附近随粒子间相互作用参数的增加而变大, 而涡旋进动的周期则随着粒子间相互作用参数的增加而减小. 关键词： 费米气体 涡旋 幺正极限     

Vortex formation in a stirred bose-einstein condensate

Using a focused laser beam we stir a Bose-Einstein condensate of 87Rb confined in a magnetic trap and observe the formation of a vortex for a stirring frequency exceeding a critical value. At larger rotation frequencies we produce states of the condensate for which up to four vortices are simultaneously present. We have also measured the lifetime of the single vortex state after turning off the stirring laser beam.     

Diagnostics of spatial structure of vortex multiplets in a swirl flow

Results on investigation of vortex unstable breakdown are presented. The structure of vortex multiplets was visualized in a vertical cylindrical container made of transparent organic glass of the optic quality with the inner diameter of 288 mm and rotating upper lid. Visualization was performed for different heights of this cylinder. The working liquid was 80-percent water-glycerin mixture, and small air bubbles were used as the tracers. The lid was rotated with a constant angular velocity under the studied conditions, and air was accumulated in the zones of decreased pressure on axes of vortices. Visualization of flow structure for unstable swirl flows and cylinder aspect ratios from 3.2 to 5.5 allowed first identification of these regimes as multispiral breakdowns with formation of helical-like vortex duplets, triplets, and quadruplets.     

Intrinsic and extrinsic vortex nucleation mechanisms in the flow

We propose very general vortex nucleation mechanisms[1] analogous to a hydrodynamic instability and calculate associated critical velocity in agreement with experiments. The creation of vortices via extrinsic mechanism is driven by a formation of the surface vorticity sheet created by the flow, which reaches a critical size. Such a sheet screens an attraction of a half-vortex ring to the wall, the barrier for the vortex nucleation disappears and the vortex nucleation is started. In the intrinsic mechanism the creation of a big vortex ring, which transforms into the vortex, is driven by a fluctuative generation of small vortex rings.     

Intrinsic and extrinsic vortex nucleation mechanisms in the flow

We propose very general vortex nucleation mechanisms[1] analogous to a hydrodynamic instability and calculate associated critical velocity in agreement with experiments. The creation of vortices via extrinsic mechanism is driven by a formation of the surface vorticity sheet created by the flow, which reaches a critical size. Such a sheet screens an attraction of a half-vortex ring to the wall, the barrier for the vortex nucleation disappears and the vortex nucleation is started. In the intrinsic mechanism the creation of a big vortex ring, which transforms into the vortex, is driven by a fluctuative generation of small vortex rings. Work supported by NORDITA and Landau Institute     

Vortex states of rapidly rotating dilute Bose-Einstein condensates

We show that, in the Thomas-Fermi regime, the cores of vortices in rotating dilute Bose-Einstein condensates adjust in radius as the rotation velocity, Omega, grows, thus precluding a phase transition associated with core overlap at high vortex density. In both a harmonic trap and a rotating hard-walled bucket, the core size approaches a limiting fraction of the intervortex spacing. At large rotation speeds, a system confined in a bucket develops, within Thomas-Fermi, a hole along the rotation axis, and eventually makes a transition to a giant vortex state with all the vorticity contained in the hole.     

Ground state and vortex states of bosons in an anisotropic trap: A variational approach

We propose a simple variational form of the wave function to describe the ground state and vortex states of a weakly interacting Bose gas in an anisotropic trap. The proposed wave function is valid for a wide range of the particle numbers in the trap. It also works well in the case of attractive interaction between the atoms. Further, it provides an easy and fast method to calculate the physical quantities of interest. The results compare very well with those obtained by purely numerical techniques. Using our wave function we have been able to verify, for the first time, the predicted behaviour of the aspect ratio. Received 7 December 1998 and Received in final form 4 February 1999     

具有尺寸限制的点接触结构自旋极化电流驱动下磁涡旋的稳态振荡

选取具有尺寸限制的点接触结构作为研究对象,采用Thiele方程对模型中磁涡旋在自旋极化电流作用下的动力学行为进行计算.计算表明磁涡旋可以在一定的电流密度范围内稳定旋转,该稳定旋转可以存在的电流密度范围与点接触区的大小和纳米点的尺寸有关.当磁涡旋核作稳态旋转时,其所处的轨道半径以及旋转频率都随电流密度的增加而增加,旋转频率可调节的范围随点接触尺寸的增加快速减小.     

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.     

Creation of solitons and vortices by bragg reflection of Bose-Einstein condensates in an optical lattice

We study the dynamics of Bose-Einstein condensates in an optical lattice and harmonic trap. The condensates are set in motion by displacing the trap and initially follow simple semiclassical paths, shaped by the lowest energy band. Above a critical displacement, the condensate undergoes Bragg reflection. For high atom densities, the first Bragg reflection generates a train of solitons and vortices, which destabilize the condensate and trigger explosive expansion. At lower densities, soliton and vortex formation requires multiple Bragg reflections, and damps the center-of-mass motion.     

Dynamical instability of a condensate induced by a rotating thermal gas

We study surface modes of the condensate in the presence of a rotating thermal cloud in an axisymmetric trap. By considering collisions that transfer atoms between the condensate and the noncondensate, we find that m>0 modes, which rotate in the same sense as the thermal cloud, damp less strongly than m<0 modes, where m is the polarity of the excitation. We show that above a critical angular rotation frequency, equivalent to the Landau stability criterion, m>0 modes become dynamically unstable, leading to the possibility of vortex nucleation. We also generalize our stability analysis to treat the case where the stationary state of the condensate already possesses a single vortex.     

Acoustic-excited vortex shedding and acoustic nonlinearity at a rectangular slit with bias flow

The acoustical response of a slit with a mean bias flow is numerically studied. By means of a potential flow model based on the discrete vortex method and a spanwise-averaged three-dimensional Green?s function, both unsteady vortical flow and slit impedance are obtained in a unified theoretical framework. The numerical simulation focuses on the acoustic-excited vortex structures of the slit flow while neglecting the viscous damping effect. Three representative flow features are demonstrated, which are the destabilized jet flow, the rolling up of vortex sheets and formation of vortex pairs, and the reversal flow with alternating vortex shedding on both sides of the slit. These features are corresponding to low, moderate, and high sound amplitude, respectively. The acoustic behavior of the slit can be divided into linear, transition, and nonlinear regimes. During its evolution through the three regimes, the resistance exhibits a constant value, a slight decrease, and a significant increase with the increasing sound amplitude. Correspondingly, the reactance first remains constant and then shows a modest decrease as the sound amplitude increases. The nonlinear effect also causes the gradual decrease of the mean bias velocity in company with the marked increase of the amplitude of the fluctuating velocity in the slit. The mean bias velocity decreases to about 80 percent of its linear value at the transition point where reversal flow begins to occur, and further decreases to only 10 percent in the highly nonlinear region. The slit impedance is also presented as a function of frequency and for different aspect ratios. And the effects of frequency and slit geometry are discussed.     

Pinning effects on the vortex critical velocity in type-II superconducting thin films

We study the influence of artificial pinning centers on the vortex critical velocity in Al thin films deposited on top of a periodic array of Permalloy (FeNi) square rings. We demonstrate that the field dependence of the flux flow velocity strongly depends on the particular magnetic state of the rings. In particular, we find that, even when the rings are in a flux closure state, i.e. with little stray field, the vortex critical velocity shows a non-monotonic magnetic field dependence. This behaviour is in sharp contrast with the results obtained in a reference plain film, with no rings underneath. A comparison with the intrinsic strong pinning Nb films previously studied, suggests an interpretation in terms of a channel-like motion of vortices, here induced by the artificial pinning structure.     

Flux cloning in Josephson transmission lines

We describe a novel effect related to the controlled birth of a single Josephson vortex. In this phenomenon, the vortex is created in a Josephson transmission line at a T-shaped junction. The "baby" vortex arises at the moment when a "mother" vortex propagating in the adjacent transmission line passes the T-shaped junction. In order to give birth to a new vortex, the mother vortex must have enough kinetic energy. Its motion can also be supported by an externally applied driving current. We determine the critical velocity and the critical driving current for the creation of the baby vortices and briefly discuss the potential applications of the found effect.     

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.