Ground-state vortex structures of a rotating binary dipolar Bose–Einstein condensate confined in harmonic plus quartic potential

We consider a binary dipolar Bose–Einstein condensate confined in a rotating harmonic plus quartic potential trap.The ground-state vortex structures are numerically obtained as a function of the contact interactions and the dipole–dipole interaction in both slow and rapid rotation cases. The results show that the vortex configurations depend strongly on the strength of the contact interactions, the relative strength between dipolar and contact interactions, as well as on the orientation of the dipoles. A variety of exotic ground-state vortex structures, such as pentagonal and hexagon vortex lattice,square vortex lattice with a central vortex, annular vortex lines, and straight vortex lines, are observed by turning such controllable parameters. Our results deepen the understanding of effects of dipole–dipole interaction on the topological defects.     

Axis-symmetric Onsager clustered states of point vortices in a bounded domain

We study axis-symmetric Onsager clustered states of a neutral point vortex system confined to a two-dimensional disc. Our analysis is based on the mean field of bounded point vortices in the microcanonical ensemble. The clustered vortex states are specified by the inverse temperature β and the rotation frequency ω, which are the conjugate variables of energy E and angular momentum L,respectively. The formation of the axis-symmetric clustered vortex states(azimuthal angle independent) involves th...     

Hyperbolic Bending of Vortex Lines with Finite Number and Length in Rotating Trapped Bose-Einstein Condensates

The minimal energy configurations of hyperbolic bending vortex lines in the rotating trapped Bose-Einstein condensates are investigated by using a variational ansatz and numerical simulation. The theoretical calculation of the energy of the vortex lines as a function of the rotation frequency gives self-consistently vortex number, curvature and configuration. The numerical results show that bending is more stable than straight vortex line along the z-axis, and the vortex configuration in the xy-plane has a little expansion by increasing z.     

The effect of the Taylor-Grtler vortex on Reynolds stress transport in the rotating turbulent channel flow

We investigates the effect of Taylor-Grtler vortex on the Reynolds stress transport in the rotating turbulent channel flow by direct numerical simulation. The Taylor-Grtler vortex is detected by longitudinal average of velocity fluctuation in the channel and defined as TG fluctuation. It has been found that turbulent diffusion is significant in the Reynolds stress transportation at the suction side of rotating turbulent channel in contrast with the turbulent channel flow without rotation and Taylor-Grtler vortex plays an important role in the turbulent diffusion in Reynolds stress transport. The paper focuses on the low and moderate rotation number, but the effect of the rotation number on the Reynolds stress transport is also reported.     

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.     

Barrier or easy-flow channel: The role of grain boundary acting on vortex motion in type-Ⅱ superconductors

Grain boundaries(GBs),as extremely anisotropic pinning defects,have a strong impact on vortex motion in type-Ⅱsuperconductors,and further on the macro level dominates the superconductivity for example the critical current density.Many previous studies indicated that mostly GB plays the role of a strong barrier for vortex motion,while an easy-flow channel just under some certain conditions.In order to thoroughly make clear of the questions of what is exactly the role of GB on vortex motion and how it works,in this article we developed a large scale molecular dynamic model and revealed the action of GB on vortex motion in type-Ⅱ superconductors.The most significant finding is that the role of GB on vortex motion can be changeable from a barrier to an easy-flow channel,and which is intrinsically determined by the competition effect correlated with its action on vortex between in the GB and no-GB regions.Such the competition effect essentially depends on the attributes of both the GB(described by the GB strength and angle θ) and no-GB pining regions(by the relative disorder strength α_p/a_v).Specifically,for a YBa_2 Cu_3 O_(7-x)(YBCO) sample,to obtain a clear knowledge of vortex motion in GB region,we visualized the three typical trajectories of vortices during the three vortex movement stages.Further,in order to understand how GB results in the macro current-carrying property,corresponding to the current-voltage relation of the YBCO conductor,we obtained the average velocity v_y of vortices varying with their driving force,which is nearly identical with the previous observations.     

Behaviour of Rotating Bose-Einstein Condensates Under Shrinking

When the repulsive interaction strength between atoms decreases, the size of a rotating Bose-Einstein condensate will consequently shrink. We find that the rotational frequency will increase during the shrinking of condensate, which is a quantum mechanical analogy to ballet dancing. Compared to a non-rotating condensate, the size of a rotating BEC will eventually be saturated at a finite value when the interaction strength is gradually reduced. We also calculate the vortex dynamics induced by the atomic current, and discuss the difference of vortex dynamics in this case and that observed in a recent experiment carried out by the JILA group [Phys. Rev. Lett.90 (2003) 170405].     

Late-Stage Vortical Structures and Eddy Motions in a Transitional Boundary Layer

A high-order direct numerical simulation of flow transition over a flat-plate at a free stream Mach number 0.5 is carried out. Formation and development of three-dimensional vortical structures, typically shown as λ-vortices, hairpin vortices and ring-like vortices, are observed. Numerical results show that there is a strong downdraft motion of fluid excited by every ring-like vortex in the late-stage of the transition process. At two sides of the vortical structure centerline, the downdraft motions induced by the ring-like vortex and the rotating legs superimpose. This is responsible for the appearance of a high-speed streak associated with the positive spike observed in a previous investigation and the appearance of a high-shear layer in the near wall region.     

Spin–orbit-coupled spin-1 Bose–Einstein condensates confined in radially periodic potential

We investigate the ground states of spin-1 Bose–Einstein condensates (BECs) with spin–orbit coupling in a radiallyperiodic potential by numerically solving the coupled Gross–Pitaevskii equations. In the radially periodic potential, wefirst demonstrate that spin–orbit-coupled antiferromagnetic BECs support a multiring petal phase. Polar–core vortex canbe observed from phase profiles, which is manifested as circularly symmetric distribution. We further show that spin–orbitcoupling can induce multiring soliton structure in ferromagnetic BECs. It is confirmed especially that the wave-functionphase of the ring corresponding to uniform distribution satisfies the rotational symmetry, and the wave-function phase ofthe ring corresponding to partial splitting breaks the rotational symmetry. Adjusting the spin–orbit coupling strength cancontrol the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs.Finally, we discuss effects of spin-independent and spin-dependent interactions on the ground states.     

Parallel numerical simulations for quantized vortices in Bose--Einstein condensates

We employ the parallel computing technology to study numerically the three-dimensional structure of quantized vortices of Bose--Einstein condensates. For anisotropic cases, the bending process of vortices is described in detail by the decrease of Gross--Pitaevskii energy. A completely straight vortex and the steady and symmetrical multiple-vortex configurations are obtained. We analyse the effect of initial conditions and angular velocity on the number and shape of vortices.     

Vortex Dynamics of Rotating Dipolar Bose-Einstein Condensates in Synthetic Magnetic Field

In the framework of time-dependent two-dimensional Gross-Pitaevskii equation, we investigate the dynamics of vortex formation in rotating dipolar Bose-Einstein condensates in synthetic magnetic field (SMF) and compare with rotating frame (RF) method. The formation of vortices are calculated, considering effects of the rotational frequency, dipole strength, tilting angle and trap ratio. The results we found are that in SMF, the formation of steady state vortices is much slower than that in RF, and it is more difficult to add large angular momentum to the condensates than to do so in RF.     

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.

     

Exotic vortex structures of the dipolar Bose–Einstein condensates trapped in harmonic-like and toroidal potential

Based on the tunable intensity and waist of Gaussian laser, harmonic-like and toroidal potentials can be achieved and the ground-state properties of the dipolar Bose–Einstein condensate (BEC) trapped in such potentials are investigated. It is found that, in the harmonic-like potential, the singly and doubly quantized vortices can exist in the scale condensate and translate respectively into vortex pairs and triangular vortex lattice with increasing dipole–dipole interaction (DDI). Especially, the sandwich-like structure can be observed in the ground-state density profiles by tuning the direction and strength of DDI for some rotating frequency. In the toroidal potential, the competition between the inter-component interaction and DDI can induce the transition between immiscible and miscible states, and results in the structures of a doubly quantized vortex surrounded by a vortex ring. It is worth emphasizing that, with the increasing of DDI, the doubly quantized vortex in the harmonic-like potential becomes two singly quantized vortices, while in the toroidal potential it is no happen due to the presence of Gaussian barrier.     

Spontaneous Formation of Antiferromagnetic Vortex Lattice in a Fast Rotating BEC with Dipole Interactions

When a Bose-Einstein condensate is set to rotate,superfluid vortices will be formed,which finally condense into a vortex lattice as the rotation frequency further increases.We show that the dipole-dipole interactions renormalize the short-range interaction strength and result in a distinction between interactions of parallel-polarized atoms and interactions of antiparallel-polarized atoms.This effect may lead to a spontaneous breakdown of the rapidly rotating Bose condensate into a novel anti-ferromagnetic-like vortex lattice.The upward-polarized Bose condensate forms a vortex lattice,which is staggered against a downward-polarized vortex lattice.A phase diagram related to the coupling strength is obtained.     

Stability of giant vortices in quantum liquids

We show how giant vortices can be stabilized for strong external potentials in Bose-Einstein condensates. We illustrate the formation of these vortices thanks to the Ginzburg-Landau dissipative dynamics for two typical potentials in two spatial dimensions. The giant vortex stability is studied for the particular case of a rotating cylindrical hard wall. Due to axial symmetry the minimization of the perturbed energy is simplified into a one dimensional relaxation dynamics. Solving this 1D minimization problem, we observe that giant vortices are either never stable, or only stable in a finite frequency range. Finally we obtain the marginal curve for the minimum frequency needed to observe a giant vortex.     

Vortex states of a superconducting film from a magnetic dot array

Using Ginzburg-Landau theory, we find novel configurations of vortices in superconducting thin films subject to the magnetic field of a magnetic dot array, with dipole moments oriented perpendicular to the film. Sufficiently strong magnets cause the formation of vortex-antivortex pairs. In most cases, the vortices are confined to dot regions, while the antivortices can form a rich variety of lattice states. We propose an experiment in which the perpendicular component of the dot dipole moments can be tuned using an in-plane magnetic field. We show that in such an experiment the vortex-antivortex pair density shows broad plateaus as a function of the dipole strength. Many of the plateaus correspond to vortex configurations that break dot lattice symmetries. In some of these states, the vortex cores are strongly distorted. Possible experimental consequences are mentioned.     

Equilibrium vortex lattices of a binary rotating atomic Bose–Einstein condensate with unequal atomic masses

We perform a detailed numerical study of the equilibrium ground-state structures of a binary rotating Bose–Einstein condensate with unequal atomic masses. Our results show that the ground-state distribution and its related vortex configurations are complex events that differ markedly depending strongly on the strength of rotation frequency, as well as on the ratio of atomic masses. We also discuss the structures and radii of the clouds, the number and the size of the core region of the vortices, as a function of the rotation frequency, and of the ratio of atomic masses, and the analytical results agree well with our numerical simulations. This work may open an alternate way in the quantum control of the binary rotating quantum gases with unequal atomic masses.     

Vortices in a Rotating Spin-Orbit-Coupled Bose-Einstein Condensate under Extreme Elongation in a Harmonic Plus Quartic Trap

We consider the ground-state properties of a rotating spin-orbit-coupled Bose-Einstein condensate under extreme elongation in a harmonic plus quartic potential. The effects of spin-orbit coupling and rotation on the ground-state vortex structures are investigated. In the absence of spin-orbit coupling, new nucleated vortices gradually form vortex lines and annular vortex structures with the increase of the rotation frequency. In the presence of spin-orbit coupling, part of the vortices arrange in a line and form a stable vortex chain, and the remanent vortices coexist in pairs aside such vortex chain. More specially, the remanent vortices of each component repel each other and form vortex pair for isotropic spin-orbit coupling, while attract each other and locate in the same positions for anisotropic spin-orbit coupling.     

Observation of long-lived vortex aggregates in rapidly rotating Bose-Einstein condensates

We study the formation of large vortex aggregates in a rapidly rotating dilute-gas Bose-Einstein condensate. When we remove atoms from the rotating condensate with a tightly focused, resonant laser, the density can be locally suppressed, while fast circulation of a ring-shaped superflow around the area of suppressed density is maintained. Thus a giant vortex core comprising 7 to 60 phase singularities is formed. The giant core is only metastable, and it will refill with distinguishable single vortices after many rotation cycles. The surprisingly long lifetime of the core can be attributed to the influence of strong Coriolis forces in the condensate. In addition we have been able to follow the precession of off-center giant vortices for more than 20 cycles.