Vortex Lattice Structures of a Bose-Einstein Condensate in a Rotating Lattice Potential

We study vortex lattice structures of a trapped Bose-Einstein condensate in a rotating lattice potential by numerically solving the time-dependent Gross-Pitaevskii equation. By rotating the lattice potential, we observe the transition from the Abrikosov vortex lattice to the pinned vortex lattice. We investigate the transition of the vortex lattice structure by changing conditions such as angular velocity, strength, and lattice constant of the rotating lattice potential.     

Dynamics of Vortex Lattice Formation in a Rotating Bose-Einstein Condensate with an Optical Lattice Potential

We study dynamics of quantized vortex lattice formation in a rotating Bose-Einstein condensate with a square blue-detuned optical lattice by solving the Gross-Pitaevskii equation. This dynamics depends on the depth of the optical lattice. Vortices tend to form a triangular lattice under the rotation, while an optical lattice likes to pin vortices at their peaks. Such a competition of two effects makes this system more interesting and complicated.     

Hydrodynamics of Superfluid Bose Gases in an Optical Lattice at Finite Temperatures

Starting from an effective action for the order parameter field, we derive a coupled set of generalized hydrodynamic equations for a Bose condensate in an optical lattice at finite temperatures. Using the linearized hydrodynamic equations, we study the microscopic mechanism of the Landau instability due to the collisional damping process between the condensate and noncondensate atoms. It is shown that the Landau criterion for the stability of a superfluid in a uniform system is modified due to the presence of the periodic optical lattice potential.     

The Condition for Existence of Complex Modes in Trapped Bose–Einstein Condensate with a Highly Quantized Vortex

We consider a trapped Bose–Einstein condensate with a highly quantized vortex. Pu et al. found numerically the parameter region in which complex eigenvalues arise. Recently, the splitting of a highly quantized vortex into two singly quantized vortices is observed in the experiment. We derive analytically the condition for the existence of complex eigenvalues by using the small coupling constant expansion and the two-mode approximation. We check that our results agree with those by Pu et al.     

Vortex Nucleation and Array Formation in a Rotating Bose-Einstein Condensate

We study the dynamics of vortex lattice formation of a rotating trapped Bose-Einstein condensate by numerically solving the two-dimensional Gross-Pitaevskii equation, and find that the condensate undergoes elliptic deformation, followed by unstable surface-mode excitations before forming a quantized vortex lattice. The dependence of the number of vortices on the rotation frequency is obtained.     

Vortex Lattice Dynamics in a Dilute Gas BEC

We study the dynamics of large vortex lattices in a dilute gas Bose–Einstein condensate. Rapidly rotating condensates are created that contain vortex lattices with up to 300 vortices. The condensates are held in a parabolic trapping potential, and rotation rates exceeding 99% of the radial trapping frequency are achieved. By locally suppressing the density while maintaining the phase singularities, we create vortex aggregates. To illustrate the underlying Coriolis force driven dynamics, oscillation frequencies of the vortex aggregate area are measured. A related technique also enables us to excite and directly image Tkachenko modes in a vortex lattice. These modes provide evidence for the shear strength that a vortex lattice in a superfluid can support.     

3-Dimensional Dynamics of Vortices in a rotating Bose-Einstein Condensate

No Heading We numerically integrate the 3-D time-dependent Gross-Pitaevskii equation suggested by Tsubota et al. [Phys.Rev.A, 65, 023603(2002)] to investigate dynamical transitions of the trapped Bose-Einstein condensate (BEC) from an initial non-vortex state to a steady vortex lattice state after the trigger of the rotation. We use the splitting-fourier method as a numerical scheme to perform stable 3-D numerical simulations with high computational efficiency. We present three stages of characteristic 3-D non-steady dynamics of vortices, i.e., the vortex penetration, the stochastic vortex wandering, the vortex lattice vibration, etc.PACS numbers: 03.75.Lm, 03.75.Kk     

Vortex Lattices in Rotating Bose-Einstein Condensate in an Optical Lattice: Analogy to Uniformly Frustrated Josephson-Junction Arrays

We investigate the effect of rotation for two-dimensional Josephson junction arrays consisting of atomic Bose-Einstein condensates trapped by both a harmonic trap and an optical lattice. This system is analogous to the superconducting Josephson junction array to which a transverse magnetic field is applied, being described by the uniformly frustrated XY model. The frustration parameter f, defined by the rotation frequency of the condensate and the lattice constant of the optical lattice, is an important parameter to determine the ground state. The numerical simulations of the Gross-Pitaevskii equation reveal that for f=1/2 the ground state possesses the checkerboard pattern of vortices, and for f<1/2 the vortex configuration is characterized by the staircase form.      

Splitting of a Multiply Quantized Vortex for a Bose-Einstein Condensate in an Optical Lattice

We study the splitting process of a multiply quantized vortex for a trapped highly oblate Bose-Einstein condensate in an optical lattice. Fourfold or sixfold splitting patterns are found in the dynamical evolution in square or triangular optical lattices, respectively. The relaxation time and angular momentum are also investigated to explore the properties of splitting. We find one singly quantized vortex or antivortex could be finally stabilized at the trap center.

     

Vortex Dynamics in Trapped Bose-Einstein Condensate

We perform numerical simulations of vortex motion in a trapped Bose-Einstein condensate by solving the two-dimensional Gross-Pitaevskii Equation in the presence of a simple phenomenological model of interaction between the condensate and the finite temperature thermal cloud. At zero temperature, the trajectories of a single, off-centred vortex precessing in the condensate, and of a vortex-antivortex pair orbiting within the trap, excite acoustic emission. At finite temperatures the vortices move to the edge of the condensate and vanish. By fitting the finite-temperature trajectories, we relate the phenomenological damping parameter to the friction coefficients α and α′, which are used to describe the interaction between quantised vortices and the normal fluid in superfluid helium.     

Self-Organization of Vortex Line Length Distribution in Dilute Quantum Turbulence

There has been an exponential growth of interest in scale-free structure of quantum turbulence in recent years. Recent studies revealed that the vortex length distribution (VLD), meaning the size distribution of the vortices, in decaying quantum turbulence at zero temperature obeys a power law. This power law is very important because it means that there is a kind of self-similarity in quantum turbulence during the decay. Unfortunately, however, there has been no practical study that answers the important question; why can the quantum turbulence acquire power law VLD? In this paper, we first propose that the nature of quantized vortices allows us to describe the decay of quantum turbulence with a simple model without loosing physical validity. This simple model well reproduces the observed power law and suggests that the emergence of power law VLD is a consequence of two mechanisms; Richardson cascade and dynamical scaling law of vortex dynamics.     

Vortices in a stirred Bose-Einstein condensate

Abstract

We stir with a focused laser beam a Bose-Einstein condensate of ⁸⁷Rb atoms confined in a magnetic trap. We observe the formation of a single vortex for a stirring frequency exceeding a critical value. At larger rotation frequencies we produce states of the condensate for which up to eleven vortices are simultaneously present. We present measurements of the decay of a vortex array once the stirring laser beam is removed.     

Direct observation of the interaction between vortices and dislocations in superconducting crystals by a cryo-Lorentz EM (interaction between vortices and dislocations)

Quantized magnetic flux lines (vortices) in a Nb foil were directly observed in different magnetic fields up to 200 G by a cryo-Lorentz electron microscope. The interaction of vortices with dislocations in the specimen was examined and clarified; edge-on dislocations weakly pin individual vortices at magnetic fields below 100 G. In higher magnetic fields the formation of a regular hexagonal vortex lattice started preferentially at in-plane dislocations. At 200 G the Abrikosov vortex lattice was formed with small domains, whose centre included the dislocations, showing their important role on the formation of the vortex lattice. For a NbTi foil no clear image of vortices could be seen, because the surface was rough due to the formation of fine grains and precipitates.     

High-power efficient multiple optical vortices in a single beam generated by a kinoform-type spiral phase plate

We propose using a solitary kinoform-type spiral phase plate structure to generate an array of vortices located in a single beam. Kinoform-type spiral surfaces allow each wavelength component of the phase modulation value to be wrapped back to its 2 pi equivalent for optical vortices of high charge. This allows the surface-relief profiles of high-charge vortices to be microfabricated with the same physical height as spiral phase plates of unity-charged optical vortices. The m-charged optical vortex obtained interacts with the inherent coherent background, which changes the propagation dynamics of the optical vortex and splits the initial m charge into /m/ unity-charged optical vortices within the same beam. Compared to a hologram, a multistart spiral phase plate is more efficient in the use of available spatial frequencies and beam energy and also is computationally less demanding. Furthermore, using microfabrication techniques will allow for greater achievable tolerances in terms of smaller feature sizes.     

Vortex Reconnection and Acoustic Emission by the Numerical Analysis of the Gross-Pitaevskii Equation

Reconnection of quantized vortices and concurrent acoustic emission are studied numerically by analyzing the Gross-Pitaevskii equation. Although vortex reconnection was studied earlier by Koplik and Levine, the present work first investigates in more detail how the singular vortex cores reconnect. Second, acoustic emission, i.e., the emission of the density waves of the condensate, is studied when two vortices annihilate or reconnect. The local drastic change of the condensate density is found to work as an acoustic source to emit the density waves. This phenomenon may be related to the vortex tangle decay observed at mK temperatures and the eddy viscosity which is thought to be an intrinsic dissipative mechanism in a vortex tangle.     

Landau and Dynamical Instabilities of Bose-Einstein Condensates in a Kronig-Penney Potential

We study elementary excitations of Bose-Einstein condensates in a one-dimensional periodic potential and discuss the stability of superfluid flow based on the Kronig-Penney model. We analytically solve the Bogoliubov equations and calculate the excitation spectrum. The Landau and dynamical instabilities occur in the first condensate band when the superfluid velocity exceeds certain critical values as in a sinusoidal potential. It is found that the onset of the Landau instability coincides with the point where the perfect transmission of low-energy excitations is forbidden, while the dynamical instability occurs when the effective mass is negative. The condensate band has a swallow-tail structure when the periodic potential is shallow compared to the mean-field energy. We find that the upper side of a swallow-tail is dynamically unstable although the excitation spectrum has a linear dispersion reflecting the positive effective mass.     

Stabilization and Pumping of Giant Vortices in Dilute Bose–Einstein Condensates

Recently, it was shown that giant vortices with arbitrarily large quantum numbers can possibly created in dilute Bose–Einstein condensates by cyclically pumping vorticity into the condensate. However, multiply quantized vortices are typically dynamically unstable in harmonically trapped nonrotated condensates, which poses a serious challenge to the vortex pump procedure. In this theoretical study, we investigate how the giant vortices can be stabilized by the application of a Gaussian potential peak along the vortex core. We find that achieving dynamical stability is feasible up to high quantum numbers. To demonstrate the efficiency of the stabilization method, we simulate the adiabatic creation of an unsplit 20-quantum vortex with the vortex pump.     

Temperature Dependence of Vortex Nucleation in Gaseous Bose-Einstein Condensates

The formation of quantized vortices in trapped, gaseous Bose-Einstein condensates is considered. The thermodynamic stability of vortex states and the essential role of the surface excitations as a route for vortex penetration into the condensate are discussed. Special focus is on finite-temperature effects of the vortex nucleation process. It is concluded that the critical angular frequencies for exciting surface modes with the relevant multipolarities yield, also at finite temperatures, the appropriate thresholds for the nucleation of vortices in dilute Bose-Einstein condensates, in fair agreement with the recent experiments.     

Three-dimensional Dammann vortex array with tunable topological charge

We describe a kind of true 3D array of focused vortices with tunable topological charge, called the 3D Dammann vortex array. This 3D Dammann vortex array is arranged into the structure of a true 3D lattice in the focal region of a focusing objective, and these focused vortices are located at each node of the 3D lattice. A scheme based on a Dammann vortex grating (DVG) and a mirror is proposed to provide a choice for changing the topological charge of the 3D Dammann vortex array. For experimental demonstration, a 5×5×5 Dammann vortex array is implemented by combining a 1×7 DVG, a 1×5 Dammann zone plate, and another 5×5 Dammann grating. The topological charge of this Dammann vortex array can be tuned (from -2 to +2 with an interval of +1) by moving and rotating the mirror to select different diffraction orders of the 1×7 DVG as the incident beam. Because of these attractive properties, this 3D Dammann vortex array should be of high interest for its potential applications in various areas, such as 3D simultaneous optical manipulation, 3D parallel vortex scanning microscope, and also parallel vortex information transmission.     

Shear instabilities of a vortex lattice in layered superconductors

We study possible structures of a vortex lattice in highly layered superconductors ( _c s) with the magnetic field parallel to the layers. When the magnetic field is large and the vortex lattice is dense enough, the shear modulus is exponentially small, and one can expect the vortex lattice to melt in between the layers and a vortex smectic to be formed. For low magnetic fields the vortices are far apart, and a triangular array becomes unstable with respect to the formation of several new types of vortex lattices.