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Laser Physics

Formation and dynamics of vortices in a Bose–Einstein condensate with a moving impenetrable disk-shaped potential

Guangping Chen, Biao Dong, Lin-Xue Wang, Zhengwei Xie, Shougang Zhang

Published Aug 31, 2016• 0 citations
Publisher

Abstract

Abstract We consider a quasi-two-dimensional Bose–Einstein condensate with a moving impenetrable disk-shaped potential. By performing direct numerical simulations, we investigate the formation and dynamics of the vortices in the wake as a function of the moving velocity and the radius of the potential. For moderate moving velocity, we observe the formation of a bound vortex pair in the wake of the potential. Its shedding period and associated patterns depend on the radius of the potential, showing V-shaped, periodic, or complex wakes. More interestingly, at high velocity both the vortex pair and vortex dipole can be formed simultaneously. Furthermore, the activation time for vortex formation is investigated for different velocities. We also give an experimental protocol to observe these phenomena in future experiments.

DOI
10.1088/1054-660x/26/10/105502

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Abstract We consider a quasi-two-dimensional Bose–Einstein condensate with a moving impenetrable disk-shaped potential. By performing direct numerical simulations, we investigate the formation and dynamics of the vortices in the wake as a function of the moving velocity and the radius of the potential. For moderate moving velocity, we observe the formation of a bound vortex pair in the wake of the potential. Its shedding period and associated patterns depend on the radius of the potential, showing V-shaped, periodic, or complex wakes. More interestingly, at high velocity both the vortex pair and vortex dipole can be formed simultaneously. Furthermore, the activation time for vortex formation is investigated for different velocities. We also give an experimental protocol to observe these phenomena in future experiments.
We study the formation and dynamics of vortices in quasi two-dimensional dipolar Bose-Einstein condensates (BECs). We solve the time dependent two-dimensional Gross-Pitaevskii equation by using a combined split-step Crank-Nicolson (SSCN) and Fast Fourier-Transform (FFT) based numerical scheme and investigate the vortex dynamics in dipolar BECs trapped with harmonic and optical lattice potentials. The consequence of dipole-dipole interaction on vortex nucleation and number of vortices has been analysed. We observe that the breaking of symmetry due to anisotropic dipolar interaction enormously increase the speed of creation of vortices.
The dynamical behaviors of a dipole Bose-Einstein condensate (BEC), which is stirred by a circular moving Gaussian potential, are numerically investigated by using the mean-field theory. In this work, the atom is assumed to polarize along the z-axis. Firstly, the stationary state of the system is obtained by solving the quasi-two-dimensional Gross-Pitaevskki equation numerically under periodic boundary conditions. And then, taking the obtained ground state as the initial condition, the dynamic evolution of the dipole BEC system is studied by the time-splitting Fourier spectrum method. Four types of emissions, namely, the stable laminar flow, vortex dipole, Bénard–von Kármán (BvK) vortex street and irregular turbulence, are observed in the wake when the velocity and size of the Gaussian potential change gradually. When the velocity of the Gaussian potential reaches the critical velocity of vortex excitation, vortex pairs with opposite circulations alternately fall off from the surface of the Gaussian potential. Owing to the interaction between the vortex dipoles, the dipoles rotate around their own centers. Finally, a ring structure will be formed and exist in the wake stably for a long time. With the increase of the velocity of Gaussian potential, the period of dipoles shedding is also shortened. For the appropriate velocity and size of the Gaussian potential, the vortex pairs with the same circulations will periodically fall off from the Gaussian potential and stably distributed on the inner and outer rings, forming BvK vortex street. Our caculation reveals that the conditions for forming BvK vortex street when the dipole BEC is stirred with a circular moving potential are very restricted. When the velocity or size of the Gaussian potential continues to increase, the phenomenon of the periodic vortex pairs shedding in the wake of the Gaussian potential will disappear, and the shedding pattern of the dipole BEC becomes irregular. Using experimental parameters, the parameter ranges of different dipole interactions are obtained through numerical calculation. The influences of dipole interactions, velocity and size of the Gaussian potential on different emission are discussed. In the end, the physical mechanisms of different emissions are analyzed by calculating the drag force acting on Gaussian potential.
We study the response of a trapped Bose-Einstein condensate to a sudden turn on of a rotating drive by numerically solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by a quasiparticle projection method. In a quadrupolar resonant regime, which depends on the trap anisotropy, simple periodic oscillations in surface-mode populations disappear and the system exhibits stochastic dynamics. In the presence of the phenomenological dissipation, an initially irrotational condensate is found to undergo damped elliptic deformation followed by unstable surface ripple excitations, some of which develop into quantized vortices that eventually form a lattice. Recent experimental results on the vortex nucleation should be explained not only by the dynamical instability but also by the Landau instability; the latter is necessary for the vortices to penetrate into the condensate.
We study vortex dynamics in a trapped Bose-Einstein condensate with tunable two- and three-body interactions. The dynamics is governed by two-dimensional cubic-quintic Gross-Pitaevskii equation. A time-dependent variational method has been used to obtain critical rotational frequency and surface mode frequency analytically and are compared with numerical simulation results. An imaginary time propagation method and Crank-Nicolson scheme for discretization have been used for numerical simulation. The numerically calculated average value of the angular momentum per particle shows very clearly its dynamical relation with the time development of the vortex formation. The rotational frequency dependence of the variation of average value of the angular momentum per particle with time shows that vortices form much faster in time for higher rotational frequency. Similarly, the vortex forms much faster in time with an increase of the strength of the repulsive three-body interaction. The simulation of the vortex lattice formation in the condensate shows that the presence of the three-body interactions does not alter the vortex lattice pattern but it helps in the shape deformations of the condensate thereby leading to vortex lattice formation. Likewise, the three-body interactions enable the vortex lattice formation in Bose-Einstein condensates even with attractive two-body interactions and in purely quintic BEC.
Abstract The dynamical behaviors of a quasi-2D Bose–Einstein condensate (BEC) with three-body interactions through a moving obstacle potential are studied numerically. Various vortex structures are discovered under different strength of three-body interactions when the two-body interaction is attractive or repulsive. When the width and moving velocity of the obstacle potential reach critical value, periodic anti-symmetric double-row vortex pairs will be released alternately in BEC, and a Bénárd–von Kármán (BvK) vortex street will be formed eventually. We noticed that the BvK vortex street can be excited when the three-body interactions are taken into account even if the two-body interaction is attractive. The mean value of the distance between two vortex rows to the distance between two vortex pairs in the same row is about 0.2. It is slightly smaller than the stability condition 0.28 without considering the three-body interaction. The parameter regions of vortex patterns at different three-body interaction are determined. It is found that an appropriate value of three-body interaction with larger velocity and lesser width is favorable to the formation of BvK vortex street. In a pair of point vortices, the distance and angular velocity between them are nearly invariant while they rotate around their center. The internal rule of vortex pair are also analyzed by calculating the drag force acting on the obstacle potential. Finally, we proposed an experimental protocol to realize the vortex street in 87Rb BEC with three-body interactions.