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arXiv:1101.2052 · Physical Review A

Nonlinear dynamics in a trapped atomic Bose-Einstein condensate induced by an oscillating Gaussian potential

Kazuya Fujimoto, Makoto Tsubota

Published May 6, 2011• 38 citations

Abstract

We consider a trapped atomic Bose-Einstein condensate penetrated by a repulsive Gaussian potential and theoretically investigate the dynamics induced by oscillating the Gaussian potential. Our study is based on the numerical calculation of the two-dimensional Gross-Pitaevskii equation. Our calculation reveals the dependence of the characteristic behavior of the condensate on the amplitude and frequency of the oscillating potential. These dynamics are deeply related to the nucleation and dynamics of quantized vortices and solitons. When the potential oscillates with a large amplitude, it nucleates many vortex pairs that move away from the potential. When the amplitude of the oscillation is small, it nucleates solitons through an annihilation of vortex pairs. We discuss three issues concerning the nucleation of vortices. The first is the phase diagram for the nucleation of vortices and solitons near the oscillating potential. The second is the mechanism and critical velocity of the nucleation. The critical velocity of the nucleation is an important issue in quantum fluids, and we propose an expression for the velocity containing both the coherence length and the size of the potential. The third is the divergence of the nucleation time, which is the time it takes for the potential to nucleate vortices, near the critical parameters for vortex nucleation.

DOI: 10.1103/physreva.83.053609

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By solving the two-dimensional, nonlocal Gross-Pitaevskii equation numerically, we study the hydrodynamics of quantized vortices in a dipolar Bose-Einstein condensate excited by an oscillating potential. We calculate the critical velocity for the vortex nucleation in the presence and absence of dipole-dipole interaction. Above a critical velocity, the oscillating potential nucleates the vortex pairs, whose impulses alternatively change their direction synchronously with the oscillation of the Gaussian potential. We study the dynamics of the vortices and also the formation of the dark solitons which have not been previously reported in a dipolar Bose-Einstein condensate.

Vortex nucleation in a Bose-Einstein condensate subject to a stirring potential is studied numerically using the zero-temperature, two-dimensional Gross-Pitaevskii equation. In the case of a rotating, slightly anisotropic harmonic potential, the numerical results reproduce experimental findings, thereby showing that finite temperatures are not necessary for vortex excitation below the quadrupole frequency. In the case of a condensate subject to stirring by a narrow rotating potential, the process of vortex excitation is described by a classical model that treats the multitude of vortices created by the stirrer as a continuously distributed vorticity at the center of the cloud, but retains a potential flow pattern at large distances from the center.

The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization, consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.

One of the key issues related to superfluidity is the existence of quantized vortices. Following recent experiments on Bose–Einstein condensates exhibiting vortices, we investigate the behavior of the wave function which solves the Gross–Pitaevskii equation. For a rotating Bose–Einstein condensate in a harmonic trap, we give a simplified expression of the Gross–Pitaevskii energy in the Thomas–Fermi regime, which only depends on the number and shape of the vortex lines. This allows us to study in detail the structure of the line of a single quantized vortex, which has a U or S shape. S type vortices exist for all values of the angular velocity Ω but are not minimizers of the energy while U vortices are minimizers and exist only for Ω sufficiently large. Finally, we study the drag created by the movement of a detuned laser beam in a condensate and the nucleation of vortices in the low density region close to the boundary layer of the cloud.

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.