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arXiv:1408.3293 · Physical Review A

Vortex excitation in a stirred toroidal Bose-Einstein condensate

A. I. Yakimenko, Karyna Isaieva, S. I. Vilchinskiĭ, Elena A. Ostrovskaya

Published Feb 9, 2015• 25 citations
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Abstract

Motivated by a recent experiment [K. C. Wright et al., Phys. Rev. A 88, 063633 (2013)], we investigate the microscopic mechanism for excitation of vortices and formation of a persistent current in an annular BEC stirred by a narrow blue-detuned optical beam. In the framework of a two-dimensional mean-field model, we study the dissipative dynamics of the condensate with parameters that reflect realistic experimental conditions. Vortex-antivortex pairs appear near the center of the stirrer in the bulk of the condensate for slow motion of the stirring beam. When the barrier angular velocity is above some critical value, an outer edge surface mode develops and breaks into the vortices entering the condensate annulus. We determine the conditions for creation of vortex excitations in the stirred toroidal condensate and compare our results with experimental observations.

DOI
10.1103/physreva.91.023607

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Motivated by a recent experiment [K. C. Wright et al., Phys. Rev. A 88, 063633 (2013)], we investigate the microscopic mechanism for excitation of vortices and formation of a persistent current in an annular BEC stirred by a narrow blue-detuned optical beam. In the framework of a two-dimensional mean-field model, we study the dissipative dynamics of the condensate with parameters that reflect realistic experimental conditions. Vortex-antivortex pairs appear near the center of the stirrer in the bulk of the condensate for slow motion of the stirring beam. When the barrier angular velocity is above some critical value, an outer edge surface mode develops and breaks into the vortices entering the condensate annulus. We determine the conditions for creation of vortex excitations in the stirred toroidal condensate and compare our results with experimental observations.
Motivated by a recent experiment [K. C. Wright et al., Phys. Rev. Lett. 110, 025302 (2013)], we investigate deterministic discontinuous jumps between quantized circulation states in a toroidally trapped Bose-Einstein condensate. These phase slips are induced by vortex excitations created by a rotating weak link. We analyze the influence of a localized condensate density depletion and atomic superflows, governed by the rotating barrier, on the energetic and dynamical stability of the vortices in the ring-shaped condensate. We simulate in a three-dimensional dissipative mean-field model the dynamics of the condensate using parameters similar to the experimental conditions. Moreover, we consider the dynamics of the stirred condensate far beyond the experimentally explored region and reveal surprising manifestations of complex vortex dynamics.
The surface excitations, shape deformation, and the formation of persistent current for a Gaussian obstacle potential rotating in a highly oblate Bose–Einstein condensate (BEC) are investigated. A vortex dipole can be produced and trapped in the center of the stirrer even for the slow motion of the stirring beam. When the angular velocity of the obstacle is above some critical value, the condensate shape can be deformed remarkably at the corresponding rotation frequency followed by surface wave excitations. After a long enough time, a small number of vortices are found to be either trapped in the condensate or pinned by the obstacle, and a vortex dipole or several vortices can be trapped at the beam center, which provides another way to manipulate the vortex.
We theoretically show that the topology of a nonsimply connected annular atomic Bose-Einstein condensate enforces the inner surface waves to be always excited with outer surface excitations and that the inner surface modes are associated with induced vortex dipoles unlike the surface waves of a simply connected one with vortex monopoles. Consequently, under stirring to drive an inner surface wave, a peculiar population oscillation between the inner and outer surface is generated regardless of annulus thickness. Moreover, a vortex nucleation process by stirring is observed that can merge the inner vortex dipoles and outer vortex into a single vortex inside the annulus. The energy spectrum for a rotating annular condensate with a vortex at the center also reveals the distinct connection of the Tkachenko modes of a vortex lattice to its inner surface excitations.
We studied the nucleation of vortices in a Bose-Einstein condensate stirred by a laser beam. The vortex cores were observed using time-of-flight absorption imaging. Depending on the stirrer size, either discrete resonances or a broad response was visible as the stir frequency was varied. Stirring beams small compared to the condensate size generated vortices below the critical rotation frequency for the nucleation of surface modes, suggesting a local mechanism of generation. In addition, we observed the centrifugal distortion of the condensate due to the rotating vortex lattice and found evidence for bent vortices.
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.
We have measured the threshold for creating long-lived excitations when a toroidal Bose-Einstein condensate is stirred by a rotating (optical) barrier of variable height. When the barrier height is on the order of or greater than half of the chemical potential, the critical barrier velocity at which we observe a change in the circulation state is much less than the speed for sound to propagate around the ring. In this regime we primarily observe discrete jumps (phase slips) from the noncirculating initial state to a simple, well-defined, persistent current state. For lower barrier heights, the critical barrier velocity at which we observe a change in the circulation state is higher, and approaches the effective sound speed for vanishing barrier height. The response of the condensate in this small-barrier regime is more complex, with vortex cores appearing in the bulk of the condensate. We find that the variation of the excitation threshold with barrier height is in qualitative agreement with the predictions of an effective one-dimensional hydrodynamic model.