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arXiv:1206.5622 · Physical Review A

Vortex dynamics in an annular Bose-Einstein condensate

Sungjong Woo, Young‐Woo Son

Published Jul 17, 2012• 16 citations
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Abstract

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.

DOI
10.1103/physreva.86.011604

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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.
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.
We analyze the excitation spectrum of a superfluid Bose-Einstein condensate rotating in a ring trap. We identify two important branches of the spectrum related to outer and inner edge surface modes that lead to the instability of the superfluid. Depending on the initial circulation of the annular condensate, either the outer or the inner modes become first unstable. This instability is crucially related to the superfluid nature of the rotating gas. In particular, we point out the existence of a maximal circulation above which the superflow decays spontaneously, which cannot be explained by invoking the average speed of sound.
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.
In a rotating two-component Bose-Einstein condensate (BEC), the traditional triangular vortex lattice can be replaced by a rectangular vortex lattice or even a structure characterized in terms of vortex sheets, depending on the interspecies interactions. We study the dynamics of this system by analyzing the Bogoliubov excitation spectrum. Excitations familiar to BEC vortex systems are found such as Tkachenko modes, hydrodynamic modes, and surface waves, however, the complex two-component morphology also gives rise to phenomena including shear flow between vortex sheets.
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 origin of the peculiar surface-mode excitations is identified to be phase fluctuations at the low-density surface regime. The obtained dependence of a distortion parameter on time and that on the driving frequency agree with the recent experiments by Madison et al. [Phys. Rev. Lett. 86, 4443 (2001)].
We consider analytically the dynamics of an arbitrary number and configuration of vortices in an annular Bose-Einstein condensate obtaining expressions for the free energy and vortex precession rates to logarithmic accuracy. We also obtain lower bounds for the lifetime of a single vortex in the annulus. Our results enable a closed-form analytic treatment of vortex-vortex interactions in the annulus that is exact in the incompressible limit. The incompressible hydrodynamics that is developed here paves the way for more general analytical treatments of vortex dynamics in non-simply-connected geometries.