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We study the collective oscillations of three-dimensional Bose-Einstein condensates (BECs) excited by a vortex ring. We identify independent, integrated, and stationary modes of the center-of-mass oscillation of the condensate with respect to the vortex ring movement. We show that the oscillation amplitude {of the center-of-mass of the condensate} depends strongly on the initial radius of the vortex ring, the inter-atomic interaction, and the aspect ration of the trap, while the oscillation frequency is fixed and equal to the frequency of the harmonic trap in the direction of the ring movement. However, when applying Kelvin wave perturbations on the vortex ring, the center-of-mass oscillation of the BEC is changed nontrivially with respect to the perturbation modes, the long-scale perturbation strength as well as the wave number of the perturbations. The parity of the wave number of the Kelvin perturbations plays important role on the mode of the center-of-mass oscillation of the condensate.
Understanding quantum dynamics in a two-dimensional Bose-Einstein condensate (BEC) relies on understanding how vortices interact with each others microscopically and with local imperfections of the potential which confines the condensate. Within a sy
In a shaken Bose-Einstein condensate, confined in a vibrating trap, there can appear different nonlinear coherent modes. Here we concentrate on two types of such coherent modes, vortex ring solitons and vortex rings. In a cylindrical trap, vortex rin
We have measured the effect of dipole-dipole interactions on the frequency of a collective mode of a Bose-Einstein condensate. At relatively large numbers of atoms, the experimental measurements are in good agreement with zero temperature theoretical
We derive a governing equation for a Kelvin wave supported on a vortex line in a Bose-Einstein condensate, in a rotating cylindrically symmetric parabolic trap. From this solution the Kelvin wave dispersion relation is determined. In the limit of an
We excite the lowest-lying quadrupole mode of a Bose-Einstein condensate by modulating the atomic scattering length via a Feshbach resonance. Excitation occurs at various modulation frequencies, and resonances located at the natural quadrupole freque