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Register a new userCollective oscillations of a Bose-Einstein condensate induced by a vortex ring
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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.
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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 system consisting of many vortices, the trajectory of a vortex-antivortex pair is often scattered by a third vortex, an effect previously characterised. However, the natural question remains as to how much of this effect is due to the velocity induced by this third vortex and how much is due to the density inhomogeneity which it introduces. In this work, we describe the various qualitative scenarios which occur when a vortex-antivortex pair interacts with a smooth density impurity whose profile is identical to that of a vortex but lacks the circulation around it.
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 ring solitons can be characterized as nonlinear Hermite-Laguerre modes, whose description can be done by means of optimized perturbation theory. The energy, required for creating vortex ring solitons, is larger than that needed for forming vortex rings. This is why, at a moderate excitation energy, vortex rings appear before vortex ring solitons. The generation of vortex rings is illustrated by numerical simulations for trapped $^{87}$Rb atoms.
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 predictions based on the Thomas Fermi approach. Experimental results obtained for the dipolar shift of a collective mode show a larger dependency to both the trap geometry and the atom number than the ones obtained when measuring the modification of the condensate aspect ratio due to dipolar forces. These findings are in good agreement with simulations based on a gaussian ansatz.
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 oblate trap and in the absence of longitudinal trapping our results are consistent with previous work. We show that the derived Kelvin wave dispersion in the general case is in quantitative agreement with numerical calculations of the Bogoliubov spectrum and offer a significant improvement upon previous analytical work.
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 frequency of the condensate and at the first harmonic are observed. We also investigate the amplitude of the excited mode as a function of modulation depth. Numerical simulations based on a variational calculation agree with our experimental results and provide insight into the observed behavior.
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