# Collective oscillations of a Bose-Einstein condensate induced by a vortex ring

## TL;DR

This paper investigates how vortex rings induce collective oscillations in three-dimensional Bose-Einstein condensates, revealing dependencies on vortex ring size, interactions, and perturbations, with fixed oscillation frequency.

## Contribution

It introduces a detailed analysis of vortex ring-induced oscillations in BECs, including effects of Kelvin wave perturbations and mode parity, expanding understanding of vortex dynamics.

## Key findings

- Oscillation amplitude depends on vortex ring radius, interactions, and trap aspect ratio.
- Oscillation frequency remains fixed at the trap frequency.
- Kelvin wave perturbations alter the center-of-mass oscillation modes.

## Abstract

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.