Stability change of a multi-charged vortex due to coupling with quadrupole mode

We have studied collective modes of quasi-2D Bose-Einstein condensates with multiply-charged vortices using a variational approach. Two of the four collective modes considered exhibit coupling between the vortex dynamics and the large-scale motion of the cloud. The vortex presence causes a shift in all frequencies of collective modes even for the ones that do not couple dynamically with the vortex-core. The coupling between vortex and large-scale collective excitations can induce the multi-charged vortex to decay into singly-charged vortices with the quadrupole mode being one possible channel for such a decay. Therefore a thorough study was done about the possibility to prevent the vortex decay by applying a Gaussian potential with its width proportional to the vortex-core radius and varying its height. In such way, we created a stability diagram of height versus interaction strength which has stable regions due the static Gaussian potential. Furthermore, by using a sinusoidal time-modulation around the average height of the Gaussian potential, we have obtained a diagram for the parametric resonance which can prevent the vortex decay in regions where static potential can not.