Effects of Dissipation Strength and Interaction Strength on the Splitting of Quadruply Quantized Vortices

Based on the dissipative Gross–Pitaevskii equation, effects of dissipation strength and interaction strength on the linear instability and the splitting processes of quadruply quantized vortices are studied. Using the linear perturbation theory to calculate out the elementary excitation modes of the quadruply quantized vortices, we reveal a novel and very important dynamical transition of the most unstable mode. It is found that the most unstable mode is the twofold rotational symmetry mode at a small dissipation strength, while it is the fourfold rotational symmetry mode at a larger dissipation strength. What’s more, the transition dissipation strength decreases with the increase in the interaction strength. The full nonlinear numerical simulations further demonstrate the process of such a dynamical transition. Our work has shed light on the long-standing puzzle in Bose–Einstein condensate, why the fourfold rotational symmetry splitting pattern of quadruply quantized vortex has not yet been observed in the laboratory. We propose a promising direction to solve this problem by increasing the dissipation strength or the interaction strength. Our predictions are likely to be tested in the laboratory in the near future.