Influence of barrier parameters in rotating double-well potential on hidden vortices in Bose-Einstein condensate

Vortex dynamics in Bose-Einstein condensates (BECs) are crucial for understanding quantum coherence, superfluidity, and topological phenomena. In this work, we investigate the influence of barrier parameters in a rotating double-well potential on the formation and evolution of hidden vortices, aiming to reveal the regulatory mechanisms of barrier width and height on vortex dynamics. By numerically solving the dissipative Gross-Pitaevskii equation for a two-dimensional BEC system confined strongly along the <i>z</i>-axis, we analyze the density distribution, phase distribution, vortex number, and average angular momentum under varying barrier widths and heights. The results show that increasing barrier width significantly promote the formation of hidden vortices, with the total number of visible and hidden vortices still satisfying the Feynman rule. For larger barrier widths, hidden vortices exhibit an oscillatory distribution due to enhanced vortex interactions. In contrast, when the barrier height is above the critical threshold (i.e. the height sufficient to completely separate the condensate), the effect of the barrier height is limited, but below this critical threshold, the hidden vortex cores become visible, thereby reducing the threshold for vortex formation. A particularly striking finding is the efficacy of a temporary barrier strategy: by reducing <inline-formula><tex-math id="M1">\begin{document}$ {V_0} $\end{document}</tex-math></inline-formula> from <inline-formula><tex-math id="M2">\begin{document}$ 4\hbar {\omega _x} $\end{document}</tex-math></inline-formula> to <inline-formula><tex-math id="M3">\begin{document}$ 0 $\end{document}</tex-math></inline-formula> within a rotating double-well trap, stable vortex states with four visible vortices are generated at <inline-formula><tex-math id="M4">\begin{document}$ \varOmega = 0.5{\omega _x} $\end{document}</tex-math></inline-formula>. Under the same parameter conditions, it is impossible to generate a stable state containing vortices at the same <inline-formula><tex-math id="M5">\begin{document}$ \varOmega $\end{document}</tex-math></inline-formula> by directly using the rotating harmonic trap. In other words, a temporary barrier within a rotating harmonic trap effectively introduces phase singularities, facilitating stable vortex states at lower rotation frequencies than those required in a purely harmonic trap. These findings demonstrate that precise tuning of barrier parameters can effectively control vortex states, providing theoretical guidance for experimentally observing hidden vortices and advancing the understanding of quantum vortex dynamics.