Study on the Influence of Barrier Parameters on Hidden Vortices in a Bose-Einstein Condensate in a Rotating Double-Well Potential

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 elucidate 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 z-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 exhibite an oscillatory distribution due to enhanced vortex interactions, as shown in Fig. (a) with vortices marked by red dots. In contrast, barrier height has a limited impact on hidden vortex numbers when above a critical threshold (i.e., the height sufficient to completely separate the condensate), but below this critical threshold, hidden vortex cores become visible, reducing the threshold for vortex formation. A particularly striking finding is the efficacy of a temporary barrier strategy: by reducing V₀ from 4ħωx to 0 within a rotating double-well trap, stable vortex states with four visible vortices are generated at Ω= 0.5ωx, as shown in Fig. (b). Under the same parameter conditions, it is impossible to generate a stable state containing vortices at the same Ω by directly using the rotating harmonic trap. In other words, a temporary barrier within a rotating harmonic trap effectively introduced 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 enables effective control of vortex states, offering theoretical guidance for experimental observation of hidden vortices and advancing the understanding of quantum vortex dynamics.