Josephson Dynamics of 2D Bose-Einstein Condensates in Dual-Core Trap: Homogeneous, Droplet-Droplet, and Vortex-Vortex Regimes

Abstract

The dynamics of a two-dimensional Bose-Einstein condensate mixture, loaded into a dual-core trap, when beyond-mean-field effects are taken into account, are considered. The effects of quantum fluctuations are described by the Lee-Huang-Yang correction terms in the extended coupled Gross-Pitaevskii equations. The spatially uniform and inhomogeneous BEC cases are studied. In the first case, the parameter regimes associated with macroscopic quantum tunnelling, self-trapping, and revival-like localisation dynamics are found. The Josephson oscillation frequencies for both the zero-phase and the $π$-phase modes are derived. As the total atom number varies, the dynamics exhibit a nontrivial bifurcation structure: along the zero-phase branch, two pitchfork bifurcations generate bistability and hysteresis, while the $π$-phase branch shows a single pitchfork bifurcation. In the second case, the Josephson dynamics for quantum droplets and vortices are investigated. Predictions for the oscillation frequencies of the atomic population between quantum droplets are obtained and fully validated by direct numerical simulations of coupled extended GP equations. The existence of the Andreev-Bashkin nondissipative drag through simulations of droplet-droplet interactions is shown. The Josephson dynamics of vortex states are studied. Vortices with topological charge $S$ and sufficiently small particle number are typically unstable, breaking up into $S+1$ (occasionally $S+2$) fundamental fragments, with the breakup time increasing as the particle number grows. Unstable asymmetric vortices show splitting and/or crescent-like instability. For vortices with sufficiently large norms, long-time simulations confirm robust stability against small perturbations; in this regime, Josephson oscillations and Andreev-Bashkin-type entrainment for vortex states with charges $S=1, 2$, and $3$ are investigated.