Three-dimensional Bose–Einstein condensate vortex soliton sunder optical lattice and harmonic confinements

We predict three-dimensional vortex solitons in a Bose–Einstein condensate under a complex potential which is the combination of a two-dimensional parabolic trap along the transverse radial direction and a one-dimensional optical-lattice potential along the z axis direction. The vortex solitons are built in the form of layer-chain structure made up of several fundamental vortices along the optical-lattice direction, which were not reported before in the three-dimensional Bose–Einstein condensate. By using the combination of the energy density functional method with the direct numerical simulation, we find three-dimensional vortex solitons with topological charge χ=1, χ=2, and χ=3. Moreover, the macroscopic quantum tunneling and the chirp phenomena of the vortex solitons are shown in the evolution. Thereinto, the occurrence of the macroscopic quantum tunneling provides a possibility for the realization of the quantum tunneling in experiment. Specifically, we manipulate the vortex solitons along the optical lattice direction successfully. The stability limits for dragging the vortex solitons from an initial fixed position to a prescribed location are further pursued.