Vortical Solitons of Three-Dimensional Bose–Einstein Condensates under Both a Bichromatic Optical Lattice and Anharmonic Potentials

We study Bose–Einstein condensate vortical solitons under both a bichromatic optical lattice and anharmonic potential. The vortical solitons are built in the form of a layer-chain structure made up of two fundamental vortices along the bichromatic optical lattice direction, which have not been reported before in the three-dimensional Bose–Einstein condensate. A variation approach is applied to find the optimum initial solutions of vortical solitons. The stabilities of the vortical solitons are confirmed by the numerical simulation of the time-dependent Gross–Pitaevskii equation. In particular, stable Bose–Einstein condensate vortical solitons with fundamental vortices of different atomic numbers in the external potential within a range of experimentally achievable timescales are found. We further manipulate the vortical solitons to an arbitrary position by steadily moving the bichromatic optical lattice, and find a stable region for the successful manipulation of vortical solitons without collapse. These results provide insight into controlling and manipulating the Bose–Einstein condensate vortical solitons for macroscopic quantum applications.