Topological excitations in rotating spin-orbit-coupled spin-1 Bose-Einstein condensates with in-plane gradient magnetic field

We investigate the topological excitations of rotating spin-1 ferromagnetic Bose-Einstein condensates with spin-orbit coupling (SOC) in an in-plane quadrupole field. Such a system sustains a rich variety of exotic vortex structures due to the spinor order parameter and the interplay among in-plane quadrupole field, SOC, rotation, and interatomic interaction. For the nonrotating case, with the increase of the quadrupole field strength, the system experiences a transition from a coreless polar-core vortex with a bright soliton to a singular polar-core vortex with a density hole. Without rotation but with a fixed quadrupole field, when the SOC strength increases, the system transforms from a central Mermin-Ho vortex into a criss-crossed vortex-antivortex string lattice. For the rotating case, we give a phase diagram with respect to the quadrupole field strength and the SOC strength. It is shown that the rotating system supports four typical quantum phases: vortex necklace, diagonal vortex chain cluster, single diagonal vortex chain, and few vortex states. Furthermore, the system favors novel spin textures and skyrmion excitations including an antiskyrmion, a criss-crossed half-skyrmion-half-antiskyrmion lattice, a skyrmion-meron necklace, a symmetric half-skyrmion lattice, and an asymmetric skyrmion-meron lattice.