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 skyrmionmeron lattice.