In-Plane Gradient Magnetic Field-Induced Topological Defects in Rotating Spin-1 Bose–Einstein Condensates with SU(3) Spin-Orbit Coupling

We study the topological defects and spin structures of rotating SU(3) spin-orbit-coupled spin <i>F</i>=1 Bose-Einstein condensates (BECs) in an in-plane quadrupole field with ferromagnetic spin interaction, and the BECs is confined by a harmonic trap. Without rotation, as the quadrupole field strength is increased, the spin <i>F</i>=1 BECs with SU(3) spin-orbit coupling (SOC) evolves from the initial Thomas-Fermi phase into the stripe phase; then, it enters a vortex-antivortex cluster state and eventually a polar-core vortex state. In the absence of rotation with the given quadrupole field, the enhancing SU(3) SOC strength can cause a phase transition from a central Mermin-Ho vortex to a vortex-antivortex cluster, subsequently converting to a bending vortex-antivortex chain. In addition, when considering rotation, it is found that this system generates the following five typical quantum phases: a three-vortex-chain cluster structure with mutual angles of approximately 2π3, a tree-fork-like vortex chain cluster, a rotationally symmetric vortex necklace, a diagonal vortex chain cluster, and a density hole vortex cluster. Particularly, the system exhibits unusual topological structures and spin textures, such as a bending half-skyrmion-half-antiskyrmion (meron-antimeron) chain, three half-skyrmion (meron) chains with mutual angles of an approximately 2π3, slightly curved diagonal half-skyrmion (meron) cluster lattice, a skyrmion-half-skyrmion (skyrmion-meron) necklace, and a tree-fork-like half-skyrmion (meron) chain cluster lattice.