A Kaleidoscope of Topological Structures in Dipolar Bose–Einstein Condensates With Weyl‐Like Spin‐Orbit Coupling in Anharmonic Trap

Abstract Dipole–dipole interaction (DDI) possesses characteristics different from the conventional isotropic s‐wave interaction in Bose‐Einstein condensates (BECs). The interplay of DDI with spin‐orbit coupling (SOC) and rotation may induce novel quantum properties. This work systematically analyzes the effects of the DDI, Weyl‐like SOC, rotation and trap anharmonicity in the ground state of two‐component BECs. The interplay of these factors leads to a kaleidoscope of quantum states, emerging in quantum defects, droplets, wheel and ring forms of density distributions, accompanied with transitions of topology of density, and manifesting a critical behavior around a revealed density‐collapse point. A bunch of exotic spin topological structures are shown, including centric vortex surrounded by layers of spin flows, compound topological structure of edge defect, and various coexistence states of skyrmions with different topological charges. In particular, quarter skyrmions and other possible fractional skyrmions are found. Rashba‐type SOC and Weyl‐like SOC are also compared. The study implies that one can manipulate both the density topology and the spin topological structure via these tunable parameters in BECs. The abundant variations of the topological structures and particularly the revealed critical behavior may provide quantum resources for potential applications in quantum metrology.