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The in-plane gradient magnetic field induced vortex lattices in spin-orbit coupled Bose-Einstein condensations

We consider the ground-state properties of the two-component spin-orbit coupled ultracold bosons subject to a rotationally symmetric in-plane gradient magnetic field. In the non-interacting case, the ground state supports giant-vortices carrying large angular momenta without rotating the trap. The vorticity is highly tunable by varying the amplitudes and orientations of the magnetic field. Interactions drive the system from a giant-vortex state to various configurations of vortex lattice states along a ring. Vortices exhibit ellipse-shaped envelops with the major and minor axes determined by the spin-orbit coupling and healing lengths, respectively. Phase diagrams of vortex lattice configurations are constructed and their stabilities are analyzed.