Excited states of two-dimensional solitons supported by spin-orbit coupling and field-induced dipole-dipole repulsion

It was recently found that excited states of semivortex and mixed-mode solitons are unstable in spin-orbit-coupled Bose-Einstein condensates (BECs) with contact interactions. We demonstrate a possibility to stabilize such excited states in a setting based on repulsive dipole-dipole interactions induced by a polarizing field, oriented perpendicular to the plane in which the dipolar BEC is trapped. The strength of the field is assumed to grow in the radial direction similar to r(4). Excited states of semivortex solitons have vorticities S and S + 1 in their two components, each being an eigenstate of the angular momentum. They are fully stable up to S = 5. The excited state of mixed-mode solitons feature interweaving necklace structures with opposite fractional values of the angular momentum in the two components. They are stable if they are built of dominant angular harmonics +/- S, with S <= 4. The characteristics and stability of these two types of previously unknown higher-order solitons are systematically analyzed. Their characteristic size is similar to 10 mu m, with the number of atoms less than or similar to 10(5).