Supersolid-like solitons in two-dimensional nonmagnetic spin-orbit coupled spin-1 and spin-2 condensates

We demonstrate spontaneous generation of spatially-periodic supersolid-like super-lattice and stripe solitons in Rashba spin-orbit (SO) coupled spin-1 and spin-2 quasi-two-dimensional nonmagnetic Bose-Einstein condensates (BECs). The solitons in a weakly SO-coupled spin-1 BEC are circularly-symmetric of (−1,0,+1) and (0,+1,+2) types and have inherent vorticity; the numbers in the parentheses are the winding numbers in hyper-spin components +1,0,−1, respectively. The circularly-symmetric solitons in an SO-coupled spin-2 BEC are of types (−2,−1,0,+1,+2) and (−1,0,+1,+2,+3) with the former being the ground state, where the winding numbers correspond to spin components +2,+1,0,−1,−2, respectively. For stronger SO-coupling strengths, these solitons acquire a multiring structure while preserving the winding numbers. Quasi-degenerate stripe and super-lattice solitons, besides a circularly-asymmetric soliton, also emerge as excited stationary states for stronger SO-coupling strengths in spin-1 and spin-2 BECs.