We numerically investigate low-energy stationary states of pseudospin-1 Bose-Einstein condensates in the presence of Rashba-Dresselhaus-type spin-orbit coupling. We show that for experimentally feasible parameters and strong spin-orbit coupling, the
ground state is a square vortex lattice irrespective of the nature of the spin-dependent interactions. For weak spin-orbit coupling, the lowest-energy state may host a single vortex. Furthermore, we analytically derive constraints that explain why certain stationary states do not emerge as ground states. Importantly, we show that the distinct stationary states can be observed experimentally by standard time-of-flight spinindependent absorption imaging.
We show theoretically that a monopole defect, analogous to the Dirac magnetic monopole, may exist as the ground state of a dilute spin-1 Bose-Einstein condensate. The ground-state monopole is not attached to a single semi-infinite Dirac string, but f
orms a point where the circulation of a single vortex line is reversed. Furthermore, the three-dimensional dynamics of this monopole defect are studied after the magnetic field pinning the monopole is removed and the emergence of antimonopoles is observed. Our scheme is experimentally realizable with the present-day state of the art.
