Vortices in spin-orbit-coupled Bose-Einstein condensates

We discuss realistic methods to create vortices in spin-orbit-coupled Bose-Einstein condensates. We show that, contrary to common intuition, rotation of the trap containing a spin-orbit-coupled condensate does not lead to an equilibrium state with static vortex structures but gives rise instead to intrinsically time-dependent Hamiltonian. We propose alternative methods to create stable static vortex configurations: (1) to rotate both the lasers and the anisotropic trap; and (2) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. We derive the effective Hamiltonians for spin-orbit condensates under such perturbations for most currently known realistic laser schemes that induce synthetic spin-orbit couplings and we solve the Gross-Pitaevskii equation for several experimentally relevant regimes. The new interesting effects include spatial separation of left- and right-moving spin-orbit condensates and the appearance of unusual vortex arrangements.