Wall-vortex composite solitons in two-component Bose-Einstein condensates

Abstract

We study composite solitons, consisting of domain walls and vortex lines attaching to the walls in two-component Bose-Einstein condensates. When the total density of the two components is homogeneous, the system can be mapped to the O(3) nonlinear $\ensuremath{\sigma}$ model for the pseudospin representing the two-component order parameter, and the analytical solutions of the composite solitons can be obtained. Based on the analytical solutions, we discuss the detailed structure of the composite solitons in two-component condensates by employing the generalized nonlinear $\ensuremath{\sigma}$ model, where all degrees of freedom of the original Gross-Pitaevskii theory are active. The domain wall pulled by a vortex is logarithmically bent as a membrane pulled by a pin. It bends more flexibly than the domain wall in the $\ensuremath{\sigma}$ model, because the density inhomogeneity results in a reduction of the domain wall tension from that in the $\ensuremath{\sigma}$ model limit. We find, however, that the curvature of the wall bending pulled by a vortex is still greater than that expected from the reduced tension due to only the density inhomogeneity. Finally, we study the composite soliton structure for actual experimental situations with trapped immiscible condensates under rotation, through numerical simulations of the coupled Gross-Pitaevskii equations.