Bose-Einstein condensates (BECs) provide a clear and controllable platform to study diverse intriguing emergent nonlinear effects that appear too in other physical settings, such as bright and dark solitons in mean-field theory as well as many-body physics. Various ways have been elaborated to stabilize bright solitons in BECs, three promising schemes among which are: optical lattices formed by counterpropagating laser beams, nonlinear managements mediated by Feshbach resonance, spin-orbit coupling engineered by dressing atomic spin states (hyperfine states of spinor atomic BECs) with laser beams. By combing the latter two schemes, we discover, from theory to calculations, that the two-component BECs with a spin-orbit coupling and cubic atom-atom interactions, whose nonlinear distributions exhibit a well-defined spatially periodic modulation (nonlinear lattice), can support one-dimensional localized modes of two kinds: fundamental solitons (with a single peak), and soliton pairs comprised of dipole solitons (anti-phase) or two-peak solitons (in-phase). The influence of three physical parameters: chemical potential of the system, strengths of both the Rashba spin-orbit coupling and atom-atom interactions, on the existence and stability of the localized modes is investigated based on linear-stability analysis and direct perturbed simulations. In particular, we demonstrate that the localized modes can be stable objects provided always that both the inter- and intraspecies interactions are attractive.

Propagations of the 1D fundamental solitons against initial small perturbations for the points A (top line), B (middle line) and C (bottom line). (Image by XIOPM)