Josephson effect and self-trapping in helicoidal spin-orbit coupled Bose-Einstein condensates with optical lattices

We consider matter-wave bright solitons in helicoidal spin-orbit coupled Bose-Einstein condensates in optical lattices with a view to study Josephson-type oscillation and self-trapping of population imbalance between two pseudo-spin states. For fixed values of nonlinear interaction and lattice parameters, the population imbalance executes Josephson-type oscillation and the frequency of oscillation decreases with the increase of helicoidal gauge potential. The frequency of oscillation, however, increases in presence of nonlinear optical lattices. We find that the population imbalance can oscillate about a non-zero value and result self-trapping for proper choices of parameters of the system. The self-trapping can be enhanced by the increase of helicoidal gauge potential and by properly tuning the lattice parameters.