Field effects on the vortex states in spin–orbit coupled Bose–Einstein condensates

•Vortex states of rotational spin–orbit coupled BEC have been studied.•Both longitudinal field and transverse field reduce vortices.•The transverse field pushes condensates to one direction.

Multi-quantum vortices can be created in the ground state of rotating Bose–Einstein condensates with spin–orbit couplings. We investigate the effects of external fields, either a longitudinal field or a transverse field, on the vortex states. We reveal that both fields can effectively reduce the number of vortices. In the latter case we further find that the condensate density packets are pushed away in the horizontal direction and the vortices finally disappear to form a plane wave phase.