Exact solitons and manifold mixing dynamics in the spin-orbit–coupled spinor condensates

¹ Department of Physics, Beijing Normal University - Beijing 100875, China
² State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences Beijing 100190, China

^(a) yangshijie@tsinghua.org.cn (corresponding author)

Received: 17 June 2014
Accepted: 17 October 2014

Abstract

We derive exact static as well as moving solitonic solutions to the one-dimensional spin-orbit–coupled F = 1 Bose-Einstein condensates. The static polar soliton is shown to be the ground state by the imaginary-time evolution method. It shows a helical modulation of the order parameter due to the spin-orbit coupling. In particular, the moving soliton exhibits a periodic oscillation among the particle numbers of the hyperfine states. We further explore the temporal evolution of the static polar soliton and find that the spin-polarization exhibits dynamical oscillations. This disappearance and re-emergence of the ferromagnetic state indicates the mixing of the ferromagnetic and the antiferromagnetic manifolds.