  We experimentally investigate the phase winding dynamics of a harmonically
trapped two-component BEC subject to microwave induced Rabi oscillations
between two pseudospin components. While the single particle dynamics can be
explained by mapping the system to a two-component Bose-Hubbard model,
nonlinearities due to the interatomic repulsion lead to new effects observed in
the experiments: In the presence of a linear magnetic field gradient, a
qualitatively stable moving magnetic order that is similar to antiferromagnetic
order is observed after critical winding is achieved. We also demonstrate how
the phase winding can be used as a new tool to generate copious dark-bright
solitons in a two-component BEC, opening the door for new experimental studies
of these nonlinear features.
