  We study the non-equilibrium dynamics of two component bosonic atoms in a
one-dimensional optical lattice in the presence of spin-orbit coupling. In the
Mott insulating regime, the two-component bosonic system at unity filling can
be described by the quantum spin XXZ model. The atoms are initially prepared in
their lower spin states. The system becomes out of equilibrium by suddenly
introducing spin-orbit coupling to the atoms. The system shows the relaxation
and non-stationary dynamics, respectively, in the different interaction
regimes. We find that the time average of magnetization is useful to
characterize the many-body dynamics. The effects of even and odd numbers of
sites are discussed. Our result sheds light on non-equilibrium dynamics due to
the interplay between spin-orbit coupling and atomic interactions.
