  We investigate the universal spatiotemporal dynamics in spin-orbit coupled
Bose-Einstein condensates which are driven from the zero-momentum phase to the
plane-wave phase. The excitation spectrum reveals that, at the critical point,
the Landau critical velocity vanishes and the correlation length diverges.
Therefore, according to the Kibble-Zurek mechanism, spatial domains will
spontaneously appear in such a quench through the critical point. By simulating
the real-time dynamics, we numerically extract the static correlation length
critical exponent v and the dynamic critical exponent z from the scalings of
the temporal bifurcation delay and the spatial domain number. The numerical
scalings consist well with the analytical ones obtained by analyzing the
excitation spectrum.
