Universal dynamics of zero-momentum to plane-wave transition in spin-orbit coupled Bose-Einstein condensates

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 nu 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.