Asymmetric bidrectional Kibble-Zurek mechanism in a spin-orbit-coupled Bose-Einstein condensate across first-order quantum phase transitions

Quench dynamics of first-order phase transitions in a homogeneous Bose-Einstein condensate with Raman-type spin-orbit coupling is investigated. By adjusting the coupling strength, the system can be driven across the critical point between the plane-wave phase and stripe phase in two opposite directions, and we find the scaling-law behaviors for both processes of phase transitions. This is different from previous studies, which only focus on the quench dynamics in the unidirectional transitions from a higher symmetric phase to a lower symmetric phase. Subsequently, we obtain the power law of the domain numbers (correlation length) and formation time (correlation time) of these phase transitions and extract the critical exponents. The results reveal the effect of the directionality of the phase transition on the dynamic scaling law.