Domain formation and universally critical dynamics through phase separation in two-component Bose-Einstein condensates

We investigate defect formation and the universal critical dynamics of two-dimensional two-component Bose-Einstein condensates (BECs) confined in both box and harmonic traps. Our focus is on the nonequilibrium universal dynamics of the miscible-immiscible phase transition, considering both linear and nonlinear quenching protocols. The general condition for a phase transition, ${g}_{11}{g}_{22}={g}_{12}^{2}$, depends exclusively on inter- and intraspecies interactions. In this system, simultaneous phase transitions occur in both the box and harmonic traps. Consequently, the nonequilibrium critical dynamics can still be described using the homogeneous Kibble-Zurek mechanism. Through an analysis of Bogoliubov excitations, we establish a power-law relationship linking the domain correlation length, phase transition delay, and quench time. Additionally, real-time simulations of phase transition dynamics demonstrate the formation of domain defects and the delay of phase transitions in nonequilibrium conditions. These simulations also reveal the universal scaling of the correlation length and phase transition delay across various quench times and nonlinear coefficients, showing well agreement with our analytical predictions. Our study confirms that the universality class of two-component BECs is independent of dimensionality. Additionally, larger nonlinear coefficients effectively suppress the growth of nonadiabatic excitations, offering a fresh perspective on achieving quasiadiabatic evolution.