Interfacial Dynamics of a Dark Soliton in a Two-Dimensional Phase-Separated Bose-Einstein Condensate

Abstract We numerically investigate the collision dynamics of a dark soliton with a domain wall in an immiscible, two-component Bose-Einstein condensate confined in a quasi-two-dimensional harmonic trap. The role of the inter-species interaction strength $\delta = g_{12}/g_{11}$ and the soliton's initial displacement $\Delta_x$ is investigated thoroughly. Our results reveal a clear bifurcation into two distinct dynamical regimes: a $penetration regime$, where the soliton decays into vortex pairs that cross the interface, and a $non-penetration regime$, where the soliton's energy is dissipated at the interface through sound emission and vortex annihilation. We present a phase diagram that maps these outcomes across the $(\delta, \Delta_x)$ parameter space. Furthermore, within the non-penetration regime, we identify a complex excited state characterized by the combination of component breakup in one component and vortex formation in the other. This work provides the systematic study of dark soliton-domain wall interactions in a 2D phase-separated binary BEC, offering new insights into interfacial dynamics and non-equilibrium transport in multi-component quantum fluids.