Dynamical quantum phase transition of a two-component Bose-Einstein condensate in an optical lattice

We study the dynamics of a two-component Bose-Einstein condensate where the two components are coupled via an optical lattice. In particular, we focus on the dynamics as one drives the system through a critical point of a first-order phase transition characterized by a jump in the internal populations. Solving the time-dependent Gross-Pitaevskii equation, we analyze the breakdown of adiabaticity, impact of nonlinear atom-atom scattering, and role of a harmonic trapping potential. Our findings demonstrate that the phase transition is resilient to both contact interaction between atoms and external trapping confinement.