Decay of the relative phase domain wall into confined vortex pairs: The case of a coherently coupled bosonic mixture

A domain wall of relative phase in a flattened harmonically trapped Bose-Einstein condensed mixture of two atomic hyperfine states, subject to a stationary Rabi coupling of intensity Omega, is predicted to decay through two different mechanisms. For small values of Omega the instability has an energetic nature and is associated with the formation of a vortex-antivortex pair of the same atomic hyperfine states, the motion of which inside the trap causes the emergence of magnetization, the bending of the domain wall, and its consequent fragmentation. For large values of Omega the domain wall instead undergoes a dynamic snake instability, caused by the negative value of its effective mass, and results in the fast fragmentation of the wall into smaller domain walls confining vortex pairs of different atomic species. Numerical predictions are given by solving the time-dependent Gross-Pitaevskii equation in experimentally available configurations of mixtures of sodium atomic gases.