  The dynamic behavior of vortex pairs in two-component coherently (Rabi)
coupled Bose-Einstein condensates is investigated in the presence of harmonic
trapping. We discuss the role of the surface tension associated with the domain
wall connecting two vortices in condensates of atoms occupying different spin
states and its effect on the precession of the vortex pair. The results, based
on the numerical solution of the Gross-Pitaevskii equations, are compared with
the predictions of an analytical macroscopic model and are discussed as a
function of the size of the pair, the Rabi coupling and the inter-component
interaction. We show that the increase of the Rabi coupling results in the
disintegration of the domain wall into smaller pieces, connecting vortices of
new-created vortex pairs. The resulting scenario is the analogue of quark
confinement and string breaking in quantum chromodynamics.
