  We study the mass exchange between two rotating, quantum massive vortices in
a two-component Bose-Einstein condensate. The vortices, in the majority
component, exhibit a filled core, where the in-filling minority component
undergoes a quantum tunneling effect. Remarkably, we observe that the
two-vortex system features stable Josephson oscillations, as well as all the
nonlinear phenomena, including the macroscopic quantum self-trapping, that
characterize a Bosonic Josephson Junction (BJJ). We propose an analytical model
for describing the inter-vortex tunneling, obtained by implementing the a
coherent-state representation of the two-mode Bose-Hubbard model. This allows
us to give the explicit expression of the model's parameters in terms of the
physical macroscopic parameters of the two-vortex system. The comparison of the
dynamical scenario predicted by the model with that emerging from the
Gross-Pitaevskii equations is very good for sufficiently small particle
numbers, while at larger particle numbers it grows less precise, presumably due
to the partial exclusion of the many-body interactions from our model. The
definition of an effective self-interaction parameter allows us to include the
many-body effects, thus restoring a quite good agreement with the numerical
results. Interestingly, the recognition of the bosonic Josephson dynamics paves
the way to the investigation of new dynamical behaviors in multi-vortex
configurations.
