  Measure synchronization (MS) in a two-species bosonic Josephson junction
(BJJ) is studied based on semi-classical theory. Six different scenarios for
MS, including two in the Josephson oscillation regime (0 phase mode) and four
in the self-trapping regime ($\pi$ phase mode), have been clearly shown.
Systematic investigations of the common features behind these different
scenarios have been performed. We show that the average energies of the two
species merge at the MS transition point. The scaling of the power law near the
MS transition has been verified, and the critical exponent is 1/2 for all of
the different scenarios for MS. We also illustrate MS in a three-dimensional
phase space; from this illustration, more detailed information on the dynamical
process can be obtained. Particularly, by analyzing the Poincare sections with
changing interspecies interactions, we find that the two-species BJJ exhibits
separatrix crossing behavior at MS transition point, and such behavior depicts
the general mechanism behind the different scenarios for the MS transitions.
The new critical behavior found in a two-species BJJ is expected to be found in
real systems of atomic Bose gases.
