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Measure synchronization (MS) in a two-species bosonic Josephson junction(BJJ) is studied based on semi-classical theory. Six different scenarios forMS, including two in the Josephson oscillation regime (0 phase mode) and fourin the self-trapping regime ($\pi$ phase mode), have been clearly shown.Systematic investigations of the common features behind these differentscenarios have been performed. We show that the average energies of the twospecies merge at the MS transition point. The scaling of the power law near theMS transition has been verified, and the critical exponent is 1/2 for all ofthe different scenarios for MS. We also illustrate MS in a three-dimensionalphase space; from this illustration, more detailed information on the dynamicalprocess can be obtained. Particularly, by analyzing the Poincare sections withchanging interspecies interactions, we find that the two-species BJJ exhibitsseparatrix crossing behavior at MS transition point, and such behavior depictsthe 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 inreal systems of atomic Bose gases.

Measure synchronization in a two-species bosonic Josephson junction