Measure synchronization in a two-species bosonic Josephson junction

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.