Measure Synchronization In Bosonic Josephson Junction

Based on the classical Hamiltonian description of a single species Bosonic Josephson jucntion, A.Smerzi firstly predicted that the transition from Josephson oscillation to macroscopic quantum self-trapping due to the increasing of nonlinear intercation[PRL,79,4950(1997)]. Later this dynamic transition has been validated in experiment in 2005[PRL,95,010402(2005)]. In the study of the tunneling dynamcis in a two-species Bosonic Joseph-son junction based on classical Hamiltonian description,we find that by increasing the inter-atomic interaction, the tunneling dynamics also expe-rience a phase transition, which is called measure synchronization. This dissertation is devoted to the study of this peculiar collective mode in Bosonic Josephson jucntions. The study is summarized below:Firstly, by setting two different initial configuration (Josephson os-cillation regime(0 phase) and macroscopic quantum self-trapping regime(Ï€phase)), we find different scenarios of measure synchronization(MS). At the transition we obtained the scaling which shown as a continuous phase transition.Secondly, besides the normal ms, we present two newly discovered scenarios of which is beyond the orginal concept. One is the transition from MS state to nonlocalized MS state. Through the analysis of the order parameter, we find that nonlocal state should be a synchronized state. Another one is nonlocalized MS transition happened in macroscopic quantum self-trapping regime. Before and after the transition, both states correspond to nonlocalized state.Thirdly, we revealed the general mechanism behind MS. We found that by applying the Poincare section to the various scenarios described above, the dynamical mechanism behind MS transition can be explicitly re-vealed. There shows that the two species BJJ exhibit dynamical separatrix crossing behavior at the critical inter-species interaction of MS transition. So we identified separatrix crossing as the underlying mechanism of MS transition. Moreover, we find the happing of chaotic MS transition is the direct result of " separatrix chaos".Finally, the occurrence of MS in the multi-species Bosonic Josephson junction is discussed. A synchronization tree from free oscillations to local clustering is found. The smaller energy difference the compnents have, the easier they reach partial MS. Then the global MS is found gradually. We also analyze the mechanism of MS in multi-species Bosonic Josephson junction and find that the occurence of partial MS also result from the transition of separatrix.