We present a new theoretical treatment of macroscopic quantum self-trapping (MQST) and quantum coherent atomic tunneling in a zero-temperature two-species Bose-Einstein condensate system in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunneling interaction. It is shown that the nonlinear interactions can dramatically affect the MQST and the atomic tunneling, and lead to the collapses and revivals (CR) of population imbalance between the two condensates. The competing effects between the self-interaction of each species and the interspecies interaction can lead to the quenching of the MQST and the suppression of the CR and the Shapiro-like steps of the atomic tunneling current. It is revealed that the interatomic nonlinear interactions can induce the coherent atomic tunneling between two condensates even though there does not exist the interspecies Josephson-like tunneling coupling.
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