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Internal Josephson phenomena in a coupled two-component Bose condensate

We discuss the coherent oscillations between two coupled quantum states of a Bose-Einstein condensate in two-dimensional space at zero temperature. In the system we consider, weak interparticle repulsive interactions occur between the particles in state one only, while the state two particles remain non-interacting. Analytical as well as numerical solution of the coupled Gross-Pitaevskii and Schroedinger equations reveals various regimes of oscillational dynamics for the relative quantum phase and population imbalance between the two subsystems of the condensate. We show that, depending on the energy detuning between the two states, the system can exhibit modified harmonic and anharmonic Rabi oscillations or can transit to the regime analogous to internal a.c. Josephson effect. Morover, at a certain value of energy detuning, the internal oscillations are fully suppressed.