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In this paper, we study a system of two-component Bose gas in an artificialmagnetic field trapped by concentric harmonic and annular potentials,respectively. The system is realized by gases with two-internal states like thehyperfine states of $^{87}$Rb. We are interested in effects of a Rabioscillation between them. Two-component Bose Hubbard model is introduced todescribe the system, and Gross-Pitaevskii equations are used to study thesystem. We first study the Bose gas system in the annular trap by varying thewidth of the annulus and strength of the magnetic field, in particular, wefocus on the phase slip and superflow. Then we consider the coupled Bose gassystem in a magnetic field. In a strong magnetic field, vortices form aAbrikosov triangular lattice in both Bose-Einstein condensates (BECs), andlocations of vortices in the BECs correlate with each other by the Rabicoupling. However, as the strength of the Rabi coupling is increased, vorticesstart to vibrate around their equilibrium locations. As the strength isincreased further, vortices in the harmonic trap start to move along theboundaries of the annulus. Finally for a large Rabi coupling, the BECs aredestroyed. Based on our findings about the BEC in the annular trap, we discussthe origin of above mentioned phenomena.

Two-component Bose gas trapped by harmonic and annular potentials: Supercurrent, vortex flow and instability of superfluidity by Rabi coupling