Macroscopic quantum tunnelling in rotating Bose-Einstein condensates

In this paper we investigate various macroscopic quantum tunnelling phenomena and the phase coherence property of rotating Bose-Einstein condensates. Based on the two-mode approximation, three different cases are studied. When the rotating frequency is independent of time t, by using the SU(2) coherent state path integral method, we discuss two cases: a superposition of two macroscopic states and a Josephson-type ground state. In addition, the specific conditions to reach the two cases are obtained. We also discuss the nonlinear Landau-Zener effect in the dynamic case in which the rotating frequency varies with time t.