Vortex-antivortex oscillation and tunneling in Bose-Einstein condensates

We study interacting condensates in anisotropic traps. Employing a two-level mean-field theory, which is valid provided the interaction energy is much smaller than ?ω_x and ?ω_y and the number of particles N is much larger than unity, we see that even a small interaction can drastically modify the dynamics of the system as predicted by García-Ripoll et al. Phys. Rev. Lett. 87, 140403 (2001)]. In the present work, we supplement the discussion of the previous work and point out the important role of coupling between population difference and phase difference between two p states in the x and y directions. We also explore the stability of the vortex state for small systems with N ～ O(1), for which the mean-field theory is inapplicable. We performed the full quantum mechanical calculations using up to six single-particle states and showed that, when N is comparable to unity, quantum tunneling between the vortex and antivortex states can occur even though the interaction coefficient is so large that the vortex-antivortex oscillation is prohibited within the mean-field theory.