Macroscopic quantum tunnelling of Bose-Einstein condensates in a finite potential well

Bose-Einstein condensates are studied in a potential of finite depth which supports both bound and quasi-bound states. This potential, which is harmonic for small radii and decays as a Gaussian for large radii, models experimentally relevant optical traps. The nonlinearity, which is proportional to both the number of atoms and the interaction strength, can transform bound states into quasi-bound ones. The latter have a finite lifetime due to tunnelling through the barriers at the borders of the well. We predict the lifetime and stability properties for repulsive and attractive condensates in one, two, and three dimensions, for both the ground state and excited soliton and vortex states. We show, via a combination of the variational and WKB approximations, that macroscopic quantum tunnelling in such systems can be observed on time scales of 10 milliseconds to 10 seconds.