Resonance States and Quantum Tunneling of Bose Einstein condensates in a 3D shallow trap

A correlated quantum many-body method is applied to describe resonance states of atomic Bose-Einstein condensates (BEC) in a realistic shallow trap (as opposed to infinite traps commonly used). The realistic van der Waals interaction is adopted as the interatomic interaction. We calculate experimentally measurable decay rates of the lowest quasi-bound state in the shallow trap. The most striking result is the observation of a new metastable branch besides the usual one for attractive BEC in a pure harmonic trap. As the particle number increases the new metastable branch appears, then gradually disappears and finally usual metastable branch (associated with the attractive BEC in a harmonic trap) appears, eventually leading to the collapse of the condensate.