Energy barrier for collapse in a pair of tunnel-coupled condensates with   the scattering lengths of opposite signs
  We predict the existence of an energy barrier for collapse in a system of two tunnel-coupled repulsive and attractive quasi two-dimensional condensates trapped in a double-well potential. The ground state in such a system can have a lower energy than that of the collapsing state. We find such ground states numerically and analytically determine the domain of their existence, they have a much larger share of atoms confined in the repulsive condensate. The energy barrier for collapse is due to the fact that the energy of the system increases if atoms tunnel from the repulsive condensate to the attractive one. 
Valery S. Shchesnovich and Solange B. Cavalcanti