Ultracold bosons in a tilted multilevel double-well potential

The N-body problem in a tilted double well requires new features for macroscopic quantum superposition in ultracold atoms. In particular, one needs to go beyond the single-particle ground state in each well. We provide explicit criteria for when two energy levels are needed to describe the state space. For typical experimental parameters, two levels are indeed required for the creation of macroscopic superposition states. Furthermore, we show that a small tilt causes the collapse of such states. However, partial macroscopic superposition states reappear when the tilt can be compensated by atom-atom interactions.