Macroscopic superposition states of cold bosons in double well with Orbital Degrees of freedom

We extend previous studies on cold bosons in double well potentials using a
Hubbard-like Hamiltonian to three dimensions and relax the one-level
assumption. We identify the criteria to distinguish between different
regimes of parameters in which different physical phenomena can be found. We
characterize the eigenstates in all these regimes and show that Macroscopic
Superposition (MS) states, i.e. NOON or NOON-like states, with a non-zero
orbital angular momentum, are found in the interactions dominated or Fock
regime. We show that, in the one dimensional case, MS states are very
sensitive to small imperfections in a symmetric potential. Nevertheless, a *embedded* MS state is obtained again for certain *resonant* values of the
tilt between wells. This is the key to obtain these states in the dynamical
propagation of a Bose-Einstein condensate initially localized in one of the
wells. We show that, for a properly prepared tilt between wells, MS states
are realized periodically along the quantum sloshing of the cold bosons,
thus paving the way for their experimental observation. We outline how to
extend these results to the three dimensional case.