Spectral Properties of Coupled Bose-Einstein Condensates

We investigate the energy spectrum structure of a system of two interacting bosonic wells occupied by $N$ bosons within the dynamical algebra $\cal A$ = su($N$+1) of its model Hamiltonian. We derive a single-boson picture of $\cal A$ and use it to make explicit the symmetry properties of the eigenstates. We show that the energy levels are nondegenerate so that the permutational symmetry (broken at the classical level) is preserved quantally. Also, the spectrum doublet structure is shown to pave the way to a consistent classical limit.