Dynamical creation of entangled bosonic states in a double well

We study the creation of a bosonic N00N state from the evolution of a Fock state in a double well. While noninteracting bosons disappear quickly in the Hilbert space, the evolution under the influence of a Bose-Hubbard Hamiltonian is much more restricted. This restriction is caused by the fragmentation of the spectrum into a high-energy part with doubly degenerate levels and a nondegenerate low-energy part. This degeneracy suppresses transitions to states of the high-energy part of the spectrum. At a moderate interaction strength this effect supports strongly the dynamical formation of a N00N state. The N00N state is suppressed in an asymmetric double well, where the double degeneracy is absent.