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We revisit the coherent or delocalized to self-trapping transition in aninteracting bosonic quantum fluid confined in a double well potential, in thecontext of full quantum calculations. We show that an $N$-particle Bose-Hubbardfluid reaches an stationary state through the two-body interactions. Thesestationary states are either delocalized or self-trapped in one of the wells,the former appearing as coherent oscillations in the mean-field approximation.By studying one- and two-body properties in the energy eigenstates and in a setof coherent states, we show that the delocalized to self-trapped transitionoccurs as a function of the energy of the fluid, provided the interparticleinteraction is above a critical or threshold value. We argue that this is atype of symmetry-breaking continuous phase transition.

journal of physics. b, atomic molecular and optical physics/journal of physics. b, atomic, molecular and optical physics

Delocalization to self-trapping transition of a Bose fluid confined in a  double well potential. An analysis via one- and two-body correlation  properties