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We consider a Bose-Einstein condensate in a double-well potential undergoinga dynamical transition from the regime of Josephson oscillations to the regimeof self-trapping. We analyze the statistical properties of the ground state (orthe highest excited state) of the Hamiltonian in these two regimes forattractive (repulsive) interactions. We demonstrate that it is impossible todescribe the transition within the mean-field theory. In contrast, thetransition proceeds through a strongly correlated delocalized state, with largequantum fluctuations, and spontaneous breaking of the symmetry.

Macroscopic self trapping in BECs: analysis of a dynamical quantum phase transition