Quantum signatures of the self-trapping transition in attractive lattice bosons

We consider the Bose-Hubbard model describing attractive bosonic particles hopping across the sites of a translation-invariant lattice and compare the relevant ground-state properties with those of the corresponding symmetry-breaking semiclassical nonlinear theory. The introduction of a suitable measure allows us to highlight many correspondences between the nonlinear theory and the inherently linear quantum theory, characterized by the well-known self-trapping phenomenon. In particular we demonstrate that the localization properties and bifurcation pattern of the semiclassical ground state can be clearly recognized at the quantum level. Our analysis highlights a finite-number effect.