" I will discuss the ground state properties of a system of interacting bosons trapped by a double-well potential, in a joint limit of large inter-well separation and high potential barrier. The leading-order physics of the model is governed by a Bose-Hubbard Hamiltonian coupling two one-body modes, each supported in the bottom of one well. Fluctuations beyond these two modes are described by Bogoliubov's theory. Our main result is that, when the system is in the ground state, the variance of the number of particles occupying the low-energy modes is suppressed. This is a violation of the central limit theorem that typically holds in the occurrence of Bose-Einstein condensation, and therefore a signature of the emergence of strong correlations in the ground state. We achieve this result by proving a precise ground state energy expansion in terms of Bose-Hubbard and Bogoliubov energies. Joint work with Nicolas Rougerie (ENS Lyon) and Dominique Spehner (Universidad de Concepciòn)."