  We investigate an atomic ensemble of interacting bosons trapped in a
symmetric double well potential in contact with a single tightly trapped ion
which has been recently proposed [R. Gerritsma et al., Phys. Rev. Lett. 109,
080402 (2012)] as a source of entanglement between a Bose-Einstein condensate
and an ion. Compared to the previous study, the present work aims at performing
a detailed and accurate many-body analysis of such combined atomic quantum
system by means of the ab-initio multi-configuration time-dependent Hartree
method for bosons, which allows to take into account all correlations in the
system. The analysis elucidates the importance of quantum correlations in the
bosonic ensemble and reveals that entanglement generation between an ion and a
condensate is indeed possible, as previously predicted. Moreover, we provide an
intuitive picture of the impact of the correlations on the out-of-equilibrium
dynamics by employing a natural orbital analysis which we show to be indeed
experimentally verifiable.
