  Manipulating many body quantum systems is a challenge. A useful way to
achieve it would be to entangle the system to a diluted system, with a small
particle number. Preparation of such entangled states can be facilitated as
ground state of a many body Hamiltonian or the steady state of a many body open
quantum system. Here we study two-site lattice models with a conserved boson
number, biased to display a large occupancy in one of the sites. The Von
Neumann entanglement entropy as well as the Logarithmic negativity show a
typical power law decay in $R$, the occupancy ratio between the two sites.
These results imply that it is feasible to entangle a large many body system to
a single atom, as recently reported experimentally.
