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Manipulating many body quantum systems is a challenge. A useful way toachieve it would be to entangle the system to a diluted system, with a smallparticle number. Preparation of such entangled states can be facilitated asground state of a many body Hamiltonian or the steady state of a many body openquantum system. Here we study two-site lattice models with a conserved bosonnumber, biased to display a large occupancy in one of the sites. The VonNeumann entanglement entropy as well as the Logarithmic negativity show atypical 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 toa single atom, as recently reported experimentally.

Power law decay of entanglement quantifiers in a single agent to a many body system coupling