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

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 the 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.