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

TL;DR

This paper investigates how entanglement measures decay with occupancy ratio in a two-site bosonic system, revealing a power law decay that supports entangling large many-body systems with a single atom, with implications for quantum control.

Contribution

It demonstrates a power law decay of entanglement quantifiers in a two-site bosonic model, linking occupancy ratio to entanglement strength and facilitating large system entanglement.

Findings

Entanglement measures decay as a power law with occupancy ratio R.

The results support the feasibility of entangling large systems with a single atom.

Power law decay observed in both Von Neumann entropy and Logarithmic negativity.

Abstract

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.