Entanglement Generation and Dynamics for a Bose-Hubbard model in a Double-Well Potential

TL;DR

This paper investigates the generation and evolution of entanglement in a two-site Bose-Hubbard model, analyzing various physical scenarios and quantifying entanglement resources using negativity and entanglement of formation.

Contribution

It provides a comprehensive analysis of entanglement dynamics in a two-site Bose-Hubbard system across multiple physical conditions, including ground state, finite temperature, and dissipation.

Findings

Entanglement is generated in various physical regimes.

Negativity effectively measures entanglement in the system.

Lower bounds of entanglement of formation are calculated.

Abstract

The study of entanglement between bosonic systems is of primary importance for establishing feasible resources needed for implementing quantum information protocols, both in their interacting atomic or photonic realizations. Atomic systems are particularly efficient in the production of large amounts of entanglement, providing higher information density than conventional qubit entangled states. Such increased quantum resources pave the way to novel fundamental tests of nature and efficient applications in quantum information, metrology and sensing. We consider a basic setup made up of two parties A and B, each one populated by a single level bosonic variable. The bosons are interacting and can hop between A and B, thus describing a two-site Bose-Hubbard Hamiltonian. We consider the generation of quantum states in several situations that cover the majority of physical realizations: ground state, finite temperature, unitary dynamics, dissipation through dephasing and loss of particles. The system is analyzed through truncated exact diagonalization, as a function of the microscopic parameters. The non separability of the obtained quantum states is estimated by means of the negativity, which has recently been proven to be a suitable measure of entanglement. Finally, we calculate lower bounds of the entanglement of formation, an indicator that quantifies the minimal amount of entanglement resources needed to build up such states.