Entanglement via a three-well Bose-Hubbard system and via an optical beamsplitter

TL;DR

This paper compares entanglement generation in a three-well Bose-Hubbard system and an optical beamsplitter, highlighting differences in input conditions, nonlinearities, and time dependence, with analytic solutions for the non-interacting case.

Contribution

It provides a detailed comparison of entangling properties between the Bose-Hubbard model and beamsplitters, including analytic solutions and criterion sensitivity analysis.

Findings

Non-interacting Bose-Hubbard system does not produce entanglement from classical states.

Entanglement detection depends on measurement criteria, which can give contradictory results.

The Bose-Hubbard model's results are time-dependent, unlike the static beamsplitter case.

Abstract

We compare and contrast the entangling properties of a three-well Bose-Hubbard model and an optical beamsplitter. The coupling between the different modes is linear in both cases, and we may identify two output modes. Obvious differences are that our Bose-Hubbard model, with only the middle well initially occupied, does not have a vacuum input port, there is no equivalent of a collisional, $\chi^{(3)}$ nonlinearity with the beamsplitter, and the results of the Bose-Hubbard model show a time-dependence. In the non-interacting case, we obtain analytic solutions and show that, like a beamsplitter, the Bose-Hubbard system will not produce entanglement for classical initial states. We also show that whether inseparability or entanglement are detected depends sensitively on the criteria measured, with different criteria giving contradictory predictions.