Correlation-based entanglement criterion in bipartite multiboson systems

TL;DR

This paper introduces a correlation-based entanglement detection criterion for bipartite multiboson systems, applicable to systems like entangled Bose-Einstein condensates and photon pairs, demonstrating broad detection capabilities.

Contribution

It presents a novel entanglement criterion based on Gell-Mann matrix correlations tailored for multi-boson systems, extending entanglement detection methods to complex quantum states.

Findings

Entanglement can be detected across all parameter regions with the proposed criterion.

The criterion is applicable to various systems, including BECs and photon pairs.

Alternative criteria are discussed with their respective advantages.

Abstract

We describe a criterion for the detection of entanglement between two multi-boson systems. The criterion is based on calculating correlations of Gell-Mann matrices with a fixed boson number on each subsystem. This applies naturally to systems such as two entangled spinor Bose-Einstein condensates. We apply our criterion to several experimentally motivated examples, such as an $ S^z S^z $ entangled BECs, ac Stark shift induced two-mode squeezed BECs, and photons under parametric down conversion. We find that entanglement can be detected for all parameter regions for the most general criterion. Alternative criteria based on a similar formalism are also discussed together with their merits.