# Entanglement criteria for two strongly interacting ensembles

## TL;DR

This paper investigates entanglement between two atomic ensembles undergoing a quantum phase transition, deriving criteria to detect entanglement that are effective even for finite particle numbers and discussing potential experimental implementations.

## Contribution

The authors introduce new entanglement criteria that can detect ensemble-ensemble entanglement in finite systems, extending beyond existing thermodynamic-limit methods.

## Key findings

- Entanglement accompanies the quantum phase transition in interacting ensembles.
- New criteria successfully detect entanglement in finite particle systems.
- All criteria work in the thermodynamic limit, with some only effective for finite systems.

## Abstract

Two interacting atomic ensembles display a Dicke-like quantum phase transition above a critical coupling strength. We show that an ensemble-ensemble entanglement accompanies the quantum phase transition. We derive entanglement criteria, which can witness the entanglement of the two interacting ensembles. We observe that all criteria are successful in the thermodynamic limit, while only the newly introduced ones~(number squeezing-like criteria) can witness the ensemble-ensemble entanglement for a finite number of particles. We also mention about implementations of these criteria to two-component condensate systems and nanoscale quantum plasmonics.