Entanglement criteria for two strongly interacting ensembles

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 (numbersqueezing-like criteria) can witness the ensemble-ensemble entanglement for a finite number of particles. We also mention the implementations of these criteria to two-component condensate systems and nanoscale quantum plasmonics.