  We study the coherent cooperative phenomena of the system composed of two
interacting atomic ensembles in the thermodynamic limit. Remarkably, the system
exhibits the Dicke-like quantum phase transition and entanglement behavior
although the governing Hamiltonian is fundamentally different from the
spin-boson Dicke Hamiltonian, offering the opportunity for investigating
collective matter-light dynamics with pure matter waves. The model can be
realized with two Bose-Einstein condensates or atomic ensembles trapped in two
optical cavities coupled to each other. The interaction between the two
separate samples is induced by virtual photon exchange.
