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.　©　2011　American　Physical　Society.