  Einstein, Podolsky & Rosen (EPR) pointed out that correlations induced
between quantum objects will persist after these objects have ceased to
interact. Consequently, their joint continuous variables (CV), e.g., the
difference of their positions and the sum of their momenta, may be specified,
regardless of their distance, with arbitrary precision. EPR correlations give
rise to two fundamental notions: {\em nonlocal ``steering''} of the quantum
state of one object by measuring the other, and inseparability ({\em
entanglement}) of their quantum states. EPR entanglement is a resource of
quantum information (QI) and CV teleportation of light and matter waves. It has
lately been demonstrated for {\em collective} CV of distant thermal-gas clouds,
correlated by interaction with a common field. Here we demonstrate that
collective CV of two species of trapped ultracold bosonic gases can be
EPR-correlated (entangled) via {\em inherent} interactions between the species.
This paves the way to further QI applications of such systems, which are atomic
analogs of coupled superconducting Josephson Junctions (JJ). A precursor of
this study has been the observation of quantum correlations (squeezing) in a
single bosonic JJ.
