  We show how one can prepare and detect entanglement and
Einstein-Podolsky-Rosen (EPR) steering between two distinguishable groups
(modes) of atoms in a Bose-Einstein condensate (BEC) atom interferometer. Our
paper extends previous work that developed criteria for two-mode entanglement
and EPR steering based on the reduced variances of two spins defined in a
plane. Observation of planar spin squeezing will imply entanglement, and
sufficient planar spin squeezing implies EPR steering, between the two groups
of atoms. By using a two-mode dynamical model to describe BEC interferometry
experiments, we show that the two-mode entanglement and EPR steering criteria
are predicted to be satisfied for realistic parameters. The reported
observation of spin squeezing in these parameter regimes suggests it is very
likely that the criteria can be used to infer an EPR steering between
mesoscopic groups of atoms, provided the total atom number can be determined to
sub-Poissonian uncertainty. The criteria also apply to a photonic Mach-Zehnder
interferometer. Finally, we give a method based on the amount of planar spin
squeezing to determine a lower bound on the number of particles that are
genuinely comprise the two-mode EPR steerable state - the so-called two-mode
EPR steering depth.
