  We propose to generate Einstein-Podolsky-Rosen (EPR) entanglement between
groups of atoms in a two-well Bose-Einstein condensate using a dynamical
process similar to that employed in quantum optics. The local nonlinear S-wave
scattering interaction has the effect of creating a spin squeezing at each
well, while the tunneling, analogous to a beam splitter in optics, introduces
an interference between these fields that results in an inter-well
entanglement. We consider two internal modes at each well, so that the
entanglement can be detected by measuring a reduction in the variances of the
sums of local Schwinger spin observables. As is typical of continuous variable
(CV) entanglement, the entanglement is predicted to increase with atom number,
and becomes sufficiently strong at higher numbers of atoms that the EPR paradox
and steering non-locality can be realized. The entanglement is predicted using
an analytical approach and, for larger atom numbers, stochastic simulations
based on truncated Wigner function. We find generally that strong tunnelling is
favourable, and that entanglement persists and is even enhanced in the presence
of realistic nonlinear losses.
