  In a recent experiment Campbell et al. [Phys. Rev. Lett. 96, 020406 (2006)]
observed degenerate four-wave mixing of matter-waves in a one-dimensional
optical lattice, a process with potential for generating entanglement among
atoms. We analyse the essential quantum features of the experiment to show that
entanglement is created between the quadratures of the two scattered atomic
clouds and is a true many-body (rather than two-body) effect. We demonstrate a
significant violation of entanglement inequalities that is robust to a moderate
level of coherent seeding. The system is thus a promising candididate for
generating macroscopically entangled atomic samples.
