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In a recent experiment Campbell et al. [Phys. Rev. Lett. 96, 020406 (2006)]observed degenerate four-wave mixing of matter-waves in a one-dimensionaloptical lattice, a process with potential for generating entanglement amongatoms. We analyse the essential quantum features of the experiment to show thatentanglement is created between the quadratures of the two scattered atomicclouds and is a true many-body (rather than two-body) effect. We demonstrate asignificant violation of entanglement inequalities that is robust to a moderatelevel of coherent seeding. The system is thus a promising candididate forgenerating macroscopically entangled atomic samples.Comment: 4 pages, 3 figure

Entanglement properties of degenerate four-wave mixing of matter waves in a periodic potential