  We study atom scattering from two colliding Bose-Einstein condensates using a
position sensitive, time resolved, single atom detector. In analogy to quantum
optics, the process can also be thought of as spontaneous, degenerate four wave
mixing of de Broglie waves. We find a clear correlation between atoms with
opposite momenta, demonstrating pair production in the scattering process. We
also observe a Hanbury Brown and Twiss correlation for collinear momenta, which
permits an independent measurement of the size of the pair production source
and thus the size of the spatial mode. The back to back pairs occupy very
nearly two oppositely directed spatial modes, a promising feature for future
quantum optics experiments.
