  We investigate the atom-optical analog of degenerate four-wave mixing of
photons by colliding two Bose-Einstein condensates (BECs) of metastable helium
and measuring the resulting momentum distribution of the scattered atoms with a
time and space resolved detector. For the case of photons, phase matching
conditions completely define the final state of the system, and in the case of
two colliding BECs, simple analogy implies a spherical momentum distribution of
scattered atoms. We find, however, that the final momenta of the scattered
atoms instead lie on an ellipsoid whose radii are smaller than the initial
collision momentum. Numerical and analytical calculations agree well with the
measurements, and reveal the interplay between many-body effects, mean-field
interaction, and the anisotropy of the source condensate.
