  We consider a multicomponent atomic Bose-Einstein condensate optically
trapped in a far-off resonant dipole trap. Drawing an analogy with the optical
situation, we show that this system can be regarded as an matter-wave analog of
optical multiwave mixing. We concentrate specifically on condenstates in the
hyperfine ground state F=1, in which case a simple analogy with optical
four-wave mixing can be established. This opens up the way to realize
matter-wave phase conjugation, whereby an atomic beam can be ``time-reversed.''
In addition to transfering population between a "central" mode and incident and
retroreflecting beams, matter-wave phase conjugation also offers novel
diagnostic tools to study the coherence properties of condensates, as well as
to measure the relative scattering lengths of hyperfine sublevels.
