Phase conjugation of multicomponent Bose-Einstein condensates

We consider a trapped multicomponent atomic Bose-Einstein condensate, concentrating specifically on condensates in the hyperfine ground state F=1, where spin exchange collisions result in a transfer of population between m=0 and m= +/-1 internal states. Drawing an analogy with the optical situation, we show that this system can be regarded as a matter-wave analog of optical multiwave mixing. This opens up the way to realize matter-wave phase conjugation, whereby an incident atomic beam can be ''time reversed.'' In addition, 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. [S1050-2947(99)03602-1].