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 $m=0\mathrm{}$ and $m=\pm 1$ 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.

• Received 12 June 1998

DOI:https://doi.org/10.1103/PhysRevA.59.1509