Phase conjugation of trapped Bose-Einstein condensates
  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. 
Elena V. Goldstein and Pierre Meystre