Wave mixing of optical pulses and Bose-Einstein condensates

We investigate theoretically the four-wave mixing of optical and matter waves resulting from the scattering of a short light pulse off an atomic Bose-Einstein condensate, as recently demonstrated by D. Schneble et al. [Science 300, 475 (2003)]. We show that atomic pair production from the condensate results in the generation of both forward- and backward-propagating matter waves. These waves are characterized by different phase-matching conditions, resulting in different angular distributions and temporal evolutions.