Investigation of four-wave mixing of matter waves in Bose-Einstein condensates

We investigate the four-wave mixing of matter wave packets created from a Bose-Einstein condensate, realized experimentally by utilizing light pulses to create two high-momentum wave packets via. Bragg diffraction from a stationary condensate. Based on the Gross-Pitaevskii equation, a set of nonlinearly coupled envelope equations including self- and cross-phase modulational effects are derived systematically using a method of multiple-scales. The exact and explicit analytical solutions are provided for the coupled envelope equations and the evolution of the wave packets after turning off trapping potential is discussed and compared with experiment.