Theory of four-wave mixing of matter waves from a Bose-Einstein condensate- art. no. 023608

A recent experiment [Deng et at, Nature (London) 398, 218 (1999)] demonstra ted four-wave mixing of matter wave packets created from a Bose-Einstein co ndensate. The experiment utilized light pulses to create two high-momentum wave packets via Bragg diffraction from a stationary Bose-Einstein condensa te. The high-momentum components and the initial low-momentum condensate in teract to form a new momentum component due to the nonlinear self-interacti on of the bosonic atoms. We develop a three-dimensional quantum- mechanical description, based on the slowly-varying-envelope approximation, for four- wave mixing in Bose-Einstein condensates using the time-dependent Gross-Pit aevskii equation. We apply this formulation to describe the experimental ob servations and to make predictions. We examine the role of phase-modulation , momentum, and energy conservation (i.e., phase matching), and particle nu mber conservation in four-wave mixing of matter waves, and develop simple m odels for understanding our numerical results.