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Theory of Four-Wave Mixing of Matter Waves from a Bose-Einstein Condensate



M Trippenbach, Y B. Band, Paul S. Julienne


A recent experiment [Deng et al., Nature 398, 218 (1999)] demonstrated the four-wave mixing of matter wavepackets created from a Bose-Einstein condensate. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose-Einstein condensate. The high-momentum components and the initial low momentum condensate interact to form a new momentum component due to the nonlinear self-interaction of the bosonic atoms. We develop a three-dimensional quantum mechanical description, based on the slowly-varying-envelop approximation, for four-wave mixing in Bose-Einstein condensates using the time-dependent Gross-Pitaevskii equation and apply this description to describe the experimental observations and to make predictions. We examine the role of phase-modulation, momentum and energy conservation (i.e., phase-matching), and particle number conservation in four-wave mixing of matter waves, and develop simple models for understanding our numerical results.
Physical Review A (Atomic, Molecular and Optical Physics)
No. 2


Bose-Einstein condensate, four-wave mixing, Gross-Pitaevskii equation, matter waves


Trippenbach, M. , Band, Y. and Julienne, P. (2000), Theory of Four-Wave Mixing of Matter Waves from a Bose-Einstein Condensate, Physical Review A (Atomic, Molecular and Optical Physics) (Accessed February 27, 2024)
Created July 31, 2000, Updated October 12, 2021