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

Marek Trippenbach, Y. B. Band, P. S. Julienne

Research output: Contribution to journalArticlepeer-review

98 Scopus citations


A recent experiment [Deng et al., Nature (London) 398, 218 (1999)] demonstrated four-wave mixing of matter wave packets created from a Bose-Einstein condensate. The experiment utilized light pulses to create two high-momentum wave packets 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-envelope approximation, for four-wave mixing in Bose-Einstein condensates using the time-dependent Gross-Pitaevskii equation. We apply this formulation 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.

Original languageEnglish
Pages (from-to)23608-23601
Number of pages8
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number2
StatePublished - 19 Jul 2000


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