Statistics of atomic populations in output coupled wave packets from Bose-Einstein condensates: Four-wave mixing

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Abstract
The statistics of the atomic population distributions in nonlinear matter-wave processes, such as four-wave mixing of matter waves (or output coupled wave packets produced by Bragg scattering) from Bose-Einstein condensates (BECs), are determined. Fluctuations of the populations of atoms in the four-wave mixing wave packet can be due to (a) fluctuations of the laser fields that produce the separate momentum wave packets of the BEC, (b) quantum fluctuations arising from finite temperature effects, and (c) the quantum-mechanical nature of the mean-field BEC wave function. We focus on the latter source of fluctuations. The distribution of the number of atoms in the four-wave mixing wave packet is binomial and reduces to a Gaussian distribution for strong conversion. We calculate the skewness and kurtosis of the distribution. The differences in the nature of the fluctuations in nonlinear phenomena for atoms (matter waves) and photons are discussed.