Statistics of atomic populations in output coupled wave packets from Bose-Einstein condensates: Four-wave mixing - art. no. 013606

The statistics of the atomic population distributions in nonlinear matter-w ave processes, such as four-wave mixing of matter waves (or output coupled wave packets produced by Bragg scattering) from Bose-Einstein condensates ( BECs), an 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 BEG, (b) quantum flu ctuations arising from finite temperature effects, and (c) the quantum-mech anical nature of the mean-field BEC wave function. We focus on the latter s ource 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 distri bution. The differences in the nature of the fluctuations in nonlinear phen omena for atoms (matter waves) and photons are discussed.