Quantum multimode model of elastic scattering from Bose Einstein condensates

Mean field approximation treats only coherent aspects of the evolution of a Bose Einstein condensate. However, in many experiments some atoms scatter out of the condensate. We study an analytic model of two counter-propagating atomic Gaussian wavepackets incorporating dynamics of incoherent scattering processes. Within the model we can treat processes of elastic collision of atoms into the initially empty modes, and observe how, with growing occupation, the bosonic enhancement is slowly kicking in. A condition for bosonic enhancement effect is found in terms of relevant parameters. Scattered atoms form a squeezed state that can be viewed as a multi-component condensate. Not only are we able to calculate the dynamics of mode occupation, but also the full statistics of scattered atoms.