Dynamics of parametric matter-wave amplification

We develop a model for parametric amplification, based on a density matrix approach, which naturally accounts for the peculiarities arising formatter waves: significant depletion and explicit time dependence of the source state population, long interaction times, and spatial dynamics of the amplified modes. We apply our model to explain the details in an experimental study on twin-atom beam emission from a one-dimensional degenerate Bose gas.