  Atoms can be extracted from a trapped Bose-Einstein condensate (BEC) by
driving spin-flips to untrapped states. The coherence properties of the BEC are
transfered to the released atoms, creating a coherent beam of matter refered to
as an atom laser. In this work, the extraction of atoms from a BEC is
investigated numerically by solving a coupled set of Gross-Pitaevskii equations
in up to three dimensions. The result is compared to experimental data and a
semiclassical rate model. In the weak-coupling regime, quantitative agreement
is reached between theory and experiment and a semiclassical rate model. In the
strong-coupling regime, the atom laser enters a trapped state that manifests
itself in a saturation of the rate of out-coupled atoms observed in new
experimental data. The semiclassical rate model fails, but the numerical
descriptions yield qualitative agreement with experimental data at the onset of
saturation.
