0 A model of a pumped continuous atom laser

At the end of the millennium a continuous wave (cw) pumped atom laser remains to be experimentally demonstrated. The prototype atom lasers that have been operated have used rapidly pulsed or continuous output coupling, but lacked pumping of the trapped atom laser mode [1,2], as is needed for a cw laser system. Indeed, apart from simple rate equation descriptions, existing theoretical models do not incorporate both pumping of the laser mode and propagation of the out-coupled beam. We have used the macroscopic wave-function approximation, or mean field approximation, which leads to the Gross-Pitaevskii (GP) equation, as the basis for a complete cw atom laser model. The macroscopic wave-function is the order parameter for a Bose-Einstein condensate of atoms. Our model system is schematically illustrated in Fig. 1. It includes a pumped reservoir of un-condensed atoms irreversibly coupled to the atom laser mode [3]. The condensed atoms in this mode, and in the output beam, undergo two-body interactions and three body recombination. The atoms are reversibly coupled from the atom laser mode to the output beam by a Raman process [1,3]. We solve the resulting system of coupled differential equations numerically in one spatial dimension. The macroscopic wave-function of the output atoms is analysed to determine quantities such as linewidth. Previous work based on systems of coupled equations of the complex Ginzburg-Landau type (GP equations with gain and loss) has either neglected important physics, such as