Markov approximation for the atomic output coupler

The regions of validity of the Markov approximation for the coupling of ato ms out of an atomic trap rut determined. We consider radio-frequency output coupling in the presence of gravity and collisional repulsion, and Raman o utput coupling. The Markov approximation is crucial in most theoretical des criptions of an atom laser that assume a continuous process of output coupl ing from a trapped Bose-Einstein condensate. In this regime many techniques that have proved to be useful for modeling the optical laser, such as mast er equations, can be used to describe the dynamics of the damping of the co ndensate mode undergoing output coupling. [S1050-2947(99)04904-5].