Abstract
The non-Markovian dynamics of a continuous-wave atom laser model is studied which includes gravitational effects and interactions inside the Bose-Einstein condensate. With the help of the time-convolutionless projection operator technique both the occupation number of the condensate and the spectrum of the atoms coupled out of the condensate are determined. A correct modeling of memory effects in the atom laser requires a generalization of the projection operator technique which takes into account correlations in the initial state of the combined atom-reservoir system. The non-Markovian evolution is shown to yield substantial deviations from results obtained in the Born-Markov approximation.