Quantum theory of an atom laser originating from a Bose-Einstein   condensate or a Fermi gas in the presence of gravity
  We present a 3D quantum mechanical theory of radio-frequency outcoupled atom lasers from trapped atomic gases in the presence of the gravitational force. Predictions for the total outcoupling rate as a function of the radio-frequency and for the beam wave function are given. We establish a sum rule for the energy integrated outcoupling, which leads to a separate determination of the coupling strength between the atoms and the radiation field.   For a non-interacting Bose-Einstein condensate analytic solutions are derived which are subsequently extended to include the effects of atomic interactions. The interactions enhance interference effects in the beam profile and modify the outcoupling rate of the atom laser. We provide a complete quantum mechanical solution which is in line with experimental findings and allows to determine the validity of commonly used approximative methods.   We also extend the formalism to a fermionic atom laser and analyze the effect of superfluidity on the outcoupling of atoms. 
Tobias Kramer and Mirta Rodriguez