Model of the atom laser with Raman outcoupling

In the present paper, the authors start from the interaction of a system of two-level atoms with an electromagnetic field to drive the interaction Hamiltonian between these two-level atoms. Second, introduce the equations of motion which describing the dynamics of atom laser depending on the interaction Hamiltonian, this interaction Hamiltonian will be used to describe the outcoupling process in a Raman atom laser. Also, the authors model the dynamics of an atom laser produced by outcoupling three-level atoms from a Bose-Einstein condensate (BEC) via a Raman transition and investigate the transfer of quantum statistics from one of the optical modes to the atomic field. Finally, the authors mathematical treatment leads to the same as equations appears in literature which allowed obtaining the dynamics for any atom laser systems.