Optical control of atoms laser instability

In this paper, we propose a method to control the quantum atom laser instability by using optical radiation. The control can be achieved by changing the scattering length via the optical coupling constant. This method is applied in the scheme of Raman induced transitions by using out of resonance CW laser, and involves three occupation levels in the condensed atoms. These atoms in Λ configuration are described by a Reformed Gross-Pitaevskii equation (RGPE), together with a rate equation. The system is considered to be nonconservative complex Ginzburg Landau equation (CGLE) description from where we use the Benjamin-Feir stability criterium. This method allows us a theoretical description of any atom beam even for a negative values of the interaction constant, as is the case for 7Li; our results are in accordance with other results obtained by numerical methods.