Steady states and instabilities of collective atomic recoil laser

Summary form only given. The collective atomic recoil laser (CARL) was proposed as an atomic analog of the free electron laser. Recently, there has been an increased interest in the CARL primarily because it can be regarded as a parametric amplifier for the momentum side modes. Our CARL model consists of a cavity CARL signal of wave number k/sub 1/, and an opposing non-depletion pump field of k/sub 2/, and a steady flow of an ultra-cold two-level atomic beam along a direction normal to the propagation of the fields. Both fields are assumed to be far-off resonance. A momentum change of /spl planck/K, where K = k/sub 1/ + k/sub 2/, takes place in each virtual two-photon process. This allows us to divide the total momentum space into different momentum families, and each momentum family into different diffraction groups.