COLLECTIVE-VARIABLES DESCRIPTION OF THE ATOMIC-RECOIL LASER

We propose a description of the collective atomic-recoil laser based o n a set of nonlinear differential equations for an appropriate set of collective variables. The main obvious advantage of this description i s that, when applicable, it can describe systems having an arbitrary n umber of particles. A comparison between the predictions of the collec tive equations and those of their microscopic counterparts shows a sat isfactory level of accuracy, even during the nonlinear stage of the ev olution. The linearized version of the collective equations is especia lly useful for the study of the small-signal gain or absorption spectr um and the analysis of the start-up process.