Theory of a collective atomic recoil laser - art. no. 053810

We perform a study of a collective atomic recoil laser (CARL) that goes bey ond the initial growth period. The study is based on a theory that treats b oth internal and external degrees of atomic freedom quantum mechanically bu t regards the laser light as a classical field obeying Maxwell's equations. We introduce the concepts of momentum families and diffraction groups and organize the matter wave equations in terms of diffraction groups. The stea dy-state lasing conditions are discussed in connection with the probe gain in the recoil-induced resonances. The nontrivial steady states and the line ar stability analysis of the steady states are both carried out by the meth od of two-dimensional continued fractions. Both stable and unstable nontriv ial steady states are calculated and discussed in the context of regarding the CARL as multiwave mixing involving many modes of matter waves and two o ptical fields.