Comparison of recoil-induced resonances and the collective atomic recoil laser

The theories of recoil-induced resonances (RIR) [J. Guo, P. R. Berman, B. D ubetsky, and G. Grynberg, Phys. Rev. A 46, 1426 (1992)] and the collective atomic recoil laser (CARL) [R. Bonifacio and L. De Salvo, Nucl. Instrum. Me thods Phys. Res. A 341, 360 (1994)] are compared. Both theories can be used to derive expressions for the gain experienced by a probe held interacting with an ensemble of two-level atoms that are simultaneously driven by a pu mp field. It is shown that the underlying formalisms of the RIR and CARL ar e equivalent. Differences between the RIR and CARL arise because the theori es are typically applied for different ranges of the parameters appearing i n the theory. The RIR Limit is one in which the time derivative of the prob e field amplitude, dE(2)/dt, depends locally on E-2(t) and the gain depends linearly on the atomic density, while the CARL limit is one in which dE(2) /dt=integral(0)(t)f(t,t')E-2(t')dt', where f is a kernel, and the gain has a nonlinear dependence on the atomic density. Validity conditions for the R IR or CARL limits are established in terms of the Various parameters charac terizing the acorn-field interaction. The probe gain for a probe-pump detun ing equal to zero is analyzed in some detail, in order to understand how ga in arises in a system which, at first glance, appears to have a symmetry th at would preclude the possibility for gain. Moreover, it is shown that thes e calculations, carried out in perturbation theory, have a range of applica bility beyond the recoil problem. Experimental possibilities for observing CARL are discussed. [S1050-2947(99)05601-2].