The theories of recoil-induced resonances (RIR) [J. Guo, P. R. Berman, B. Dubetsky, and G. Grynberg, Phys. Rev. A 46, 1426 (1992)] and the collective atomic recoil laser (CARL) [R. Bonifacio and L. De Salvo, Nucl. Instrum. Methods Phys. Res. A 341, 360 (1994)] are compared. Both theories can be used to derive expressions for the gain experienced by a probe field interacting with an ensemble of two-level atoms that are simultaneously driven by a pump field. It is shown that the underlying formalisms of the RIR and CARL are equivalent. Differences between the RIR and CARL arise because the theories are typically applied for different ranges of the parameters appearing in the theory. The RIR limit is one in which the time derivative of the probe field amplitude,
dE2/dt, depends locally on
E2(t) and the gain depends linearly on the atomic density, while the CARL limit is one in which ${\mathrm{dE}}_{2}/dt={\ensuremath{\int}}_{0}^{t}{f(t,t}^{\ensuremath{'}}{)E}_{2}{(t}^{\ensuremath{'}}{)dt}^{\ensuremath{'}},$ where f is a kernel, and the gain has a nonlinear dependence on the atomic density. Validity conditions for the RIR or CARL limits are established in terms of the various parameters characterizing the atom-field interaction. The probe gain for a probe-pump detuning equal to zero is analyzed in some detail, in order to understand how gain arises in a system which, at first glance, appears to have a symmetry that would preclude the possibility for gain. Moreover, it is shown that these calculations, carried out in perturbation theory, have a range of applicability beyond the recoil problem. Experimental possibilities for observing CARL are discussed.
We present a theoretical study of the interaction between light and a cold gasof three-level, ladder configuration atoms close to two-photon resonance. In particular, weinvestigate the existence of collective atomic recoil lasing (CARL) instabilities in differentregimes of internal atomic excitation and compare to previous studies of the CARL instabilityinvolving two-level atoms. In the case of two-level atoms, the CARL instability is quenchedat high pump rates with significant atomic excitation by saturation of the (one-photon)coherence, which produces the optical forces responsible for the instability and rapid heatingdue to high spontaneous emission rates. We show that in the two-photon CARL schemestudied here involving three-level atoms, CARL instabilities can survive at high pump rateswhen the atoms have significant excitation, due to the contributions to the optical forces frommultiple coherences and the reduction of spontaneous emission due to transitions betweenthe populated states being dipole forbidden. This two-photon CARL scheme may form thebasis of methods to increase the effective nonlinear optical response of cold atomic gases.
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.