Phase-dependent nonlinear optics with double-A atoms

We present a theory of a continuous-wave light propagation in a medium of a toms with a double-Lambda configuration of levels. This is a configuration with a dosed cycle of radiation-induced transitions. An interference of exc itation channels in such closed-loop systems leads to a strong dependence o f the atomic state on the relative phase and the relative amplitudes of app lied electromagnetic waves. Therefore, the medium response may be controlle d by the phases. On the other hand, the phases themselves change during the propagation. Thus the state of the medium and all the field parameters are tightly coupled to each other in the present problem. We consider the prop agation of four-frequency laser radiation through the double-Lambda medium for two situations. At resonant or near-resonant excitation of atoms, both the medium and the held evolve into a nonabsorbing state. This state implie s specific coherent superposition for atoms ("dark state''), and particular relations for the held phases, amplitudes, and frequencies. In this way, t he propagation results in the phase, amplitude, and frequency matching of t he laser waves. In the second case, one Lambda system in double-Lambda atom s is excited resonantly, while the second Lambda system is far off resonanc e. Such an excitation scheme ensures the preparation of atoms in the nearly dark state throughout the medium. Therefore, the total light energy is dis sipated very weakly, whereas each individual laser wave can vary considerab ly along the propagation path. We have found that the resonant fields chang e as much as the far-detuned ones. The intensities oscillate sinusoidally w ith the optical length, with the energy being transferred back and forth be tween two waves in each frequency pair, resonant and far detuned. This give s the possibility for an almost lossless amplification of two of the laser waves, or an even generation of one of them. [S1050-2947(99)04412-1].