Polariton-Type Dispersion Laws for Three-Level Atoms Interacting with Two Laser Radiation Pulses

Abstract

Behavioral features of polariton dispersion laws are studied for three-level atoms interacting with two coherent laser radiation pulses with frequencies ω1 and ω2 that are in resonance with optically resolved one-photon transitions between levels $$1 \leftrightarrows 2$$ and $$2 \leftrightarrows 3$$ , respectively, and with regard to the direct two-photon transition between levels 1 and 3. The approximation of given photon densities of both pulses compared with the densities of atoms is used. It is shown that the dispersion law consists of three branches whose position and shape are determined by the Rabi frequencies of the above three optical transitions and the photon densities in both pulses. The direct consideration of all three optical transitions leads to the dependence of the dispersion law of atomic polaritons on a new quantum parameter—the phase difference between the three Rabi frequencies. The values of the system parameters are found for which the branches of the dispersion law may intersect. The concept of the surface of the dispersion law is introduced in the dependence of the eigenfrequencies of atomic polaritons on the photon wave vectors in both pulses.