Normal modes of strictly resonant and quasi-resonant regimes of electromagnetically induced transparency

Abstract

We report the results of a theoretical study of the evolution of a probe pulse under electromagnetically induced transparency conditions in the lambda scheme of degenerate inhomogeneously broadened quantum transitions. It is assumed that the interacting fields are elliptically polarised, and their effect on the medium can be either strictly resonant or quasi-resonant. It is shown that probe light in a medium can be represented as the sum of two normal modes, i.e. quasi-monochromatic elliptically polarised fields propagating independently of each other. The major axis of the polarisation ellipse of the normal mode of the first type is parallel, and that of the second type is perpendicular to the major axis of the polarisation ellipse of the control light. Due to the fact that velocities of normal-mode pulses are different, a single probe pulse entering a medium splits into individual pulses inside the medium, each of which transfers the energy of one of the normal modes. In the case of quasi-resonance, the splitting occurs at a shorter distance than in the case of strict resonance. If normal modes are not phase modulated at the input surface of the medium, then in the case of quasi-resonance they become phase modulated during their propagation inside the medium, whereas this does not occur in the case of strict resonance. It is shown that in the case of quasi-resonance, the phase modulation value of the mode of the second of the above types significantly exceeds that of the first type. The medium transparency for the normal mode of the first type slightly decreases with the transition from the case of strict resonance to the case of quasi-resonance, while the medium transparency for the mode of the second type decreases significantly. The total probe field, which is the sum of the normal modes, has phase modulation before it splits into mode pulses in cases of both strict resonance and quasi-resonance, even if it does not have it on the input surface.