Short pulses of normal modes of electromagnetically induced transparency

The process of propagation of short probe pulses of electromagnetically induced transparency has been analyzed theoretically in the case of elliptically polarized control radiation. As a model of a resonant medium, a $\Lambda$ scheme of quantum transitions between the $^{3}$P$_{0}$, $^{3}$P$_{1}^{0}$ и $^{3}$P$_{2}$ degenerate levels of the $^{208}$Pb isotope has been used. The situation in which the probe radiation is rather weak compared to the control radiation has been examined. In this case, the field of the probe pulse can be represented as a sum of the fields of two elliptically polarized pulses that propagate in the medium independently of one another without changing their polarization state, which makes it possible to interpret them as nonstationary normal modes. Numerical simulation has shown that the structure of normal modes depends on the ratio of the width of the spectrum of the input probe pulse to the Doppler frequency broadening of the quantum transition that is resonant to the probe field. If this ratio is small, each mode in the medium is a single pulse similar to the input probe pulse. Under these conditions, the propagation of each normal mode in the medium can be fairly well characterized by the group velocity depending on the intensity and the state of polarization of the control radiation. As this ratio increases, normal modes in the medium initially acquire the shape of a regular decaying train of pulses, and then their structure becomes chaotic. The described evolution is accompanied by an increase in the energy absorption of the probe radiation by the medium and by a significant deterioration in the applicability of the notion of group velocity for describing the propagation process of normal modes.