Reduced density matrix descriptions for electromagnetically induced transparency and related pump-probe optical phenomena in atomic systems

Reduced density matrix descriptions are developed for linear and non-linear electromagnetic interactions of moving atomic systems, taking into account applied magnetic fields. Atomic collision processes are treated as environmental interactions. Applications of interest include electromagnetically induced transparency and related pump-probe optical phenomena in atomic vapors. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified manner. The standard Bonn (lowest-order perturbation-theory) and Markov (short-memory-time) approximations are systematically introduced within the framework of the general non-perturbative and non-Markovian formulations. A preliminary semiclassical treatment of the electromagnetic interaction is introduced. However, the need for a fully quantum mechanical approach is emphasized. Compact Liouville-space operator expressions are derived for the linear and the general (n'th order) non-linear electromagnetic-response tensors occurring in a perturbation-theory treatment of the electromagnetic interaction. These expressions can be evaluated for coherent initial atomic excitations and for the full tetradic-matrix form of the Liouville-space self-energy operator representing the environmental interactions in the Markov approximation. Intense-field electromagnetic interactions can be treated by means of an alternative method, which is based on a Liouville-space Floquet representation of the reduced density operator. Collisional interactions between atoms in a vapor can be treated in various approximations for the self-energy operator and the influence of Zeeman coherences on the electromagnetic response can be incorporated.