Microscopic and macroscopic descriptions of electromagnetic-field propagation relevant to resonant pumpprobe optical phenomena, such as electromagnetically induced transparency, in quantized many-electron systems are formulated within the framework of a general reduced-density-matrix approach. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified and self-consistent manner. A semiclassical perturbation-theory treatment of the electromagnetic interaction is adopted, in which the electromagnetic field is described as a classical field satisfying either the microscopic form or the macroscopic form of the Maxwell equations. However, it is emphasized that a quantized-field approach is essential for a fully self-consistent quantummechanical formulation. Compact Liouville-space operator expressions are obtained for the linear and the general (n'th order) non-linear electromagnetic-response tensors for moving many-electron systems. These expressions can be evaluated for coherent initial electronic excitations and for the full tetradic-matrix form of the Liouville-space selfenergy operator in the Markov (short-memory-time) approximation. Environmental interactions can be treated in terms of the Liouville-space self-energy operator, and the influence of Zeeman coherences on electromagnetic-field propagation can be investigated by including an applied magnetic field together with the electromagnetic field.
A reduced-density-matrix description is developed for linear and non-linear electromagnetic interactions of quantized electronic systems in the presence of environmental decoherence and relaxation phenomena. Applications of interest include many-electron atomic systems (in electron-ion beam interactions, gases, and high-temperature plasmas) and semiconductor materials (bulk crystals and nanostructures). Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified manner. The standard Born (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. Compact Liouville-space operator expressions are derived for the linear and the general (n’th order) non-linear electromagnetic-response tensors, allowing for coherent initial electronic excitations and for the full tetradic-matrix form of the Liouville-space self-energy operator representing the environmental interactions. It is emphasized that quantum-coherent many-body interactions cannot be adequately treated as environmentally induced phenomena.
Linear and nonlinear (especially coherent) electromagnetic interactions of moving many-electron atoms are investigated using a reduced-density-matrix description, which is applied to electromagnetically induced transparency and related resonant pump-probe optical phenomena. External magnetic fields are included on an equal footing with the electromagnetic fields and spin-Zeeman interactions are taken into account. Complimentary time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the reduced-density-matrix description are self-consistently developed. The general nonperturbative and non-Markovian formulations provide a fundamental framework for systematic evaluations of corrections to the standard Born (lowest-order-perturbation) and Markov (short-memory-time) approximations. The macroscopic electromagnetic response is described semiclassically, employing a perturbation expansion of the reduced-density operator in powers of the classical electromagnetic field. Our primary results are compact Liouville-space operator expressions for the linear and general (
nth-order) nonlinear macroscopic electromagnetic-response tensors, which can be evaluated for nonlocal and nonstationary optical media described by multilevel atomic-system representations. Interactions among atoms and with environmental photons are treated as line-broadening effects by means of a general Liouville-space self-energy operator, for which the tetradic-matrix elements are explicitly evaluated in the diagonal, lowest-order, and Markov approximations. The compact Liouville-space operator expressions that are derived for the macroscopic electromagnetic-response tensors are introduced into the dynamical description of the electromagnetic-field propagation. It is pointed out that a quantized-electromagnetic-field approach will be required for a fully self-consistent quantum-mechanical treatment of local-field effects and radiative corrections.