Classical, semi-classical, and quantized-field descriptions of light propagation in general non-local and non-stationary dispersive and absorbing media

摘要

Classical, semi-classical, and quantum-field descriptions for the interaction of light with matter are systematically discussed. Applications of interest include precise determinations of the linear and the non-linear electromagnetic response relevant to resonant pump-probe optical phenomena, such as electromagnetically induced transparency. In the quantum-mechanical description of matter systems, we introduce a general reduced-density-matrix framework. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified and self-consistent manner, using a Liouville-space operator representation. A preliminary semi-classical perturbation treatment of the electromagnetic interaction is adopted, in which the electromagnetic field is described as a classical field satisfying the Maxwell equations. Compact Liouville-space operator expressions are derived for the linear and the general (n'th order) non-linear electromagnetic-response tensors describing moving many-electron systems. The tetradic matrix elements of the Liouville-space self-energy operators, which are introduced in the time-domain and frequency-domain formulations, are evaluated for environmental collisional and radiative interactions, in order to provide explicit forms for the quantum kinetic equations and the spectral-line shape formulas. It is emphasized that a quantized-field approach is essential for a fully self-consistent quantum-mechanical description of the interacting light-matter system.