Title : Classical, Semi-Classical, and Quantum-Field Descriptions for Light-Matter Interactions
Abstract: Classical, semi-classical, and quantum-field descriptions for the interaction of light with matter are systematically discussed. The primary applications of interest include the precise determination 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. The 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 formalism. 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. It is emphasized that a quantized-field approach is essential for a fully self-consistent quantum-mechanical formulation. Compact Liouville-space operator expressions are derived for the linear and general (n'th order) non-linear electromagnetic-response tensors describing moving many-electron atomic systems. The tetradic matrix elements of the Liouville-space self-energy operators are evaluated for environmental collisional and radiative interactions to provide explicit forms for the kinetic equations and the spectral line shape formulas. Work supported by the Office of Naval Research through the Basic Research Program at The Naval Research Laboratory.