PROCEEDINGS ARTICLE | March 7, 2016

Proc. SPIE. 9763, Slow Light, Fast Light, and Opto-Atomic Precision Metrology IX

KEYWORDS: Slow light, Transparency, Optical properties, Particles, Magnetism, Nonlinear optics, Electromagnetism, Radio propagation, Charged particle optics, Maxwell's equations

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 (nth 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.