Reduced-density-matrix description for pump-probe optical phenomena in moving atomic systems

Abstract

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 ($n\text{th}$-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.