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physica status solidi (b)

Interaction of Crystal Impurity Centres with a Coherent Electromagnetic Field

Pavel A Apanasevich, Vladimir I. Kruglov, Igor E. Tralle

Published Oct 1, 1986• 2 citations
Publisher

Abstract

Abstract By the projection operator technique the non‐Markovian kinetic equation for the density matrix of a crystal impurity centre in an external electromagnetic field is derived, taking into account the electron–phonon interaction. The analytical solutions of this equation are obtained for the external field as an ultrashort pulse and in the case of a monochromatic wave.

DOI
10.1002/pssb.2221370226

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Abstract By the projection operator technique the non‐Markovian kinetic equation for the density matrix of a crystal impurity centre in an external electromagnetic field is derived, taking into account the electron–phonon interaction. The analytical solutions of this equation are obtained for the external field as an ultrashort pulse and in the case of a monochromatic wave.
Abstract The polarization in a crystal containing impurities which is caused by the interaction with an electromagnetic field is given in terms of the Fourier transforms of the first‐order emission and absorption spectra due to the impurities. The results are obtained by means of the time‐dependent perturbation theory using the diagram technique. It is also shown that electron density matrix of the impurities satisfies the equations with two relaxation constants γ and Γ if the first‐order spectra are supposed to be of Lorentzian type.
Abstract A reduced-density-matrix description is developed for coherent 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 and semiconductor materials. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the reduced-density-matrix approach are developed in a unified manner. The general non-Markovian formulations provide a rigorous foundation for the systematic introduction of the commonly used Born (lowest-order perturbation-theory) and Markov (short-memory-time) approximations. A preliminary semiclassical perturbation-theory treatment of the electromagnetic interaction is introduced, based on a coupled hierarchy of relationships for the field components of the reduced density operator.
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.
Liouville-space (reduced-density-operator) descriptions are developed for resonant and coherent electromagnetic interactions of quantized electronic systems, taking into account environmental decoherence and relaxation phenomena. Applications of interest include electromagnetically-induced transparency and related pump-probe optical phenomena in 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 perturbationtheory) and Markov (short-memory-time) approximations are systematically introduced within the framework of the general non-perturbative and non-Markovian formulations. A preliminary semiclassical description of the entire 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 occurring in a perturbation-theory treatment of the semiclassical electromagnetic interaction. These expressions can be evaluated for coherent initial electronic excitations and for the full tetradic-matrix form of the Liouville-space self-energy operator representing the environmental interactions in the Markov approximation. Intense-field electromagnetic interactions are treated by means of an alternative, non-perturbative method, which is based on a Liouville-space Floquet-Fourier representation of the reduced density operator. Electron-electron quantum correlations are treated by the introduction of a cluster decomposition of the reduced density operator and a coupled hierarchy of reduced-density-operator equations.