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Journal of Experimental and Theoretical Physics

Kinetic equations for a density matrix describing nonlinear effects in spectral line wings

А. И. Пархоменко, Anatolii M. Shalagin

Published Nov 1, 2011• 3 citations
Publisher

Abstract

Kinetic quantum equations are derived for a density matrix with collision integrals describing nonlinear effects in spectra line wings. These equations take into account the earlier established inequality of the spectral densities of Einstein coefficients for absorption and stimulated radiation emission by a two-level quantum system in the far wing of a spectral line in the case of frequent collisions. The relationship of the absorption and stimulated emission probabilities with the characteristics of radiation and an elementary scattering event is found.

DOI
10.1134/s106377611114007x

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Kinetic quantum equations are derived for a density matrix with collision integrals describing nonlinear effects in spectra line wings. These equations take into account the earlier established inequality of the spectral densities of Einstein coefficients for absorption and stimulated radiation emission by a two-level quantum system in the far wing of a spectral line in the case of frequent collisions. The relationship of the absorption and stimulated emission probabilities with the characteristics of radiation and an elementary scattering event is found.
Using the eikonal approximation, we have calculated effective collision frequencies in density-matrix kinetic equations describing nonlinear effects in the wings of spectral lines. We have established the relation between the probabilities of absorption and stimulated emission and the characteristics of the radiation and elementary scattering event. The example of the power interaction potential shows that quantum mechanical calculation of the collision frequencies in the eikonal approximation and previously known spectral line wing theory give similar results for the probability of radiation absorption.
The spectral densities of Einstein coefficients for absorption and stimulated emission in a two-level quantum system are not equal to each other beyond the absorption (emission) line if the homogeneous broadening caused by interaction with a thermostat is much larger than the natural width. In this study, a relationship between these coefficients is derived on the basis of general thermodynamic requirements. This relationship is associated with new effects such as population inversion upon the nonresonant absorption of continuous radiation and radiation amplification without population inversion.
An analysis is made of the general aspects of the physics of processes occurring in a system of colliding atoms in the presence of a radiation field. The attention is concentrated on the relationship between the spectral characteristics and various photon absorption (emission) processes in a system of interacting atoms (regarded as a quasimolecule). Nonlinear optical effects in the far wings of atomic lines are considered and the effects are interpreted. A relationship between these effects and the change in the atomic collision dynamics due to the presence of a radiation field is considered.
Amplification of probe radiation by an inversionless two-level system in the 'red' wing of its spectral line is studied theoretically during the resonance absorption of intense cw laser radiation. The effect is caused by the inequality of the spectral densities of the Einstein coefficients for absorption and stimulated emission outside the absorption line under conditions when homogeneous broadening, due to the interaction of particles with the buffer gas, significantly exceeds the natural broadening (at high pressures of the buffer gas). It is found that the larger the inversionless gain, the higher the buffer gas pressure and the pump radiation intensity. It is established that at high enough pump intensity, the probe field is amplified along the entire region of the 'red' wing of the line (at any negative detunings of the probe field frequency).
It is shown that, in general, the interaction between relaxing quantum systems and radiation is described by non-Markov transport equations for the density matrix ρ p and the relaxation matrix depends on the properties of the radiation. The usual Markov-type equations for ρ p are obtained from these equations if γτ c ≪1 and (∊ 2 +4 V 2 ) 1/2 τ c ≪1 (γ is the width of the investigated transition in a quantum system, rc is the correlation time of the perturbations causing relaxation, e is the frequency detuning, and V is the energy of the interaction between the system and the radiation field). When the second inequality is disobeyed, the relaxation process deviates strongly from the Markov type. In the case of small values of V , this results in a non-Lorentzian profile of the absorption lines characterized by a steep descent in the wings. In the range of high values of V , when 2 V τ c 1, the whole relaxation process becomes greatly modified: the dependence of the relaxation coefficients on V becomes strong and a coupling appears between the relaxations of the diagonal and the nondiagonal elements of the density matrix. This is manifested, in particular, in the saturation effect: the term describing saturation in the expression for the polarizability changes considerably and the expression for the line width loses the component due to the adiabatic (elastic) perturbation.