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Broadening of Resonance Induced by High-order Spatial Harmonics

Oleg V. Belai, David A. Shapiro

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Coherent preparation of quantum states of atoms and ions by laser light can lead to electromagnetically induced transparency and related effects. In particular, the standing wave at the adjacent transition induces a new type of nonlinear resonance in the probe-field spectrum of a three-level system. The resonance is due to the effect of high- order harmonics of atomic coherence. However, the resonance is broadened in experiment and the reason of the broadening was unclear. The paper describes how the velocity changing collisions broaden the resonance. The analytic theory taking into account up to 4-th order of the perturbation theory is presented. The numerical solution of density matrix equations is discussed. The analytical formulas are shown to describe the experiment qualitatively while the numerical computation demonstrates quantitative agreement. The Coulomb dephasing is shown to be the physical mechanism of the broadening.

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Physical Review A•Apr 11, 2003•28 citations
Coherent preparation of quantum states of atoms and ions by laser light can lead to electromagnetically induced transparency and related effects. In particular, the standing wave at the adjacent transition induces a new type of nonlinear resonance in the probe-field spectrum of a three-level system. The resonance is due to the effect of high- order harmonics of atomic coherence. However, the resonance is broadened in experiment and the reason of the broadening was unclear. The paper describes how the velocity changing collisions broaden the resonance. The analytic theory taking into account up to 4-th order of the perturbation theory is presented. The numerical solution of density matrix equations is discussed. The analytical formulas are shown to describe the experiment qualitatively while the numerical computation demonstrates quantitative agreement. The Coulomb dephasing is shown to be the physical mechanism of the broadening.
Coherent preparation of quantum states of atoms and ions by laser light can lead to electromagnetically induced transparency and related effects. In particular, the standing wave at the adjacent transition induces a new type of nonlinear resonance in the probe-field spectrum of a three-level system. The resonance is due to the effect of high-order harmonics of atomic coherence. However, the resonance is broadened and the reason of the broadening was unclear. The paper describes how the velocity changing collisions broaden the resonance. The analytic theory taking into account up to 4-th order of the perturbation theory is presented. The numerical calculations are described. The analytical formulas are shown to describe the experiment qualitatively while the numerical computation demonstrates quantitative agreement. The Coulomb dephasing is discussed as the physical mechanism of the broadening.
The problem of probe-field spectrum is considered for a three-level ion placed in a field of an intense standing light wave. The ion interaction with plasma and the velocity-changing Coulomb scattering are taken into account within the weak-collision model. The system of kinetic equations for the density matrix is solved by the expansion in spatial harmonics and eigenfunctions of the collision operator. The profile of nonlinear addition to the probe-wave absorption is determined for various values of the effective ion-ion collision frequencies and various amplitudes and frequencies of standing wave. It is shown that the broadening of the central nonlinear structure in the spectrum is caused by the Coulomb dephasing effect. The computational results are in qualitative agreement with the available experimental data.
The spectrum of a test field in a three-level ArII Λ scheme in the presence of a strong standing wave on the adjacent transition was measured. The known light-induced transparency peak was observed; the peak shifted as the detuning of the strong field was varied. In addition, a new resonance in the line center arose whose position was independent of the strong-field frequency. The resonance was caused by the higher spatial coherence harmonics on the test transition. Perturbation theory for a low and numerical calculations for a high standing wave intensity give qualitative agreement with experiment and substantiate the nature of the central transition.
The probe field spectrum of a three-level A scheme with a strong standing wave at the adjacent transition is calculated numerically taking into account velocity-varying collisions. It is shown that even a small population of the upper level changes the shape of the spectrum and increases the absorption in the line center. Taking into account the excitation of the level and the saturation of the adjacent transition allows a quantitative explanation of the experiment on argon ions in plasma of a high-current discharge.
The interaction of a two-level system with a strong standing wave is examined by the probe field resonant to the adjacent transition in the $\ensuremath{\Lambda}$ configuration of Ar II. The known peak of electromagnetically induced transparency is observed in the absorption spectrum at the detuning of the probe field proportional to the detuning of the strong field. Along with it, the different structure has been found at the line center, independently of the strong-field frequency. The calculations clarify that the central structure is induced by the higher-order spatial harmonics of the atomic coherence induced at the probe transition. The effect results in steep frequency dependence of the refractive index at the line center.