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Zeitschrift für Naturforschung A

Application of the Model Microfield Method to Stark Profiles of Alkali Metal Resonance Lines

A. Mazure, Gérard Nollez

Published Dec 1, 1978• 13 citations
Publisher

Abstract

Abstract Stark widths and shifts of alkali metal resonance lines are calculated by the model microfield method (MMM). The im pact results of Griem for the prevailing electronic broadening are recovered by the unified MMM. Both theories are in close agreement with recent experimental results. It is shown further that the shift values are very sensitive to the line strength values of the involved transitions. The reliability of the experimentally observed regularities through the alkali sequence is next discussed. On the basis of the MMM results these regularities can be understood in term s of the line strengths and frequencies of transitions from the main levels actually involved.

DOI
10.1515/zna-1978-1223

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Abstract Stark widths and shifts of alkali metal resonance lines are calculated by the model microfield method (MMM). The im pact results of Griem for the prevailing electronic broadening are recovered by the unified MMM. Both theories are in close agreement with recent experimental results. It is shown further that the shift values are very sensitive to the line strength values of the involved transitions. The reliability of the experimentally observed regularities through the alkali sequence is next discussed. On the basis of the MMM results these regularities can be understood in term s of the line strengths and frequencies of transitions from the main levels actually involved.
When atoms are placed in a static magnetic field, they undergo shifts of their energy levels and changes in their transition probabilities. These two effects must be taken into account when considering absorption profiles of alkali-metal D lines, which result from the contribution of many transitions influenced by the laser spectrum and Doppler broadening. The model presented here gives the D-line absorption coefficients of alkali-metal vapors in the presence of an arbitrary static magneitc field. They are evaluated considering various laser polarizations. Experimental measurements of D-line absorption profiles for 85Rb^{85}\mathrm{Rb}85Rb, 87Rb^{87}\mathrm{Rb}87Rb, and 133Cs^{133}\mathrm{Cs}133Cs isotopes show excellent agreement with theoretical predictions.
We have presented a novel method to calculate the widths of the avoided crossings of Rydberg states in a static electric field. The widths of avoided crossings can be decided not directly connected by scanning the static field, but indirectly connected through the Stark electric dipole moments. The method is restricted to the case in which both the two relevant states have linear Stark shifts or only one of the two involved states has linear Stark shifts, but another has no Stark shift. As test examples, we calculated the widths of avoided crossings of Li, Na and K. The Stark electric dipole moments are determined by using the Stark state wavefunctions which are obtained from the diagonalization method at a fixed static electric field amplitude. The results are in excellent agreement with experimental and other theoretical data.
The purpose of this work is the evaluation of the linewidth w and lineshift d of the sodium resonance line 3p − → 3s when the excited atoms are evolving in their parent gas. Assuming the Baranger impact approximation, these two quantities are given in terms of the phase shifts of the ground Na(3s) + Na(3s) and the excited Na(3p)+Na(3s) states. The quantal calculations and the semi-classical method, developed by Mott and Massey and Landau and Lifshitz, show that the cross sections σ and λ vary with the energy like E−1/2, the width w and the shift d do not depend on the temperature, the long-range interactions have a big influence on w and d, and the rate coefficients depend on the dispersion coefficients like w/n ≈ +7.298 × 10−8C3(Σ) and d/n ≈ +8.893 × 10−9C3(Σ). The study also shows that the sodium results can be extended to the other alkali-metal atoms (Li, K, Rb, Cs, and Fr) by a simple scaling. Keywords: potential energy curve, broadening cross section, rate coefficient, linewidth, lineshift, dispersion coefficient
The authors describe practical methods for calculating the Stark structure of Rydberg states of the alkali metals based on diagnolization of the energy matrix. A survey of Stark structures is presented for all of the alkali metals in the vicinity of n=15n=15n=15. Topics discussed include general methods for evaluating radial matrix elements, the treatment of fine structure, oscillator-strength distribution, scaling laws, the structure of a level anticrossing, and sources of error. Experimental Stark maps are compared with calculated results for lithium and cesium. Experimental studies of the oscillator-strength distribution within a Stark manifold and the structure of a level anticrossing are also presented.
Abstract High-contrast sub-Doppler resonances observed in alkali-metal atomic vapors in the field of counterpropagating bichromatic laser beams are perspective in quantum metrology for designing a miniature optical frequency standard. Until now, these nonlinear resonances have been investigated only experimentally or using numerical calculations. In our opinion, the development of a simplified theoretical model of the observed resonances, which would provide explicit compact analytic expressions describing the line shape of the resonance, would be extremely important for further evolution of the theory. In this study, we perform such theoretical analysis based on the three-level Λ scheme of the atom. We investigate two regimes, viz., the regime of a low-intensity standing wave with close intensities of counterpropagating beams (I1 ≈ I2) and the regime of a probe wave, in which one of the beams has a noticeably lower intensity than that of the oppositely propagating beam (I2 ≪ I1). The resulting analytic expressions make it possible to determine qualitative differences between these regimes and to separate explicitly the contributions from different nonlinear effects to the light field absorption, including the terms responsible for the formation of a high-contrast sub-Doppler peak. The expressions derived here are in qualitative agreement with experimental data obtained earlier.