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Physical Review A

Nonlinear-resonance line shapes: Dependence on the transverse intensity distribution of a light beam

А. В. Тайченачев, Anatolii M Tumaikin, Valeriy I. Yudin, M. Stähler, R. Wynands, John E. Kitching, Leo W. Hollberg

Published Feb 26, 2004• 56 citations
Publisher

Abstract

We analyze the line shape and width of atomic coherent-population-trapping (CPT) resonances excited by laser beams with different transverse intensity profiles. A dramatic difference in the resonance line shape is found when comparing a beam with a ``steplike'' profile to a beam with a Gaussian profile. In particular, for nonuniform profiles, a non-Lorentzian functional form is given that is more appropriate for describing the nonlinear resonance line shape than is a conventional Lorentzian. Our analysis is supported by measurements of CPT line shapes in a thermal vapor of ${}^{85}\mathrm{Rb}.$

DOI
10.1103/physreva.69.024501

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We calculated the coherent population trapping (CPT) for the open D1D1D1 line transition ${F}_{g}=2\ensuremath{\rightarrow}{F}_{g}=1$ in 87Rb^{87}\mathrm{Rb}87Rb by solving the time-dependent optical Bloch equations, integrating the results for the total excited state populations over atomic trajectories, and averaging over velocities (components perpendicular and parallel to the laser beam) and over atom incident angles to the laser beam. We obtained a square root dependence of the CPT linewidths as a function of the laser intensity for both steplike and Gaussian transverse beam profiles. The results obtained with the Gaussian transverse laser beam profile are in good agreement with recent experimental results. Results for both steplike and Gaussian profiles of the laser beam show asymptotic 1∕d1∕\sqrt{d}1∕d​ dependence (ddd is the laser beam diameter) of the CPT linewidths, for a large range of the laser intensity.
Abstract For coherent population trapping (CPT) resonance excited by a bichromatic field in a closed Λ-system, we have obtained an analytical expression for the line shape in the case of a Gaussian profile of the radiation intensity distribution, taking into account the light shift of the reference transition frequency. Due to the spatial inhomogeneity of the light shift, the line shape is asymmetric. The dependence of the shift of the resonance peak position on the light intenisty is investigated.
A model for description of the shapes of the coherent population trapping (CPT) resonances at different geometries of excitation and observation is developed. The numerical calculations, based on the irreducible tensor operator formalism, take into account the experimental geometry, the velocity distribution of the atoms, the Gaussian distribution of the laser beam intensity and the high rank polarization moments (HRPM). The results for different laser beam diameters, aperture of the detection, position of the photodetector etc. are compared with the experimental data. A method for description of the experimental shapes is proposed.
Coherent population trapping (CPT) resonances study in Hanle configuration is reported for different polarizations of the exciting light field, on the D2{D}_{2}D2​ line of Cs atoms. While for linear/circular polarization dip/peak in the fluorescence is registered, in case of elliptical polarization, a complex shape resonance is evidenced experimentally, whose profile strongly depends on the ellipticity of polarization. A theoretical model is proposed and developed, which includes the influence on the resonance of polarization ellipticity, transverse magnetic field, and spatial intensity profile of the laser beam. Good agreement is found between the theoretical and experimental results. The reported results allow one to accomplish more profound than in previous research analysis of the CPT resonances behavior pointing out their sensitivity to the light polarization and power as well as to transverse magnetic fields. The presented study is of general importance for the wide application of the coherent resonances in high resolution spectroscopy and precise measurements. The purity of linear/circular polarization of the light needed in different applications can be estimated implementing the proposed model.
We calculated line-shapes of the coherent population trapping (CPT) for the open transition in 87Rb by solving time-dependent optical Bloch equations and averaging results for the total excited state populations over atomic trajectories and velocities, while taking into account incident angles to the laser beam. Comparison with experiment produces good agreement for the laser intensity dependence of the CPT line-widths when the laser transverse beam profile is Gaussian. This theoretical model was used to calculate the probe laser CPT in the case of spatially separated pump beam. The probe beam is placed inside the cylindrically-shaped pump beam. The calculations as well as measurements show narrowing of the Hanle resonance due to Ramsey effect.