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Quantum Electronics

Line shape of the coherent population trapping resonance in the case of a Gaussian spatial profile of a light beam

Valeriy I. Yudin, M. Yu. Basalaev, Д. В. Коваленко, А. В. Тайченачев, J. W. Pollock, Azure Hansen, William McGehee, John E. Kitching

Published Feb 1, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qel17975

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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.
We study the field shift of coherent population trapping (CPT) resonance excited by a bichromatic field in an open Λ system with account for the Gaussian profile of the laser radiation intensity. Two methods for error signal formation are considered: the harmonic frequency modulation and the step phase modulation (phase jumps). It is shown that the spatial inhomogeneity of the light beam leads to an essentially nonlinear dependence of the error signal shift on the laser radiation intensity. We propose an approach for the linearization of this dependence, which is important for the development of methods for suppressing the field shift in atomic clocks based on CPT resonances.
Abstract We study the field shift of coherent population trapping (CPT) resonance excited by a bichromatic field in an open Λ system with account for the Gaussian profile of the laser radiation intensity. Two methods for error signal formation are considered: the harmonic frequency modulation and the step phase modulation (phase jumps). It is shown that the spatial inhomogeneity of the light beam leads to an essentially nonlinear dependence of the error signal shift on the laser radiation intensity. We propose an approach for the linearization of this dependence, which is important for the development of methods for suppressing the field shift in atomic clocks based on CPT resonances.
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This paper presents a theoretical study of the light-induced shift of the coherent population trapping resonance. An analytical model is proposed that describes the interaction of two radiation components with an atomic system using a ΛΛΛ scheme and takes into account an additional level of excited state. Both weak and strong coupling regimes with off-resonant transitions are considered. It is shown that, in addition to the conventional dynamic Stark shift, an extra shift arises due to the distortion of the resonance line shape when bichromatic laser radiation interacts with off-resonant atomic transitions. An analytical expression for this additional shift is derived in the weak-coupling limit, and its significant impact on the resonance shape and sensitivity to the intensities of the laser field components is demonstrated. It is found that under strong coupling conditions, the additional shift can deviate substantially from a linear dependence on light intensity, suggesting new opportunities for controlling light shifts in precision atomic devices such as quantum frequency standards.
This work is concerned with the line profiles, amplitudes and widths of the coherent population trapping (CPT) resonances due to low frequency Zeeman coherences, in the Hanle configuration, applied to 87Rb atoms in the vacuum cell. Detailed calculations of the fluorescence were done with two different transverse intensity profiles of the excitation laser tuned to the open Fg = 2 → Fe = 1 transition. Comparison with experiment produces good agreement for the laser intensity dependence of CPT line-widths in the wide range of the laser intensity, when the laser transverse beam profile is Gaussian. Results for both step-like and Gaussian profile of the laser beam show asymptotic 1/√d dependence (d is the laser beam diameter) of CPT line-widths, for large range of the laser intensity.
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.