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Physical Review A

Coherent population trapping linewidths for open transitions: Cases of different transverse laser intensity distribution

Milan Radonjić, D. Arsenović, Z. D. Grujić, B. M. Jelenkovic

Published Feb 4, 2009• 18 citations
Publisher

Abstract

We calculated the coherent population trapping (CPT) for the open $D1$ line transition ${F}_{g}=2\ensuremath{\rightarrow}{F}_{g}=1$ in $^{87}\mathrm{Rb}$ 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 $1∕\sqrt{d}$ dependence ($d$ is the laser beam diameter) of the CPT linewidths, for a large range of the laser intensity.

DOI
10.1103/physreva.79.023805

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We calculated the coherent population trapping (CPT) for the open D1D1D1 line transition Fg=2\ensuremath→Fg=1{F}_{g}=2\ensuremath{\rightarrow}{F}_{g}=1Fg​=2\ensuremath→Fg​=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.
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.
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 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 85Rb.{}^{85}\mathrm{Rb}.85Rb.
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 investigate experimentally and theoretically the coherent population trapping (CPT) effect occurring in 87Rb^{87}\text{R}\text{b}87Rb D1{D}_{1}D1​ line due to the interaction with linearly polarized laser light ($\text{lin}\ensuremath{\parallel}\text{lin}$ CPT). In this configuration, the coherence is strongly influenced by the structure of the excited state; consequently, the quantum interference between dark states is an essential feature of this interaction scheme. We study the $\text{lin}\ensuremath{\parallel}\text{lin}$ CPT resonance as a function of the laser optical detuning. The comparison between experimental and theoretical results allows us to quantify the contribution from different dark states to the total signal. Based on these results, we investigate the signal depending on both the pressure broadening of the optical transition and the laser linewidth, and we find in which conditions the laser linewidth does not degrade the $\text{lin}\ensuremath{\parallel}\text{lin}$ CPT resonance.
The dependence of the width of the coherent population trapping (CPT) resonance on the atomic interaction time is studied theoretically. The optical Bloch equations are solved for the Hanle/CPT schemes corresponding to the open ${F}_{g}\ensuremath{\rightarrow}{F}_{e}$ transitions of the sodium D1{D}_{1}D1​ line interacting with linearly polarized laser light. The mechanism producing the narrowing of the Hanle/CPT resonance is examined, the role of the population losses is pointed out, and the law describing the narrowing of the width of the resonance with the interaction time is determined. Our results are compared with the Hanle/CPT linewidth dependence on the interaction time occurring for a closed optical transition.