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Journal de physique

Dependence of Hanle signals on the spectral distribution of the exciting light

D. Lecler, R. Ostermann, Wulfhard K. Lange, J. Luther

Published Jan 1, 1975• 7 citations
Publisher

Abstract

The shape of Hanle (zero field level crossing) signals may be strongly distorted if the spectral profile of the exciting light varies rapidly on the scale of the natural linewidth, provided that the Doppler width in the scattering region is not very large compared with the natural width. A Hanle experiment has been performed at the resonance line of calcium. The exciting light had a spectral profile with a very narrow hole at the resonance frequency and was produced by a calcium hollow-cathode with an absorbing atomic beam of calcium inserted in its light path, The observed level crossing signals are in very good agreement with theoretical predictions.

DOI
10.1051/jphys:01975003607-8064700

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•Jan 1, 1988•0 citations
The shape of Hanle (zero field level crossing) signals may be strongly distorted if the spectral profile of the exciting light varies rapidly on the scale of the natural linewidth, provided that the Doppler width in the scattering region is not very large compared with the natural width. A Hanle experiment has been performed at the resonance line of calcium. The exciting light had a spectral profile with a very narrow hole at the resonance frequency and was produced by a calcium hollow-cathode with an absorbing atomic beam of calcium inserted in its light path, The observed level crossing signals are in very good agreement with theoretical predictions.
The optical Hanle effect (light-shift-induced zero-field level crossing) has been investigated theoretically and experimentally. In the case of a $J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0$ three-level system and of a $J=0\ensuremath{\rightarrow}1$ two-level system, the resonance line shape has been obtained using a nonlinear-response-function method. Approximate expressions, valid under the conditions for the observation of light shifts, are obtained and compared with exact calculations as well as with the corresponding expression for the magnetic Hanle effect. As concerns the weak laser beam which produces the coherent excitation of atomic substates, we have calculated the linear response in the limiting case of monochromatic and of broad-band excitation. The experimental investigation has been performed for the Ba resonance line using two cw dye lasers at $\ensuremath{\lambda}=5535$ \AA{} and an atomic beam. The absorption- and dispersion-shaped level crossing resonances have been observed, for narrow- and broad-band excitation, by varying the power of the strong nonresonant laser beam. We have checked that the line shapes are only dependent upon the reduced variable $\frac{{P}_{L}}{\ensuremath{\delta}}$ (PL{P}_{L}PL​; beam power; $\ensuremath{\delta}$: frequency detuning). Using the theoretical expressions, we have tried to fit the experimental curves. Provided that the Gaussian distribution of the beams is taken into account, we have obtained a good agreement between theory and experiment for the whole set of experimental data.
We have carried out experimental and theoretical investigations of the Hanle effect in the 1S0^{1}\mathrm{S}_{0}1S0​${\ensuremath{\rightarrow}}^{3}$P1{\mathrm{P}}_{1}P1​ transition at \ensuremath{\lambda}=555.6 nm in 174Yb^{174}\mathrm{Yb}174Yb, emphasizing the dependence of the Hanle signal on the intensity and on the statistical parameters of a well-characterized phase-diffusing optical field. The phase and frequency fluctuations imposed on the laser beam by a system of modulators are described by two parameters corresponding to the bandwidth \ensuremath{\beta} and the spectral density b of the noise spectrum. The shape of the laser power spectrum is continuously variable between nearly Gaussian (b/\ensuremath{\beta}\ensuremath{\gg}1) and nearly Lorentzian (b/\ensuremath{\beta}\ensuremath{\ll}1). Measurements are made with a well-collimated Yb atomic beam crossed at right angles by a linearly polarized laser beam. In accord with theoretical predictions, the full width at half maximum (FWHM) of the Hanle effect coherence dip is found to increase as the square root of the laser intensity for monochromatic excitation. For a given intensity, the FWHM decreases as the laser bandwidth increases. With the same laser intensity and spectral width, the FWHM of the Hanle coherence dip increases as the laser spectral profile approaches the Gaussian limit, particularly when \ensuremath{\beta}/2\ensuremath{\pi} is within an order of magnitude of the natural width of the atomic line. The Hanle signal shapes agree well with theoretical calculations using a Brownian motion phase-diffusion model of the laser field. For large \ensuremath{\beta}, it suffices to apply substitution rules for simple phase diffusion to the density-matrix equations.
We measure and simulate numerically the Hanle effect and non-zero field level crossing signals in 85 Rb and 87 Rb atoms in a magnetic field at room temperature. Diode laser radiation from 4 mW cm −2 to 3.3 W cm −2 tuned to the D 2 absorption line of each isotope excites atoms into all the excited-state hyperfine levels simultaneously inside the unresolved Doppler profile. Polarization fluorescence detection is used to observe dark and bright resonances, as well as non-zero field level crossing resonances, for several excitation lines. A broad spectral line excitation model is applied to analyse the measured signals. The non-linear Zeeman effect is included in the model for both ground and excited states. Although the applied magnetic field does not exceed 80 G, several hyperfine levels of the excited state show a substantial deviation from the linear Zeeman effect.
We present experimental verification of a certain number of theoretical predictions given in the preceding paper. The narrowing of the different Hanle-effect signals by multiple diffusion is clearly weaker if observed using the light scattered in the backward direction than if observed using the laterally scattered light. This narrowing can become very small if the vapor is illuminated with light whose frequency is in the wings of the Doppler absorption width of the vapor. The values of the ratios of the widths and intensities of the different Hanle-effect signals that were measured are in good agreement with the values predicted by theory.
In this paper we describe an experimental investigation of a zero- field level crossing resonance in the observed fluorescence at 555.6 nm resulting from excitation of the /sup 1/S/sub O/ ..-->.. /sup 3/P/sub 1/ transition in transition in Yb/sup 174/ by a linearly polarized laser field. The essential new feature of this investigation is the use of an optical field for which the phase coherence is well-characterized and variable over a wide range. We have developed, and apply here, experimental techniques for synthesizing constant amplitude laser fields with phase/frequency fluctuations which follow Gaussian (normal) statistics and which have spectral dependences which can be varied over a range from nearly Lorentzian to nearly Gaussian profiles. These synthesized fields correspond, to a good approximation, to the so-called phase-diffusion fields described in theoretical studies of the ac Stark effect with Lorentzian and non-Lorentzian laser line shapes, and have been applied previously in several related experimental investigations. 13 refs., 6 figs., 1 tab.