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Physical Review A

Optical Hanle effect

V.Paul Kaftandjian, Christian Delsart, J. Keller

Published Mar 1, 1981• 13 citations
Publisher

Abstract

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 $\frac{{P}_{L}}{\ensuremath{\delta}}$ (${P}_{L}$; 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.

DOI
10.1103/physreva.23.1365

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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.

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Non-optical observation of laser-induced zero-field level-crossing effects in an atomic beam

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

D. Lecler, R. Ostermann, Wulfhard K. Lange +1 more

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.

Journal de physique•Jan 1, 1975•7 citations
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→1\ensuremath→0J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0J=0\ensuremath→1\ensuremath→0 three-level system and of a J=0\ensuremath→1J=0\ensuremath{\rightarrow}1J=0\ensuremath→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 \ensuremathλ=5535\ensuremath{\lambda}=5535\ensuremathλ=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 PL\ensuremathδ\frac{{P}_{L}}{\ensuremath{\delta}}\ensuremathδPL​​ (PL{P}_{L}PL​; beam power; \ensuremathδ\ensuremath{\delta}\ensuremathδ: 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 studied the ground-state Hanle effect (GSHE) excited by linearly polarized laser light on the DDD1{}_{1}1​ line of cesium atoms. We have solved algebraically the Liouville equation using the irreducible tensor formalism, and derive an analytical expression for the resonance line shapes in a magnetic field of arbitrary direction. The model predictions are in excellent agreement with experimental observations in various field geometries. Our model is valid for arbitrary $F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}$ transitions in the low-power limit. We discuss the relation between the GSHE and electromagnetically induced transparency or absorption. Our approach allows a full understanding of the mechanism of the GSHE and provides tools for quantifying the resonance contrast, a crucial parameter for metrological applications of level crossing resonances.
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.
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.
Level-crossing effects have been detected non-optically with the use of a Rabi-type atomic-beam method. The sodium beam was excited by intense linearly polarised radiation from a CW narrow-band dye laser. Several superimposed resonances were observed in the atomic-beam signal when scanning the magnetic field around zero. The two narrower resonances are interpreted as high-order non-linear effects. They arise from the coupling of laser-induced Zeeman coherences in the ground state (including a hexa-decapole moment) with the populations of the Zeeman sublevels.
In a previous paper, I have presented a general theory of the optical pumping of atoms by a polarized multimode-laser beam, in the presence of a magnetic field. Equations of motion, valid at arbitrary laser intensities for the density matrix of the atomic system, have been obtained. In this paper, these equations are exactly solved for a linearly $\ensuremath{\sigma}$-polarized laser and levels having small angular momenta. More precisely, I consider the laser transitions ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=0$, ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=1$, and ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$. Two particular results are emphasized: (i) For $J=1\ensuremath{-}J=0$ and $J=1\ensuremath{-}J=1$ transitions and for the J=2J=2J=2 level of a $J=1\ensuremath{-}J=2$ transition, the laser-induced Hanle effects keep a Lorentzian shape, independent of the laser intensity. For the $J=1\ensuremath{-}J=1$ transition, it is shown that the depolarizing relaxation processes play a leading part in the coupling induced by the laser between the transverse alignments of the two levels. On the other hand, the power broadenings of the Hanle effects are shown to be similar. For the J=1J=1J=1 level of a $J=1\ensuremath{-}J=2$ transition, the Hanle-effect shape presents a departure from the Lorentzian one, owing to a coupling with the laser-induced hexadecapole moment in the J=2J=2J=2 level. (ii) The populations of the levels exhibit a "zero-field saturation resonance" which is due to the coupling with the Zeeman coherences. These resonances, which reproduce the Hanle effects of the transition, can be observed on the $\ensuremath{\pi}$-polarized fluorescence from the levels. In general, these resonances appear as a saturation effect, i.e., they reduce the laser-induced fluorescence of the levels in zero magnetic field. However, for the ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$ transition, the ${J}_{a}=2\ensuremath{\rightarrow}{J}_{f}=2 \ensuremath{\pi}$ fluorescence presents an anomalous behavior; the saturation resonance increases the zero-field laser-induced fluorescence. The theoretical study shows the prominent part played by the value of the Jb=1{J}_{b}=1Jb​=1 level lifetime in the interpretation of this anomaly. Other results, such as the laser-induced depolarization of the fluorescence, are also obtained. All the theoretical predictions have been experimentally checked and will be presented in forthcoming papers.
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.