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Physical Review Letters

Asymmetric line shapes for weak transitions in strong standing-wave fields

Carl Wieman, Martin Charles Noecker, Bernard P. Masterson, J. Cooper

Published Apr 27, 1987• 20 citations
Publisher

Abstract

We have observed the resonance line shape for a very weak atomic transition excited when an atomic beam intersects a strong standing-wave laser field. The line shape has a dramatic intensity-dependent distortion which is Doppler free and independent of the excitation rate. We have calculated the line shape predicted by optical Bloch equations that include a spatially varying ac Stark shift, and find good agreement with our experimental results.

DOI
10.1103/physrevlett.58.1738

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Journal of Experimental and Theoretical Physics•Dec 1, 2021•7 citations
We have observed the resonance line shape for a very weak atomic transition excited when an atomic beam intersects a strong standing-wave laser field. The line shape has a dramatic intensity-dependent distortion which is Doppler free and independent of the excitation rate. We have calculated the line shape predicted by optical Bloch equations that include a spatially varying ac Stark shift, and find good agreement with our experimental results.
Owing to the ac-Stark effect, the lineshape of a weak optical transition in an atomic beam can become significantly distorted when driven by an intense standing wave field. We use an Yb atomic beam to study the lineshape of the 6s2S10→5d6sD31 transition, which is excited with light circulating in a Fabry–Perot resonator. We demonstrate two methods to avoid the distortion of the transition profile. Of these, one relies on the operation of the resonator in multiple longitudinal modes, and the other in multiple transverse modes.
We report on an experimental and theoretical study of the dynamic (ac) Stark effect on a forbidden transition. A general framework for parametrizing and describing off-resonant ac-Stark shifts is presented. A model is developed to calculate spectral line shapes resulting from resonant excitation of atoms in an intense standing light wave in the presence of off-resonant ac-Stark shifts. The model is used in the analysis and interpretation of a measurement of the ac-Stark shifts of the static-electric-field-induced $6{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5d6s^{3}D_{1}$ transition at 408nm408\phantom{\rule{0.3em}{0ex}}\mathrm{nm}408nm in atomic Yb. The results are in agreement with estimates of the ac-Stark shift of the transition under the assumption that the shift is dominated by that of the 6s21S06{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}6s21S0​ ground state. A detailed description of the experiment and analysis is presented. A biproduct of this work is an independent determination (from the saturation behavior of the 408-nm transition) of the Stark transition polarizability, which is found to be in agreement with our earlier measurement. This work is part of the ongoing effort aimed at a precision measurement of atomic parity-violation effects in Yb.
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.
The influence of ac Stark shifts on the three-photon ionization of cesium in a moderate-intensity laser beam is investigated. The ionization process involves a two-photon resonance with the 8d8d8d fine-structure levels. The work consists of two related parts. In the first part, atomic parameters, such as the two-photon Rabi rate and the ac Stark shift, are calculated in the nonrelativistic Hartree-Fock approximation. In the second part, the atomic parameters thus obtained are used as coefficients in a system of coupled differential equations representing the time evolution of the density matrix. Ionization line shapes are generated for a transform-limited pulsed laser of moderate intensity with a single-mode transverse structure. As the time history of the intensity profile is varied from square to smooth, the ionization line shape becomes asymmetric due to the time dependence of the ac Stark shift. The effects of varying the spatial intensity distribution of the laser light to include transverse centering and longitudinal focusing are also studied.
A weak excitation transit-time resolution limited analytic line shape is derived for a Doppler broadening-free degenerate two-photon transition from a standing wave with a TEM00 transverse profile. This approximation is appropriate when the collisional mean free path is much larger than the transverse width of the TEM00 beam. It is considerably simpler than the two-photon absorption line shape previously published, Bordé, C. R. Hebd. Seances Acad. Sci., Ser. B 282, 341–344 (1976), which was derived for more general experimental conditions. The case of a saturating field, with an intensity-dependent shift of the resonance frequency, is treated and expressed in reduced units. Numerical calculations are presented for the line shape for a range of the reduced intensity and light intensity shifts values.
Abstract High-contrast sub-Doppler resonances observed in alkali-metal atomic vapors in the field of counterpropagating bichromatic laser beams are perspective in quantum metrology for designing a miniature optical frequency standard. Until now, these nonlinear resonances have been investigated only experimentally or using numerical calculations. In our opinion, the development of a simplified theoretical model of the observed resonances, which would provide explicit compact analytic expressions describing the line shape of the resonance, would be extremely important for further evolution of the theory. In this study, we perform such theoretical analysis based on the three-level Λ scheme of the atom. We investigate two regimes, viz., the regime of a low-intensity standing wave with close intensities of counterpropagating beams (I1 ≈ I2) and the regime of a probe wave, in which one of the beams has a noticeably lower intensity than that of the oppositely propagating beam (I2 ≪ I1). The resulting analytic expressions make it possible to determine qualitative differences between these regimes and to separate explicitly the contributions from different nonlinear effects to the light field absorption, including the terms responsible for the formation of a high-contrast sub-Doppler peak. The expressions derived here are in qualitative agreement with experimental data obtained earlier.