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Journal de physique

Line-shapes in Doppler-free two-photon spectroscopy. The effect of finite transit time

F. Biraben, M. Bassini, Bernard Cagnac

Published Jan 1, 1979• 66 citations
Publisher

Abstract

A general formalism is developed with the aim of calculating the line-shapes in two-photon absorption for the case of non monochromatic fields. This formalism is applied to the problem of the finite transit time of the atoms through the Laser beam; and it permits a precise expression to be obtained for the line-shape (convolution of a Lorentzian curve and a double-exponential curve). The comparison is made using experimental profiles.

DOI
10.1051/jphys:01979004005044500

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A general formalism is developed with the aim of calculating the line-shapes in two-photon absorption for the case of non monochromatic fields. This formalism is applied to the problem of the finite transit time of the atoms through the Laser beam; and it permits a precise expression to be obtained for the line-shape (convolution of a Lorentzian curve and a double-exponential curve). The comparison is made using experimental profiles.
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.
The line shape and strength of two-photon absorption in an atomic vapor are studied both theoretically and experimentally for the case of absorption of unequal-frequency photons. Special attention is given to the situation in which the intermediate state is resonant or nearly resonant. It is shown that for the resonant case, maximum absorption rates and Doppler-free spectra are simultaneously obtained. Either counterpropagating or copropagating beams can be used. With counterpropagating beams the two-photon linewidths are quite insensitive to power broadening of the intermediate state. With copropagating beams the two-photon spectra can also reveal the intermediate-state structure with a resolution determined mainly by the intermediate-state lifetime (nearly as well as can be done using any spectroscopic technique). The theoretical analysis provides a closed-form solution for the line shape and strength of the two-photon spectrum. In general the line shape is composed of two features. One is Doppler broadened and predominates when the intermediate state is nonresonant. The second feature is Doppler free, and it predominates with a resonant intermediate state. Detailed comparisons of experimental measurements of the line shape and strength of two-photon absorption in Na vapor are made with the theory and found to be in excellent agreement. Signal strengths for the onresonance case are 6 \ifmmode\times\else\texttimes\fi{} 109{10}^{9}109 larger than the case of equal-frequency photons with no loss in resolution.