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The Journal of Chemical Physics

Two-photon absorption line shapes in the transit-time limit

Kevin K. Lehmann

Published Mar 8, 2021• 6 citations

Abstract

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.

DOI: 10.1063/5.0040868

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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.

A density-matrix calculation of the line shape for a Doppler-broadened two-level system subjected to a plane-standing-wave laser field with a Gaussian intensity profile is presented to fifth order in perturbation theory. The primary new result is that, for fixed pressure and intensity, the power-broadening contribution to the linewidth is at a minimum when the beam radius is approximately equal to the mean free path. In addition, an analytic solution for the linewidth in the collision-dominated regime is presented for general collision parameters.

We describe the influence of the intensity variation of the light in a standing wave on the lineshape of a Doppler-free multi-photon transition. We show that as long as the light shifts and the saturation are small compared to the Doppler width, a motional narrowing effect occurs and the line remains Lorentzian, the centre being shifted by an amount equal to the mean value of the dynamic Stark effect. We consider also the case of transients. We show that at resonance, it is possible to observe different responses according to the light intensity. In particular, it is possible to observe Rabi oscillations only if the Rabi frequency is larger than the natural width and smaller than the Doppler width of the transition.

The profile of a two-photon resonant absorption line of a particle subjected to a standing optical wave is calculated allowing for the quadratic Doppler effect. It is shown that the line profile is governed entirely by the ratio of the homogeneous line width to the quadratic Doppler frequency shift. An exact expression is obtained for the line profile in the second order in ν/c and the main approximations are considered. The profiles are calculated for the 1S-2S and 1S-3S transitions in the hydrogen atom.

We generalize the two-photon probe-absorption coefficient to include any amount of Doppler broadening and an arbitrarily intense saturator wave. By analytically performing integrals over a Lorentzian velocity distribution we are able to examine the transition from homogeneous broadening to extreme Doppler broadening for both zero and nonzero Stark shifts. For Doppler widths much larger than the saturator Rabi flopping frequency, the probe-absorption spectrum approaches a Doppler-free Lorentzian with width equal to the homogeneous linewidth and center displaced by the dynamic Stark shift.