Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Journal of Quantum Electronics

Line shape and atomic efficiency of two-photon absorption using counter-propagating beams to reduce Doppler effects

John E. Bjorkholm, P. F. Liao

Published Dec 1, 1974• 8 citations
Publisher

Abstract

Doppler effects can be reduced or eliminated for two-photon absorption if the atoms are made to absorb one photon from each of two counter-propagating beams. We derive the line shape for the transition as a function of the frequency difference of the two beams and specifically consider the variation of the linewidth and of the efficiency of utilization of the available atoms.

DOI
10.1109/jqe.1974.1068117

Related papers

Experimental Evidence of Two-Photon Transition without Doppler Broadening

F. Biraben, Bernard Cagnac, G. Grynberg

Experiments on the $3S\ensuremath{-}5S$ two-photon transition in sodium give evidence that Doppler broadening is eliminated if the atom absorbs two photons propagating in opposite directions. The proof is given by the comparison of the two-photon absorption line shape in traveling and standing waves.

Physical Review Letters•Mar 25, 1974•299 citations

Line shape and strength of two-photon absorption in an atomic vapor with a resonant or nearly resonant intermediate state

John E. Bjorkholm, P. F. Liao

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{} ${10}^{9}$ larger than the case of equal-frequency photons with no loss in resolution.

Physical Review A•Aug 1, 1976•149 citations

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

F. Biraben, M. Bassini, Bernard Cagnac

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.

Journal de physique•Jan 1, 1979•66 citations

Reduced Doppler absorption profile in atomic and molecular beams

Nikolai N. Bezuglov, M. Yu. Zakharov, Andrey N. Klyucharev +5 more

The formation of the Doppler absorption profile P(ν) upon optical excitation of particles in the volume of effusion or gas-dynamic atomic and molecular beams by laser light propagating in a direction orthogonal (reduced) to the beam axis is considered. The analytical expressions for P(ν) are obtained for different types of beams and the specific features of the reduced absorption profile are studied as functions of the beam parameters. The function P(ν) is shown to be considerably different from the standard Gaussian shape. It is demonstrated that the calculated absorption spectrum at the frequencies of the sodium resonance lines D 1,2 agrees well with experiment.

Optics and Spectroscopy•Jun 1, 2007•3 citations

Profile of the two-photon absorption line due to the 1S-2S transition in atomic hydrogen

E. V. Baklanov, V. P. Chebotaev

An analysis is made of the profile of a two-photon absorption line of hydrogen free of the first-order Doppler broadening. The possibility of eliminating the quadratic Doppler effect with the aid of a narrow peak of the second derivative of the line profile is considered. It is shown that for a realistic temperature stability it should be possible to achieve a reproducibility of the order of 10 −15 .

Soviet Journal of Quantum Electronics•Mar 31, 1975•1 citation

Two-photon spectroscopy. II. Effects of residual Doppler broadening

Rainer Salomaa, Stig Stenholm

For pt.I see ibid., vol.8, p.1795 (1975) where the theory of Doppler-free two-photon transitions was discussed for the case of one single laser frequency. Here, the effects of two different frequencies are considered. When the residual Doppler width of the two-photon transition is less than the natural linewidth, the previous results are essentially regained. For large residual Doppler shifts, the absorption profile is a power-broadened Lorentzian if the frequency of the probe field is larger than the frequency of the strong field. In the opposite case, the absorption peak splits because of the AC Stark effect. The high-intensity distortions are minimized when equal frequencies can be used. Power-dependent shifts do not ordinarily occur with a resonantly tuned intermediate level. Some modifications of the spectra are introduced by phase-disturbing collisions.

Journal of Physics B Atomic and Molecular Physics•Jun 1, 1976•41 citations
Doppler effects can be reduced or eliminated for two-photon absorption if the atoms are made to absorb one photon from each of two counter-propagating beams. We derive the line shape for the transition as a function of the frequency difference of the two beams and specifically consider the variation of the linewidth and of the efficiency of utilization of the available atoms.
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.
The formation of the Doppler absorption profile P(ν) upon optical excitation of particles in the volume of effusion or gas-dynamic atomic and molecular beams by laser light propagating in a direction orthogonal (reduced) to the beam axis is considered. The analytical expressions for P(ν) are obtained for different types of beams and the specific features of the reduced absorption profile are studied as functions of the beam parameters. The function P(ν) is shown to be considerably different from the standard Gaussian shape. It is demonstrated that the calculated absorption spectrum at the frequencies of the sodium resonance lines D 1,2 agrees well with experiment.
For pt.I see ibid., vol.8, p.1795 (1975) where the theory of Doppler-free two-photon transitions was discussed for the case of one single laser frequency. Here, the effects of two different frequencies are considered. When the residual Doppler width of the two-photon transition is less than the natural linewidth, the previous results are essentially regained. For large residual Doppler shifts, the absorption profile is a power-broadened Lorentzian if the frequency of the probe field is larger than the frequency of the strong field. In the opposite case, the absorption peak splits because of the AC Stark effect. The high-intensity distortions are minimized when equal frequencies can be used. Power-dependent shifts do not ordinarily occur with a resonantly tuned intermediate level. Some modifications of the spectra are introduced by phase-disturbing collisions.