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Soviet Journal of Quantum Electronics

Profile of a two-photon resonant absorption line calculated allowing for the quadratic Doppler effect

Vladimir G. Minogin

Published Sep 30, 1976• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qe1976v006n09abeh011857

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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.
An investigation is made of the two-photon absorption line profile in a standing-wave field for particles trapped in an oscillator potential at right angles to the optical beam. It is found that this profile is an equidistant lattice of resonances if the oscillation frequency and the amplitude of the ion thermal oscillations are greater than the homogeneous line width and the size of the optical beam, respectively. Allowance for the thermal quadratic Doppler and Stark effects results in broadening of each resonance and changes its profile. A new method of eliminating thermal broadening of the spectral components of the line profile is discussed
The two-photon absorption line profile in a standing wave field is found for particles captured in a three-dimensional trap. When the transverse dimension of the optical beam is comparable with the size of the trap, transit broadening is eliminated and the line profile is that of a resonance having the homogeneous width. For optical beams of small dimensions, homogeneous-width resonances occur in the line profile if the frequency of the ion oscillations in the trap is greater than the homogeneous width.
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.
An analysis is made of the feasibility of obtaining two-photon absorption resonances of 10–100 Hz width under conditions of longitudinal interaction with a standing-wave field. The long atom– field interaction time makes it possible to increase the resonance intensity. It is established that in a system with a beam of atoms propagating along an optical beam, the contribution of slow atoms results in the formation in the second derivative of the line profile of a resonance characteristic with a radiative width. An analysis is made of the influence of the quadratic Doppler effect, Stark effect, and saturation.
The problem of two-photon interaction of atoms with the field of two standing-wave pulses is solved. It is shown that the transit broadening of the line caused by a finite pulse duration and finite transit time of atoms through the light beam is eliminated. On focusing the field a transverse velocity selection of atoms occurs that lends to a decrease of the quadratic Doppler shift of the frequency. A new value of the amplitude of the induced 1S--2S two-photon transition of hydration is obtained that is used for the calculation of the signals. The resonance amplitude in hydrogen proves to be larger for existing pulsed radiation sources than that in continuous excitation by the field.