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Soviet Journal of Quantum Electronics

Two-photon resonance in a standing-wave field under conditions of longitudinal interaction with an atomic beam

E. V. Baklanov, B Ya Dubetskiĭ, V. A. Ulybin

Published Aug 31, 1980• 2 citations
Publisher

Abstract

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.

DOI
10.1070/qe1980v010n08abeh010539

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Soviet Journal of Quantum Electronics•May 31, 1982•1 citation
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.
An analysis is made of the influence of transit effects on the profile of a two-absorption line of a gas interacting with a standing wave field. It is shown that in the case of a confined light beam the resonance width is governed by the transit times of atoms across the beam. When two light beams separated by a large distance are present, there is an additional resonance line of width which is the reciprocal of the transit time between the beams. This resonance is analyzed allowing for the relaxation of atomic levels.
A theoretical analysis is made of a resonant interaction of two-level atoms with the field of three strong spatially separated standing waves. It is shown that this interaction should give rise to a resonance of width equal to the reciprocal of the transit time between the fields and this resonance should be observed for all rational values of the ratio of the distances by which the waves are separated in space. Calculations are made of the corrections to the flux of particles excited in an atomic beam and to the power absorbed by a gas because of the interaction of atoms with the three fields. It is found that because of recoil a resonance of this kind splits into an infinite series of components separated by intervals of the order of the recoil frequency. The results are given of a numerical calculation of the strongest components of this resonance. The shift and deformation of lines due to quadratic Doppler effect are considered. The results of the calculations are compared with the available experimental data.
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.
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.
It is shown that the interaction of three standing-wave light beams with a low-pressure gas gives rise to a narrow absorption power resonance. The width of this resonance is related to the transit time of gas atoms between the beams. The weak-field case is analyzed. A formula for a Held of arbitrary intensity is obtained for the situation when the dimensions of the beams are much smaller than the distances between them. Numerical calculations are reported of the resonance amplitude and profile. Optimal (in respect of the field intensity) conditions for the observation of the effect are determined. If the distances between the beams are sufficiently large, it should be possible to observe resonances of width equal to the homogeneous width of atomic radiation lines in spite of the considerable field and transit broadening. The possibility of using this power resonance in stabilization of the emission frequency of gas lasers is considered.
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