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Soviet Journal of Quantum Electronics

Nonlinear Ramsey resonance of the number of excited particles

B Ya Dubetskiĭ, Семибаламут Владимир Михайлович

Published Jan 31, 1978• 0 citations
Publisher

Abstract

An analysis is made of the interaction of three spatially separate standing Gaussian waves with an atomic beam. The case of a Doppler-broadened transition is considered. An expression is obtained for the correction to the resonance in the number of excited particles, the width of the correction being inversely proportional to the transit time between the waves. The analysis is carried out for a weak field. Numerical calculations of the amplitude and profile of the resonance are reported. The optimal (in respect of the field intensity) conditions for the observation of this resonance are determined.

DOI
10.1070/qe1978v008n01abeh008435

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An analysis is made of the interaction of three spatially separate standing Gaussian waves with an atomic beam. The case of a Doppler-broadened transition is considered. An expression is obtained for the correction to the resonance in the number of excited particles, the width of the correction being inversely proportional to the transit time between the waves. The analysis is carried out for a weak field. Numerical calculations of the amplitude and profile of the resonance are reported. The optimal (in respect of the field intensity) conditions for the observation of this resonance are determined.
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.
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 field dependence of the susceptibility of a gas interacting with a standing wave is calculated near the center of a line for a field of arbitrary profile. An allowance is made for the effects of spatial modulation of the gas. Numerical calculations are reported for a field with a Gaussian profile allowing for degeneracy. These calculations can be checked directly against experimental results for a transition corresponding to a line at λ = 3.39 μ in CH4 , which should make it possible to determine accurately the dipole moment of the transition. The amplitude and half-width of a Lamb dip are calculated for a field of arbitrary profile on the basis of perturbation theory. The problem of approximation of a real Gaussian field with a model field characterized by an amplitude constant over a circular cross section is considered. The precision of model calculations is determined for weak and strong fields. Resonances in atomic beams are discussed under transit conditions. It is shown that in this case there is a slow atom effect, which is responsible for lines with a characteristic width that is a linear function of the homogeneous width of a transition when excited particles are detected on the basis of their fluorescence.
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 nonlinear absorption or gain characteristics of an optical-frequency, Doppler-broadened atomic resonance involving levels with closely spaced structure are analyzed. The level structures are assumed to be resolved with respect to their natural widths, but not necessarily with respect to the Doppler width at the optical transition. The radiation field consists of two closely spaced monochromatic frequencies lying within the Doppler width of the resonance. This type of radiation field may be obtained, for example, from a laser operating in two of its Fabry-Perot resonator modes. It is shown that, because of saturation of level populations and double-quantum Raman transitions between levels, appreciable nonlinear coupling takes place between the two fields. This coupling shows a resonance behavior when the frequency separation of the two applied fields becomes equal to the frequency splitting between two of the components which form either level structure. The width of this resonance is determined entirely by the natural widths of these two level components and not by the Doppler width of the optical transition or the natural width of other level components. When such a resonance occurs, the over-all gain or attenuation characteristics of the atomic resonance change drastically. In practice the frequency spacing of the fields may be kept constant while the level structures are tuned, e.g., magnetically. The effects are analyzed for cases of running-wave and standing-wave radiation fields. The use of this effect in precise determination of level structures as well as mode or transition coupling of a gas laser is discussed. Portions of the analysis are applicable to resonances with more general forms of inhomogeneous broadening.