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Soviet Journal of Quantum Electronics

Theory of the nonlinear Ramsey resonance in the optical part of the spectrum

B Ya Dubetskiĭ

Published Jun 30, 1976• 11 citations
Publisher

Abstract

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.

DOI
10.1070/qe1976v006n06abeh011587

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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.

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Transit effects in saturated absorption resonances

E. V. Baklanov, B Ya Dubetskiĭ

An important problem in saturated absorption spectroscopy is discussed: the width of a nonlinear absorption resonance in a low-pressure gas in a standing wave field. It is shown that the results reported by A.N. Titov et al. are incorrect. These authors stated that at weak saturations the resonance width is of the order of the reciprocal transit time of an atom traveling at the thermal velocity across a light beam. The specific source of the error is indicated, which is an incorrect mathematical treatment of the correct initial equations. It is also shown that the saturated absorption line profile in the transit limit is almost independent of the laser field configuration.

Soviet Journal of Quantum Electronics•Jul 31, 1988•1 citation
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 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.
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.
The paper theoretically establishes and studies the sub-Doppler linear optical Ramsey resonances that arise under certain conditions near centers of optical transitions in the absorption of a sufficiently weak monochromatic light beam during its stationary propagation in the normal direction through an ultrathin gas cell whose internal thickness is less than or of the order of the wavelength of this radiation. We consider a situation when the cross section of this beam consists of two coaxial spatially separated regions, with the absorption signal being detected in a comparatively narrow central part of the beam. The paper studies the significant dependence of the linear optical Ramsey resonances, that arise in such an absorption spectrum, on the distance between these regions, as well as on the phase difference between them. In particular, it is shown that if this phase difference is close to pi, then instead of absorption, amplification of the central part of the incident beam can occur. The Ramsey resonances under consideration are most clearly manifested when the internal thickness of the gas cell is equal to a small halfinteger number of wavelengths of the resonant radiation. However, these resonances do not arise if this thickness is equal to an integer number of such waves. The established Ramsey resonances, under certain conditions, can find application in ultrahigh resolution atomic (molecular) spectroscopy, as well as effective references in compact optical frequency standards.
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.
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.
An important problem in saturated absorption spectroscopy is discussed: the width of a nonlinear absorption resonance in a low-pressure gas in a standing wave field. It is shown that the results reported by A.N. Titov et al. are incorrect. These authors stated that at weak saturations the resonance width is of the order of the reciprocal transit time of an atom traveling at the thermal velocity across a light beam. The specific source of the error is indicated, which is an incorrect mathematical treatment of the correct initial equations. It is also shown that the saturated absorption line profile in the transit limit is almost independent of the laser field configuration.