Quadratic Doppler Effect Research Articles

Interaction of a standing frequency-modulated wave with a gas in a flight region

A formula is obtained for the power of the nth harmonic absorbed upon interaction of a standing frequency-modulated wave with a gas for an arbitrary modulation frequency and amplitude of the frequency deviation. The flight effects, the quadratic Doppler effect, and the recoil effect are taken into account.

On the Cross‐Correlation between Dark Matter Distribution and Secondary Cosmic Microwave Background Anisotropies of the Ionized Intergalactic Medium

We investigate a cross-correlation between the weak gravitational lensing field of the large-scale structure κ and the secondary temperature fluctuation field Δ of the cosmic microwave background (CMB) induced by Thomson scattering of CMB photons off the ionized medium in the mildly nonlinear structure. The cross-correlation is expected to observationally unveil the biasing relation between the dark matter and ionized medium distributions in the large-scale structure. We develop a formalism for calculating the cross-correlation function and its angular power spectrum based on the small angle approximation. As a result, we find that the leading contribution to the cross-correlation comes from the secondary CMB fluctuation field induced by the quadratic Doppler effects of the bulk velocity field v of the ionized medium since the cross-correlations with the O(v) Doppler effect and the Ostriker-Vishniac effect of O(vδ) are suppressed on relevant angular scales because the linear dependence on the bulk velocity field leads to cancellations between positive and negative contributions among the scatterers for the ensemble average. The magnitude of the cross-correlation can be estimated as κΔ ~ 10-10 on small angular scales (l 1000) under the currently favored cold dark matter model of the structure formation and the simplest scenario of homogeneous reionization after a given redshift of zion 5. Although the magnitude turns out to be small, we find several interesting aspects of the effect. One of them is that the density-modulated quadratic Doppler effect of O(δev2) produces the cross-correlation with the weak lensing field that has linear dependence on the electron density fluctuation field δe or, equivalently, on the biasing relation between the dark matter and electron distributions. In other words, the angular power spectrum could be either positive or negative, depending on the positive biasing or antibiasing, respectively. Detection of the cross-correlation thus offers a new opportunity to observationally understand the reionization history of intergalactic medium connected to the dark matter clustering.

Frequency shifts of a methane standard

Frequency shifts are calculated for a methane standard the reproducing the frequency of the molecular transition generating λ = 3.39 μm radiation by the methods of absorption saturation and dispersion. Allowance is made for the simultaneous influence of the quadratic Doppler effect, of splitting because of the recoil effect, of collisional and transit broadening, and of a magnetic hyperfine structure of the spectral line.

Transit-time effects and quadratic Doppler effect in saturated absorption and dispersion spectroscopy

An investigation is made of the resonance profile in saturated absorption and dispersion spectroscopy for arbitrary saturation of the absorption, subject to allowance for transit-time effects and the quadratic Doppler effect. Expressions are obtained for saturated absorption and dispersion signals in the rate approximation for a beam of rectangular shape in the case of two opposite waves with very different intensities and a standing wave. The widths of the resonances and the maximum resolving power of saturated absorption and dispersion spectroscopy are considered. General expressions are obtained for the frequency shifts, due to the quadratic Doppler effect, of stabilized lasers in the case of arbitrary values of the absorption saturation, frequency deviation, and number of the signal harmonic used in frequency stabilization. An analysis of these expressions is made in some limiting cases.

High-resolution high-contrast excitation of calcium in separated fields

A procedure is suggested for compensating the broadening due to the quadratic Doppler effect and for band shifts caused by phase mismatch in the observation of a Ramsey signal in an atomic calcium beam. The relative error in the frequency stabilized by this method is estimated to be 2 × 10− 12.

Influence of the quadratic Doppler effect on the shift of a dispersion resonance in the transit limit

An expression is obtained for the shift of a dispersion resonance because of the quadratic Doppler effect in the transit limit.

Nonlinear resonances in a system of separated optical fields under the influence of the recoil and quadratic Doppler effects

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.

Collinear laser spectroscopy of the Balmer-α line

A pilot study on the usability of collinear laser spectroscopy in fast beams for metrological purposes is reported. The method combines high resolution and high sensitivity, and allows the measurements on free atoms without perturbing interactions. The Balmer-α line was choosen for this purpose. Possible applications include the determination of the Rydberg constant, the quadratic Doppler effect and high precision measurements of high voltages.

Influence of the quadratic Doppler effect on the absorption line profile of particles captured by a trap

It is found that allowance for the quadratic Doppler effect broadens and changes the resonance absorption line profile of particles trapped in an oscillator potential comprising a periodic lattice of resonances having an envelope in the form of a conventional Doppler profile, if the particle oscillation frequency is greater than the homogeneous line width. When the quadratic Doppler shift is small compared with the homogeneous line width, its influence is reduced to a shift of the resonances. A new possibility for eliminating thermal broadening of individual resonances is discussed.

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

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.

Field broadening and shifts of nonlinear power resonances in low-pressure gases

A calculation is made of the absorption coefficient of a standing-wave field in a gas of two-level molecules allowing for transit effects to within the second order of the saturation parameter. The rate of the field broadening of a nonlinear power resonance is investigated for various dimensions of a light beam. An analysis is also made of the rates of the field shift of the maximum of such a nonlinear resonance because of the quadratic Doppler effect and hyperfine structure of the line.

Prospects for precision physical experiments in optics

Until recently the sources of electromagnetic waves in the radio and γ-ray bands were much more monochromatic than optical sources. The advent of stable lasers with frequency reproducibility ~1014 has uncovered new possibilities of performing experiments of interest in physics. To illustrate these possibilities, results are cited of the measurements of the quadratic Doppler effect in a gas, the magnetic hyperfine structure of a vibrational-rotational transition of methane, and the recoil effect. A number of experiments that lasers will make possible in the near future are discussed, namely, high-accuracy measurements of the Rydberg constant using two-photon absorption, measurement of the quadratic Doppler shift, measurements of the gravitational frequency shift of the earth's field, and the possibility of observing parity nonconservation in atomic transitions.

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

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.

Influence of transit effects on the frequency of a stabilized gas laser

A theoretical analysis is made of the influence of the quadratic Doppler effect, magnetic hyperfine splitting of a line into several components, and transit effects on the emission frequency of a gas laser. This laser is assumed to be stabilized by the frequency modulation method and the modulation frequency is arbitrary.

Quadratic Doppler effect for a light beam of finite dimensions

A theoretical analysis is made of the shift of a Lamb dip due to the quadratic Doppler effect in the case of a light beam of finite size. The shift is less than in the spatially homogeneous case because of an increase in the role of slow atoms in the formation of the dip. The case of a Gaussian beam is analyzed. The example of a beam with a constant transverse field distribution is used to demonstrate that the shift due to the quadratic Doppler effect increases with rising field.

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

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.

Quantum optical frequency standards (review)

When the optical absorption of gases is saturated by a coherent field, resonance peaks of widths several orders of magnitude greater than the Doppler width appear at the centers of the lines. These resonance peaks are used as high-precision frequency standards. The present review is concerned with various optical frequency standards based onresonance peaks of saturated gas lines. These methods include stabilization of a laser with the aid of the Lamb dip, the absorption peak in internal and external cells, etc. It is shown that frequency stability better than 10–14 in 100 sec and a reproducibility of 5·10–13 can be achieved. It is reported that the quadratic Doppler effect in the emission of optical-frequency photons influences the precision of the frequency reproducibility. A review is given of the measurements of an infrared frequency (approximately 88.386.2 GHz, wavelength 3.39 μ) by comparison with a klystron harmonic. Potentialities of quantum optical frequency standards are discussed and future tasks are outlined.

THE MÖSSBAUER EFFECT

A classical theory of the Mossbauer effect is developed which agrees completely with the quantum calculations. A calculation of the quadratic Doppler effect, thermal motion of the nuclei in a lattice, is made and agreement with the width of the isomeric lie for Fe/sup 57/ in the Pound and Rebka experiments is obtained. Coherent effects are important only in monoisotopes of substances whose Mossbauer line intensity is close to unity. The effect is also calculated for an admixture and shown to depend on the crystalline and chemical structure. The spectral gamma rays of gaseous and liquid sources have a line width of 10/ sup -3/ ev, which is too great in comparison with natural line widths. Mosshauer effects have been investigated for Sn/sup 119/, which has a width of 2.4 x 10/sup -8/ ev for the 23.8-kev gamma particle. Magnetic field dependence and intensity as a function of source and absorber relative velocity for Sn and SnNb/ sub 3/ have been measured. Similar measurements on Zn/sup 67/ and Ag/sup 107/ are underway. (TTT)