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Soviet Journal of Quantum Electronics

Intensity of a linear resonance of the absorption by trapped particles

E. V. Baklanov, Е. А. Титов

Published Aug 31, 1980• 1 citation
Publisher

Abstract

A study is made of the intensity of a resonance with homogeneous width, which appears at the center of an absorption line for particles trapped in a potential well. A calculation is made of the dependence of the amplitude of the resonance on geometric factors (such as the orientation of a light beam relative to the symmetry axes of the well) and on the anharmonicity.

DOI
10.1070/qe1980v010n08abeh010631

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Soviet Journal of Quantum Electronics•May 31, 1982•1 citation
A study is made of the intensity of a resonance with homogeneous width, which appears at the center of an absorption line for particles trapped in a potential well. A calculation is made of the dependence of the amplitude of the resonance on geometric factors (such as the orientation of a light beam relative to the symmetry axes of the well) and on the anharmonicity.
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.
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.
Within the framework of the classical model, which describes electrons as damped harmonic oscillators in an external electromagnetic field, expressions for the absorption and dispersion coefficients in the second order of smallness in the saturation parameter are found for a uniformly broadened line at a low concentration of oscillators, when the amplitude of the field produced by neighboring electrons is significantly less amplitude of the external field. It is shown that with increasing saturation parameter, the shape of the dispersion resonance becomes asymmetric, that at small saturation parameter leads to its linear shift to the "red" region. At the same time, as the saturation parameter increases, the dispersion resonance broadens (increases the interval between the maximum and minimum of the dispersion curve) and, in addition, there is a relative increase in the low-frequency amplitude compared to the high-frequency one. As for the shape of the absorption line, just as for the dispersion resonance, as saturation parameter increases, an asymmetry of the line shape appears which is accompanied by a shift to the "red" region. Because the low-frequency wing of the absorption line shifts toward the resonance center faster than the high-frequency wing moves away from the center, a narrowing of the resonance from the saturation parameter is observed. The dependence of this narrowing is nonlinear. In this case, the maximum of the absorption resonance linearly shifts to the "blue" region at the same speed as the dispersion line shifts to the "red" one.
The effect of a force of resonance pressure of light on the amplitude and frequency properties of saturated-absorption resonance in a gas of two-level atoms was studied. On the basis of numerical solutions of the Liouville and Fokker-Planck equations, dynamics of changes in the velocity-distribution function of an ensemble of atomic particles, depending on the saturation parameter and time of their interaction with a strong field of light, was evaluated. The shape of a resonance line, related to saturated absorption, and its location relative to the frequency of the atomic transition were determined taking into account the dynamics of the distribution function. The results of the calculations are compared with the experimental data.
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