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Journal of Experimental and Theoretical Physics Letters

Diffusion-broadened line shape near a turning point

David A. Shapiro, М. Г. Степанов

Published Jul 1, 1998• 1 citation
Publisher

Abstract

The absorption spectrum of a gas with a large Doppler width and soft collisions between particles is studied. The particles are assumed to have a nonlinear dependence of the resonance frequency on velocity. The shape of the narrow peak in the spectrum resulting from an extremum of this dependence is calculated analytically for the first time. In the absence of collisions it has a characteristic asymmetric shape. Collisions are shown to broaden the line and change its shape. The profile of the probe-field spectrum is obtained for a three-level system with the strong field at an adjacent transition. The components of the Autler-Townes doublet are found to spread and repel each other because of collisions.

DOI
10.1134/1.567829

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The absorption spectrum of a gas with a large Doppler width and soft collisions between particles is studied. The particles are assumed to have a nonlinear dependence of the resonance frequency on velocity. The shape of the narrow peak in the spectrum resulting from an extremum of this dependence is calculated analytically for the first time. In the absence of collisions it has a characteristic asymmetric shape. Collisions are shown to broaden the line and change its shape. The profile of the probe-field spectrum is obtained for a three-level system with the strong field at an adjacent transition. The components of the Autler-Townes doublet are found to spread and repel each other because of collisions.
An analytical expression is found for the profile of Bennett hole with different level lifetimes under strong field and weak collisions. The expression is valid while the diffusion and field broadening being more than the homogeneous one, but less than the thermal width. It is shown that the square of the total width being equal to the sum of the squares of the diffusion and field widths. The shape of saturation curve is calculated including weak collisions. The formula obtained describes the smooth transition from homogenous to inhomogeneous saturation throughout the new intermediate region. Probe-field spectrum of the three-level system is computed in the presence of the strong field at the adjacent transition. The Autler-Townes doublet components are shown to broaden and repel each other under the collisions. The main reason of both the effects occurs to be the diffusion of phase due to quadratic frequency shift.
An expression is found for the profile of Bennett hole with different level lifetimes under strong field and weak collisions. It is shown that the square of the total width being equal to the sum of the squares of the diffusion and field widths. Probe-field spectrum of the three-level system is obtained in the presence of the strong field at the adjacent transition. The Autler - Townes doublet components are shown to broaden and repel each other under the collisions. The main reason of both the effects occurs to be the diffusion of phase due to quadratic frequency shift.
A previously developed diagrammatic method for calculating the nonlinear response of a dilute gas at near resonance with strong classical radiation fields is extended to include velocity-dependent homogeneous and inhomogeneous broadening phenomena. The method is applied to two-level saturated-absorption (Lamb-dip) spectroscopy. Expressions are obtained for the collision-broadened Lamb dip probed by a weak field in the presence of an arbitrarily strong saturating field and are compared to the usual infinite-Doppler-width, weak-saturation expression. We study the effects of velocity and momentum transfer on the line-shape parameters and discuss the effect of phase-changing and strong inelastic collisions on the intensity.
The Rautian-Sobelman approach describing the collision-Doppler shape of spectral line that takes into account both soft and hard velocity-changing collisions is extended to the case when correlation between Doppler and collision broadening as well as the dispersion line asymmetry should be considered. Numerical calculations show that speed-dependent effects can produce the additional line narrowing as well as broadening and also the line asymmetry. It is shown that speed-dependent profiles based on the soft and hard collision models differ much more one from another than those which omit the speed-dependent effects.
As a rule the thermal motion removes the dark resonance from the spectrum of a three-level system driven by two strong fields. An example has been found where, conversely, the dark resonance manifests itself even after averaging over the velocities. The four-level system is studied with a closed cycle of four resonant fields, when two relatively strong fields interact with opposite transitions. If Rabi frequencies exceed relaxation constants, then the frequency dependence of the nonlinear susceptibility consists of several narrow peaks. Each peak corresponds to a ‘turning point’, the resonant frequency with zero derivative with respect to the velocity. It is shown that two peaks disappear when non-absorbing states coincide with the turning points. The coincidence occurs for equal Rabi frequencies of relatively weak fields.