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Journal of Physics B Atomic Molecular and Optical Physics

Diffusion-broadened lineshape under a strong field

David A. Shapiro, М. Г. Степанов

Published Jun 14, 1997• 1 citation
Publisher

Abstract

The Bennett hole is analysed for a medium of two-level particles with weak collisions beyond the scope of the perturbation theory. In the limit of small homogeneous width, the analytical expression for the hole shape is of the form of a Bessel function. The result is compared with data obtained by the variational approximation and numerical calculation. It is shown that the approximation gives the correct width, but an incorrect shape.

DOI
10.1088/0953-4075/30/11/001

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The Bennett hole is analysed for a medium of two-level particles with weak collisions beyond the scope of the perturbation theory. In the limit of small homogeneous width, the analytical expression for the hole shape is of the form of a Bessel function. The result is compared with data obtained by the variational approximation and numerical calculation. It is shown that the approximation gives the correct width, but an incorrect shape.
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.
We derive an expression in terms of cylinder functions for the shape of a nonlinear resonance in a two-level system with a rapidly decaying level. We show that when the natural linewidth is negligible, the square of the total width is the sum of squares of the power and diffusion widths. The traditional variational approximation yields a correct value for the full width at half maximum, but distorts the line profile. We derive a formula for the absorbed power as a function of the incident wave intensity for comparable power and diffusion broadening. The formula is found to be valid for a power width that is small or large compared to the diffusion width, and in a new intermediate domain where homogeneous saturation becomes inhomogeneous.
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.
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.
We develop an expansion for the absorption line shape of a two-level system in a strong radiation field being perturbed by dephasing collisions with a thermal bath of foreign atoms. We assume that the bath atoms do not interact with the radiation field and with each other. The microscopic information relevant for line broadening in a strong field is expressed in terms of a hierarchy of dipole correlation functions. The latter may be calculated with the use of the Franck-Condon factors for the nuclear wave functions. The present theory reduces in the weak-field limit to the well-known linear unified theory of line broadening and in the impact limit we recover the Karplus-Schwinger formula.