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Physical Review A

Strong saturation of Doppler-broadened spectra in the presence of weak collisions

Abraham G. Kofman

Published Oct 1, 1998• 1 citation
Publisher

Abstract

Steady-state saturation of Doppler-broadened spectra of gases by strong near-resonant field in the presence of weak velocity-changing collisions (VCC), which causes the Gaussian-Markovian frequency fluctuations, is considered nonperturbatively. A stochastic rate equation is derived, and its applicability to different systems is discussed. The field-matter interaction is approximated by a \ensuremath{\delta}-function sink in the velocity space. The necessary and sufficient conditions for the validity of this contact model (CM) are obtained. The CM is shown to hold for not too strong fields and/or sufficiently frequent VCC. The CM has allowed us to obtain nonperturbative analytical results for the velocity distribution of the populations of the resonant transition, the integral populations, and the absorption (induced emission) rate. We show that the CM, together with the quasistatic limit, describes the saturation for all values of the parameters, except for the region of the transition between the above models. For the exactly resonant case the CM, together with the previously obtained nonperturbative solution, provides the full solution of the problem. The most striking feature of the saturation in the case of weak VCC is the intermediate saturation, i.e., the existence of the interval of the field intensities, where the populations and absorption (emission) rate are almost independent of the field. In this region the sink is very strong, whereas the coupling of the field with nonresonant atoms is still weak, so that the saturation is controlled by the diffusion of the active atoms in the velocity space towards the sink. The results of the present theory are shown to differ significantly from the results of the strong-collision model of the VCC. The present theory is verified by independent numerical calculations.

DOI
10.1103/physreva.58.3012

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Steady-state saturation of Doppler-broadened spectra of gases by strong near-resonant field in the presence of weak velocity-changing collisions (VCC), which causes the Gaussian-Markovian frequency fluctuations, is considered nonperturbatively. A stochastic rate equation is derived, and its applicability to different systems is discussed. The field-matter interaction is approximated by a \ensuremath{\delta}-function sink in the velocity space. The necessary and sufficient conditions for the validity of this contact model (CM) are obtained. The CM is shown to hold for not too strong fields and/or sufficiently frequent VCC. The CM has allowed us to obtain nonperturbative analytical results for the velocity distribution of the populations of the resonant transition, the integral populations, and the absorption (induced emission) rate. We show that the CM, together with the quasistatic limit, describes the saturation for all values of the parameters, except for the region of the transition between the above models. For the exactly resonant case the CM, together with the previously obtained nonperturbative solution, provides the full solution of the problem. The most striking feature of the saturation in the case of weak VCC is the intermediate saturation, i.e., the existence of the interval of the field intensities, where the populations and absorption (emission) rate are almost independent of the field. In this region the sink is very strong, whereas the coupling of the field with nonresonant atoms is still weak, so that the saturation is controlled by the diffusion of the active atoms in the velocity space towards the sink. The results of the present theory are shown to differ significantly from the results of the strong-collision model of the VCC. The present theory is verified by independent numerical calculations.
We study the effects of velocity-changing collisions (VCC's) on nearly degenerate forward four-wave mixing (FWM) in the presence of a strong pump. The calculations include the effects of both VCC's and phase-interrupting collisions. Explicit calculations and results for FWM in two-level systems for the case of strong collisions are presented in the Doppler limit. Effects of saturation on VCC-induced narrowing and those of VCC's on strong-field-induced resonances are discussed in detail.
The authors present an approach that allows the study of the influence of velocity-changing collisions (VCC) on the spectrum of resonance fluorescence. They give a theoretical framework yielding general, though quite complicated results. Working in the dressed-atom basis and describing the VCC by a strong-collision model, they focus their attention on the particular case of well separated spectral lines, which leads to relatively simple expressions. The results allow the authors to compare the effects of Doppler shifts and VCC on the profiles of the central line and on the spectra sidebands. They predict that VCC cause a narrowing of the spectral lines, which they attribute to Dicke narrowing. This prediction is also confirmed by numerical results. The adopted method of dealing with VCC in terms of collision operators can be applied to a larger class of collision models than just the strong-collision model used here.
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.
A theory of saturation spectroscopy in three-level gas-vapor systems, including collisional effects, is presented. Using a model of collisions in which they are phase interrupting in their effect on level coherences and velocity changing in their effect on level population densities, the authors calculate the absorption profile of a weak probe field on a given transition when an arbitrarily strong pump field acts on a coupled transition. Line shapes are derived for an arbitrary collision kernel describing the velocity-changing collisions, and these line shapes are evaluated for the collision kernel proposed by Keilson and Storer. Various limiting forms for the line shapes are derived and representative line shapes are displayed. Several new features of the line shapes, including collisionally induced increased probe absorption are discussed. The line shapes are seen to reflect the various collisional processes that may occur in atomic or molecular systems.
The velocity changing collisions (vcc) play an important role in the description of velocity redistribution of particles caused by nearly resonant interaction with the laser light and collisions (1). Collision relaxation rates are conveniently described by collision kernels which, in turn, depend on interatomic potential and scattering amplitudes and is proportional to the collision cross section. The population kernel gives the probability density per unit time that an active particle in state 1 i> undergoes collisions with perturbers (usually a noble gas atom or impurity), which changes the active particle velocity from v′ to v. Due to the fact that perturber-active particle interaction is state dependent the collisions cause different changes in the ground and excited states of active particle. Although the shape of the populations distributions resembles those from well-known Bennett hole theory, the distribution of the total population has two peaks and obviously is asymmetrical (2). Vcc together with velocity selective laser excitation lead to the asymmetry of the ground and excited state population. The flux of excited particles has properties which are different from that of ground state because of interaction collision potentials for both states. The intensity of the laser light strongly influences the velocity distributions of the ground and excited state populations.