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Physical Review A

Effects of saturation and velocity-changing collisions on nonlinear mixing in resonant systems

Sunita Singh, G. S. Agarwal

Published Sep 1, 1990• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.42.3070

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Physical Review A•Jul 1, 1994•1 citation
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.
We examine the effects of velocity-changing collisions (VCC’s) on nonlinear mixing in a Doppler-broadened vapor. We use a model in which both velocity-changing and phase-interrupting collisions are accounted for. We present explicit calculations and results for four-wave mixing in two-level systems for the case of strong collisions. We give results for both phase-conjugate and forward geometries. We discuss new features and modifications of signal line shapes due to VCC’s. The line shapes reflect the various collisional processes that occur in the system. VCC-induced line narrowing is discussed in detail.
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.
The phase-conjugate signal observed in resonant degenerate four-wave mixing on the 6/sup 3/P/sub 2/ to 7/sup 3/S/sub 1/ transition of atomic mercury in a Hg-Ar discharge is investigated. At a fixed argon pressure the variation of the signal with pump powers is explained by a model that includes the effects of velocity-changing collisions (VCCs). As the argon pressure was varied from 0 to 1 torr an increase in the phase conjugate signal was observed and is ascribed to a change in the discharge dynamics with argon pressure and to the influence of VCCs. To further clarify the role of collisions and optical pumping, degenerate four-wave mixing spectra are examined as a function of pump power. Line shapes are briefly discussed.>
A theory of four-wave mixing including effects of velocity-changing collisions is presented. Three fields with frequencies \ensuremath{\omega}, \ensuremath{\omega}, and \ensuremath{\omega}+\ensuremath{\delta} are incident on a vapor of ``two-level'' atoms having upper state b and lower state a. Two of the fields are counterpropagating and the third (of frequency \ensuremath{\omega}+\ensuremath{\delta}) makes a small angle with one of the others. The frequency \ensuremath{\omega} is a nearly resonant (inside the Doppler width) with the a-b transition frequency. The phase-conjugate signal emitted at frequency \ensuremath{\omega}-\ensuremath{\delta} is calculated as a function of \ensuremath{\delta}. Using a simple collision model in which collisions are phase interrupting in their effect on atomic coherence and velocity-changing in their effect on level populations, we discuss the conditions under which resonances characterized by the upper or lower radiative and collision rates can be observed. Assuming that the total (a+b) state population is conserved in the absence of collisions, it is shown that velocity-changing collisions can ``open'' the system and lead to a resonance characterized by the lower-state width (convoluted with the residual Doppler width). With increasing pressure, the width of this induced resonance structure decreases monotonically. For sufficiently high pressure, the collisional redistribution of velocity classes is complete---the system ``recloses'' and the narrow resonance disappears. The interplay of the collision-induced opening, line narrowing, and reclosing of the system is discussed, as is the relationship of these narrow resonances to the so-called pressure-induced extra resonances of Bloembergen and co-workers [Indian J. Pure Appl. Phys. 16, 151 (1978); Phys. Rev. Lett. 46, 111 (1981)].
We present in this paper a theory of the saturation effects in degenerate four-wave mixing which makes use of the dressed-atom method. We mainly study the case of a Doppler-broadened line, but several results can be applied to the case of nearly degenerate four-wave mixing for a Doppler-free medium. We show that a close relationship does exist between the two problems : the generated beam is mainly created when the detuning between two incident beams is equal to the Rabi frequency. In the degenerate case, this condition is fulfilled by two velocity groups because of the Doppler shift. We analytically calculate the lineshapes for two-level atoms in the case of forward saturation (the intense pump beam propagates in the same direction than the probe beam) and in the case of backward saturation (the intense pump beam and the probe beam propagate in opposite directions). We also study collisional effects and the influence of the intensity of the weak pump beam when perturbation theory can no longer be applied.
The effects of velocity-selective optical pumping in nearly degenerate four-wave mixing are studied using a model in which the radiation fields interact with ``three-level'' atoms in the \ensuremath{\Lambda} configuration. The conditions under which it is possible to observe resonances characterized by an effective ground-state width are explored. It is shown that saturation of the system by optical pumping can lead to the disappearance of these narrow resonances in some limiting cases.