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Journal of the Optical Society of America B

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

Sunita Singh, G. S. Agarwal

Published Dec 1, 1988• 7 citations
Publisher

Abstract

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.

DOI
10.1364/josab.5.002515

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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.
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.
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)].
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.>
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 theory of the influence of binary collisions on the line shapes associated with Doppler-free spectroscopy is presented. The specific calculation is for two-photon absorption through a real or virtual intermediate state, but the extension of the results to alternative level schemes is included. Collisions are treated quite generally at first, but, ultimately, a simple but reasonable collision model is adopted to properly account for both the "phase-interrupting" and "velocity-changing" aspects of collisions. It is shown that collisional processes can be used to distinguish between the "two-quantum" and "stepwise" contributions to the two-photon excitation rate. Moreover, it is demonstrated that systematic experimental line-shape investigations, in addition to providing tests of current collision theories, can lead to values for collision broadening and shift parameters, excitation transfer rates, magnetic substate relaxation rates, velocity-changing collision rates, and collision kernels. Consequently, Doppler-free spectroscopy can provide a new and important probe of collision effects in atomic and molecular systems.