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Physical Review Letters

Collisionally Induced Narrowing of the Longitudinal Relaxation Linewidth in Nearly Degenerate Four-Wave Mixing

Jenny Lam, Duncan G. Steel, R. A. McFarlane

Published Nov 29, 1982• 36 citations
Publisher

Abstract

This paper reports the observation of collisionally induced spectral narrowing of the longitudinal relaxation linewidth with use of the nearly degenerate four-wave mixing process. A theoretical model, which takes into account strong velocity-changing collisions for the population and phase-interrupting collisions for the optical coherence, leads to a good qualitative understanding of this new effect.

DOI
10.1103/physrevlett.49.1628

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Physical Review A•Jun 1, 1988•16 citations
This paper reports the observation of collisionally induced spectral narrowing of the longitudinal relaxation linewidth with use of the nearly degenerate four-wave mixing process. A theoretical model, which takes into account strong velocity-changing collisions for the population and phase-interrupting collisions for the optical coherence, leads to a good qualitative understanding of this new effect.
Recently, we have shown that the nearly degenerate four-wave mixing (NDFWM) process can provide a direct and simultaneous measurement of the longitudinal (1/T1) and transverse (1/T2) relaxation rates of a resonant two-level atom. Furthermore, we observed that in the presence of buffer gases, the linewidth of the resonance describing the longitudinal relaxation process experiences a significant narrowing, belowo that of the natural width. Using a theoretical model, the narrowing was accounted for as arising from collisional effects in the ground-state population. 1 These observations were made for the case where the radiation fields are co-polarized, and we concluded that NDFWM offers a unique technique for the measurement of the ground-state velocity-changing cross section.2
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.
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)].