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Physical Review A

Effect of velocity-changing collisions upon optical coherences in a three-level system

J.-L. Le Gouët, P. R. Berman

Published Jan 1, 1978• 18 citations
Publisher

Abstract

In this work, a theory of laser nonlinear spectroscopy and its application to the study of atomic collisions is developed. A three-level system (TLS) is considered in low-pressure gases. The effect of weak velocity-changing collisions (vcc) upon atomic coherences is introduced into the TLS equations established by H\"ansch and Toschek. It appears that a TLS is suitable for the observation of the effect of vcc upon optical coherences.

DOI
10.1103/physreva.17.52

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In this work, a theory of laser nonlinear spectroscopy and its application to the study of atomic collisions is developed. A three-level system (TLS) is considered in low-pressure gases. The effect of weak velocity-changing collisions (vcc) upon atomic coherences is introduced into the TLS equations established by H"ansch and Toschek. It appears that a TLS is suitable for the observation of the effect of vcc upon optical coherences.
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 general theory of atomic dipole coherence under the influence of collisional phase changes, inelastic effects and optically active atom velocity changes, including those due to anisotropic interactions is presented. Velocity change effects are obtained in closed form. Line shapes appear as convolutions of standard pressure broadening contours with velocity-change contours. Width and shift parameters for the He-broadened Na D lines at 2 m bar pressure, 380 K are calculated, as are He-induced photon echo decay rates for these lines. Overall agreement with xperiment is reasonably good.
A theoretical model for the pressure dependence of the intensity of a gas laser is presented in which only velocity-changing collisions with foreign-gas atoms are included. This is a special case where the phase shifts are the same for the two atomic-laser levels or are so small that deflections are the dominant effect of collisions. A collision model for hard-sphere repulsive interactions is derived and the collision parameters, persistence of velocity and collision frequency, are assumed to be independent of velocity. The collision theory is applied to a third-order expansion of the polarization in powers of the cavity electric field (weak-signal theory). The resulting expression for the intensity shows strong pressure dependence. The collisions reduce the amount of saturation and the laser intensity increases with pressure in a characteristic fashion. It is recommended that the best way to look for this effect is to make the measurements under conditions of constant relative excitation.
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.
We present a detailed theoretical treatment of a three-level $\ensuremath{\Lambda}$ system in a hot atomic vapor interacting with a coupling and a probe field of arbitrary strengths, leading to electromagnetically induced transparency and slow light under the two-photon resonance condition. We take into account all the relevant decoherence processes including collisions. Velocity-changing collisions (VCCs) are modeled in the strong-collision limit effectively, which helps in achieving optical pumping by the coupling beam across the entire Doppler profile. The steady-state expressions for the atomic density-matrix elements are numerically evaluated to yield the experimentally measured response characteristics. The predictions, taking into account a dynamic rate of influx of atoms in the two lower levels of the $\ensuremath{\Lambda}$, are in excellent agreement with the reported experimental results for ${^{4}\text{H}\text{e}}^{\ensuremath{\ast}}$. The role played by the VCC parameter is seen to be distinct from that by the transit time or Raman coherence decay rate.