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Physical Review A

Stationary states and their stability for a mixture of molecular gases under velocity-selective excitation

Alexander V. Ghiner, Michael A. Vaksman

Published Oct 1, 1996• 1 citation
Publisher

Abstract

We consider a mixture of resonant two-level molecules under velocity-selective excitation and a buffer gas. The corresponding kinetic equations are augmented by a strong-collision model with free parameters. We obtain the equilibrium velocity distribution functions of the resonant and buffer components. We then use the Boltzmann kinetic equations to derive the H-theorem analog for this mixture (valid for arbitrary values of the collision rates \ensuremath{\nu} and the spontaneous decay rate \ensuremath{\gamma}) and discuss the implications for the stability of the stationary solutions. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.3270

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We consider a mixture of resonant two-level molecules under velocity-selective excitation and a buffer gas. The corresponding kinetic equations are augmented by a strong-collision model with free parameters. We obtain the equilibrium velocity distribution functions of the resonant and buffer components. We then use the Boltzmann kinetic equations to derive the H-theorem analog for this mixture (valid for arbitrary values of the collision rates \ensuremath{\nu} and the spontaneous decay rate \ensuremath{\gamma}) and discuss the implications for the stability of the stationary solutions. \textcopyright{} 1996 The American Physical Society.
The authors consider a system of two-level atoms coupled to a radiation field and immersed in a buffer gas. The corresponding Bloch-like equations are augmented by collision operators stemming from the linear Boltzmann equation. Collision operators describe velocity-changing collisions that give rise to various kinetic effects of light. They study the general properties of collision operators, the main one consisting of the fact that such operators are Hermitian in a suitably defined space of velocity distribution functions They introduce a set of functions that serve as approximations to the eigenfunctions. The eigenvalues are connected with transport coefficients (they give an example of such a relation), but they keep eigenvalues as free parameters of the approach. In this way the authors can describe the whole class of collision operators, the Keilson-Storer model being a particular example. Employing the introduced eigenfunctions they derive and formally solve the equations of motion for the expansion coefficients of the elements of the density matrix of active atoms.
Method of stimulated photon echo with specially chosen linear polarizations of exciting pulses of coherent resonant radiation is applied for investigation of collisional decay of orientation and alignment in molecular gas SF6 and its mixtures with buffers He and Xe. These relaxation rates are measured as a function of longitudinal velocities. Within experiment accuracy, no remarkable velocity dependence of depolarizing collisions rates was detected. This result confirms conventional approach of depolarizing collisions theoretical treatment.
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 role played by a buffer gas in the ground-state superposition created in coherent-population-trapping experiments is investigated theoretically. The density matrix equations are solved on the basis of the coupled-noncoupled states. The velocity-changing collisions are examined in the limit of strong collisions. The relaxation rate for transfer of the ground-state superposition between atoms with different velocities is derived from a fit of available experimental results. \textcopyright{} 1996 The American Physical Society.
The interaction of a plane monochromatic traveling wave with two-level particles suffering collisions with buffer-gas particles is considered. Collision rates are assumed to be velocity dependent. The collision integral is obtained on the basis of the strong-collision model, generalized to the case of velocity-dependent collision rates (the so-called ``kangaroo'' model). We obtained the exact analytical solution of the problem for arbitrary intensity of radiation, arbitrary ratio of homogeneous and Doppler widths of the absorption line, and arbitrary mass ratio between absorbing- and buffer-gas particles. The obtained analytical solutions of the quantum kinetic equations allowed us to analyze the spectral shape of the strong-field absorption line as well as the probe-field absorption line (the nonlinear part of the work done by the probe field) and the frequency dependence of the light-induced drift (LID) velocity. A comprehensive comparative analysis for the three- and one-dimensional versions of the model is given. On the basis of this analysis, we reach the conclusion that the one-dimensional quantum kinetic equation has quite a wide range of application. We also reveal the conditions for the strongest manifestation of the velocity dependence of the collision rates, which affects most strongly the anomalous LID.