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Journal of Physics B Atomic Molecular and Optical Physics

The spectra of radiation redistribution in the presence of velocity-changing collisions

S Kryszewski, Gerard Nienhuis

Published Sep 28, 1991• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/24/18/011

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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.
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.
The effect of collisions on the resonance fluorescence spectrum of three-level atoms with a V-configuration of levels when excited by two monochromatic resonance fields has been theoretically investigated. The analysis has been carried out for the systems with a small Doppler broadening compared to the collision frequency (high buffer gas pressures) and for the general case of an arbitrary change (from complete failure to complete preservation) of the phase memory at any of the three transitions in the V-system. It has been shown that in the three-level V-type atoms excited by two monochromatic fields, the resonant fluorescence spectrum (the number of spectral lines and their widths) at one of the transitions strongly depends on the presence of resonant radiation at the adjacent transition. Under certain conditions, the line widths will be completely determined by the relaxation characteristics of the adjacent transition and, in particular, can be repeatedly narrowed with an increase in the radiation intensity at the adjacent transition. It has been shown that despite the homogeneous nature of the broadening of the absorption lines, the resonance fluorescence spectrum has a pronounced anisotropy with respect to the mutual orientation of the wave vectors of spontaneous and exciting radiation. It has been established that the line widths in the resonance fluorescence spectrum are proportional to the diffusion coefficient of the atoms interacting with radiation under certain conditions. This fact can serve as the basis for a spectroscopic method for measuring the transport frequencies of the collisions of the radiation-absorbing particles with the buffer ones. It has been shown that the effects of phase memory in the collisions lead to a strong qualitative and quantitative modification of the resonance fluorescence spectrum.
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.
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.
The effect of collisions on the resonance fluorescence spectrum of two-level atoms excited by monochromatic resonance radiation is studied. Analysis is performed for systems where the Doppler broadening is small compared to the collision frequency (high buffer gas pressures) and for the general case where collisions arbitrarily change the phase of the radiation-induced dipole moment (from completely interrupted to completely unaffected phase of the dipole moment). Both at a relatively low and at a high excitation radiation intensity, the resonance fluorescence spectrum is shown to depend on whether the two-level system is closed or open. This is especially true for the narrow unshifted Rayleigh scattering line. It is shown that, although the absorption line is homogeneously broadened, the resonance fluorescence spectrum exhibits a clearly pronounced anisotropy. In a direction close to the direction of propagation of the excitation radiation, the Rayleigh scattering line is maximally narrowed. Under certain conditions (that can easily be created in experiments), the width of this line is proportional to the diffusion coefficient of atoms interacting with the radiation.
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.