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Journal of Experimental and Theoretical Physics

Effects of the velocity dependence of the collision frequency on the Dicke line narrowing

А. И. Пархоменко, Anatolii M. Shalagin

Published Oct 1, 2001• 10 citations
Publisher

Abstract

The effect of the velocity ( v ) dependence of the transport collision frequency ν tr v on the Dicke line narrowing is analyzed in terms of the strong-collision model generalized to velocity-dependent collision frequencies (the so-called kangaroo model). This effect has been found to depend on the mass ratio of the resonance ( M ) and buffer ( M b ) particles, β = M b / M : it is at a minimum for β ≪ 1 and reaches a maximum for β ≳ 3. A power-law particle interaction potential, U ( r ) ∝ r − n , is used as an example to show that, compared to ν tr v ( v ) = const ( n = 4), the line narrows if ν tr v ( v ) decreases with increasing v ( n < 4) and broadens if ν tr v ( v ) increases with v ( n > 4). At β ≳ 3, the line width can increase [compared to ν tr v ( v ) = const] by 5 and 12% for the potentials with n = 6 and n ≳ 10, respectively; for the potentials with n = 1 (Coulomb potential) and n = 3, it can decrease by more than half and 6%, respectively. The line profile I (Ω) has been found to be weakly sensitive to ν tr v ( v ) at some detuning Ω c of the radiation frequency Ω. Dicke line narrowing is used as an example to analyze the collisional transport of nonequilibrium in the resonance-particle velocity distribution in a laser field. The transport effect is numerically shown to be weak. This allows simpler approximate one-dimensional quantum kinetic equations to be used instead of the three-dimensional ones to solve spectroscopic problems in which it is important to take into account the velocity dependence of the collision frequency when the phase memory is preserved during collisions.

DOI
10.1134/1.1420441

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The effect of the velocity ( v ) dependence of the transport collision frequency ν tr v on the Dicke line narrowing is analyzed in terms of the strong-collision model generalized to velocity-dependent collision frequencies (the so-called kangaroo model). This effect has been found to depend on the mass ratio of the resonance ( M ) and buffer ( M b ) particles, β = M b / M : it is at a minimum for β ≪ 1 and reaches a maximum for β ≳ 3. A power-law particle interaction potential, U ( r ) ∝ r − n , is used as an example to show that, compared to ν tr v ( v ) = const ( n = 4), the line narrows if ν tr v ( v ) decreases with increasing v ( n < 4) and broadens if ν tr v ( v ) increases with v ( n > 4). At β ≳ 3, the line width can increase [compared to ν tr v ( v ) = const] by 5 and 12% for the potentials with n = 6 and n ≳ 10, respectively; for the potentials with n = 1 (Coulomb potential) and n = 3, it can decrease by more than half and 6%, respectively. The line profile I (Ω) has been found to be weakly sensitive to ν tr v ( v ) at some detuning Ω c of the radiation frequency Ω. Dicke line narrowing is used as an example to analyze the collisional transport of nonequilibrium in the resonance-particle velocity distribution in a laser field. The transport effect is numerically shown to be weak. This allows simpler approximate one-dimensional quantum kinetic equations to be used instead of the three-dimensional ones to solve spectroscopic problems in which it is important to take into account the velocity dependence of the collision frequency when the phase memory is preserved during collisions.
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.
In this paper, we present a formalism for the exact calculation of spectral profile of an isolated line undergoing speed-dependent collisional broadening and shifting and Dicke narrowing. It is couched in the language of the density matrix as in the closely related fields of transport phenomena, laser physics, and nonlinear optics. The formalism is ab intio in spirit, permitting the calculation of the line shape starting only from a given interaction potential. The line shape is obtained by solving a transport/relaxation equation for the off-diagonal element of the density matrix, a macroscopic quantity. The collision operator in the transport/relaxation equation, which is determined from the (microscopic) interaction between the active molecule and the perturber, is presumed known.
We study theoretically how the dependences of transport collision frequencies n i , collision broadening g and collision shift D of the levels on the velocity u of resonant particles influence lightinduced diffusive pulling (pushing) (LDP) effects in the framework of a generalised model of strong collisions in the case of velocitydependent collision rates (so-called kangaroo model).It is found that allowance for the dependences n i (u), g(u) and D(u) does not change the spectral shape of an LDP signal.In particular, in the case of low-intensity radiation, the spectral dependence of the LDP signal coincides with the absorption line shape.It is shown that the magnitude of the LDP effect is proportional to the difference between the diffusion coefficients of particles in the excited and ground states.It is found that the spectral anomalies previously predicted in the LDP effect [Gel'mukhanov F.Kh. JETP Lett., 55, 214 (1992)] for an idealised model of the Lorentz gas (the limiting case of heavy buffer particles), which arise due to the dependences n i (u), g(u) and D(u), are typical only for this gas.At a realistic ratio of the masses of absorbing and buffer particles, spectral anomalies do not occur in the LDP effect.
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.
The absorption (amplification) spectrum of a weak probe field by two-level atoms located in a strong resonant laser field and colliding with buffer-gas atoms is analyzed theoretically. The analysis is performed for low collision frequencies compared to the Doppler absorption linewidth (low gas pressure) and with allowance made for an arbitrary change in the phase of the radiation-induced dipole moment at elastic collisions between gas particles. The phase memory effects have been found to lead to a strong qualitative and quantitative transformation of the probe-field spectrum even at rare collisions, when the well-known Dicke manifestation mechanism of the phase memory effects (the removal of Doppler broadening due to the restriction of the spatial particle motion by collisions) is inoperative. The strong influence of the phase memory effects on the spectral resonances at low gas pressures stems from the fact that the phase-conserving collisions change the velocity dependence of the partial refractive index n ( v ) (the refractive index for particles moving with velocity v ).
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.