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Quantum Electronics

Spectral shape of a signal in light-induced diffusive pulling (pushing) of particles into a light beam

А. И. Пархоменко, Anatolii M. Shalagin

Published Feb 27, 2015• 2 citations
Publisher

Abstract

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.

DOI
10.1070/qe2015v045n02abeh015556

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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.
We study theoretically the drift of resonant particles in a buffer medium when a traveling light wave impinges on the medium, with allowance for the velocity dependence of the transport collision rate. When the pressure of light dominates over the light-induced drift (low pressure of the buffer gas or the drift of conduction electrons in semiconductors), we discover a new sudden transformation of the spectral dependence of the drift velocity of the resonant particles: Instead of the ordinary bell-shaped function representing the velocity spectrum we have a double-humped curve with deep dip at the center of the absorption line. We show that the largest transformation of the drift velocity spectrum occurs in the atmosphere of a heavy buffer gas in the case of Coulomb interaction between the resonant and buffer particles. The transformation effect is caused by the variation of the transport rate of the collisions of the resonant and buffer particles due to the recoil effect in the absorption of radiation.
The anomalous light-induced drift (LID) of atoms caused by a velocity dependence of collision frequencies has been investigated in the frame of the theory without adjustable parameters. Our results open the possibility of experimental probing of models of interatomic potentials. The extension of the strong-collision model to the case of velocity-dependent collision rates, is the basis of our approach. The obtained model describes the anomalous LID both in the case of arbitrary mass ratio of absorbing- and buffer-gas particles and in the case of arbitrary ratio of the homogeneous and Doppler widths. In particular, we applied our model to describe the anomalous LID in alkali - noble-gas mixtures (Rb - Kr and Li - Ne systems). Qualitatively another anomaly of the LID velocity was also found in the low-pressure region. As pointed out, the optical pumping effect and the hyperfine structure of the ground electronic state, but not the velocity dependence of the collision rates, are the sources of this new anomaly.
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.
This paper is a theoretical study of the spectral features of the velocity of light-induced drift (LID) of lithium atoms ( 7 Li and 6 Li) in a binary mixture of noble gases: Ne + Ar, Ne + Kr, and Ne + Xe. The spectral shape of the LID signal is predicted to depend strongly on the fraction ξ of neon in the buffer mixture in the range ξ≈0.8–0.9 (ξ= N Ne / N b , where N Ne is the neon concentration, and N b is the total concentration of the buffer particles). When the velocity of anomalous LID is treated as a function of the radiation frequency, it is found to have one, three, five, or seven zeros and to differ substantially from the dispersion-curve-like behavior with one zero predicted by the standard LID theory with velocity-independent transport collision rates. The reason for these additional zeros of the drift velocity is the alternating-sign dependence on the lithium-atom velocity of the relative difference of transport rates of collisions between buffer particles and excited and unexcited atoms. What is also established is that the anomalous LID of lithium atoms can be observed at almost all temperatures, depending on the value of ξ. At a fixed temperature, anomalous LID can be observed only in a narrow range of values of the fraction of neon in the buffer mixture, Δξ≈0.02. The results make possible highly precise testing in the LID experiments of the interatomic potentials used in calculations of the velocity spectrum of anomalous LID.