We address theoretically the effects of a large laser intensity on the phenomenon of light-induced drift. The velocity selectivity of the atom-field interaction decreases due to saturation broadening and this leads to a maximum of the drift velocity as a function of the laser intensity. Analytical expressions for the drift velocity are derived in the case of two-level atoms, assuming a strong collision model. Consequences of this high-field effect are discussed for various manifestations of light-induced drift such as propagation of a soliton in an infinitely long cell, described by the Burgers equation, and collisions of such solitons. The analogy with hydrodynamic shock waves, described by the same Burgers equation, is fruitfully explored. We also address high-field effects on the density distribution produced by light-induced drift in a finite cell. In all these manifestations of light-induced drift the cases of high field and low field show qualitatively different behaviors which are of a complementary nature.
We address theoretically the effects of a large laser intensity on the phenomenon of light-induced drift. The velocity selectivity of the atom-field interaction decreases due to saturation broadening and this leads to a maximum of the drift velocity as a function of the laser intensity. Analytical expressions for the drift velocity are derived in the case of two-level atoms, assuming a strong collision model. Consequences of this high-field effect are discussed for various manifestations of light-induced drift such as propagation of a soliton in an infinitely long cell, described by the Burgers equation, and collisions of such solitons. The analogy with hydrodynamic shock waves, described by the same Burgers equation, is fruitfully explored. We also address high-field effects on the density distribution produced by light-induced drift in a finite cell. In all these manifestations of light-induced drift the cases of high field and low field show qualitatively different behaviors which are of a complementary nature.
Light-induced drift arises when optically excited atoms with a Doppler-selected velocity suffer a diffusive friction that is different from that of ground-state atoms. When the atoms form an optically dense system, this drift can cause a piston effect, which sweeps the atoms in the propagation direction of the field. We derive coupled differential equations for the density of atoms and the light intensity, with an explicit expression for the drift velocity in terms of easily accessible parameters. Solutions of these equations are obtained for the stationary state in a closed cell. The density at the dark end of the cell, considered as the response to the incident-light intensity as its driving force, exhibits a discontinuity resembling a second-order phase transition for an optically dense system. We also obtain solutions with a soliton character, describing a localized density packet moving at uniform speed.
Light-induced drift has many applications in astrophysics, semiconductor physics, and isotope separation. Light-induced drift velocity is a key parameter to characterize the effect of light-induced drift. Laser linewidth exerts a great influence on light-induced drift velocity through influencing the velocity selectivity of atomic excitation, so it is an important factor that cannot be ignored in the study of light-induced drift. However, in existing theoretical studies, the influence of laser linewidth is seldom considered and the exciting light is always treated as monochromatic light. Furthermore, in a few theoretical studies about laser linewidth, the numerical model adopted does not include all the factors of light-induced drift, such as energy level degeneracy, hyperfine structure, and collision model, which will cause the error of calculation. In order to study the influence of laser linewidth on light-induced drift velocity, a four-level rate equation model is established to describe the atomic energy level transition in the process of light-induced drift. In the theoretical model, we introduce strong collision model to describe collisions between atoms and buffer gas. The influences of energy level degeneracy and hyperfine structure are also taken into account. Numerical method is used to calculate the four-level rate equation. According to the calculation results, the influence of laser linewidth on drift velocity of alkali metal atoms is analyzed. The results show that as the linewidth increases, the value of drift velocity first increases and then decreases. There is an optimal linewidth that maximizes the drift velocity. For the best light-induced drift effect, the laser should work under the optimal linewidth condition. When the laser linewidth fluctuates near the optimum linewidth, the laser linewidth should be set to be slightly wider than the optimal linewidth. This can reduce the influence of fluctuation and obtain a better drift effect. In addition, as the laser linewidth increases, the optimum power density corresponding to the maximum drift velocity decreases. When the laser linewidth is narrow, small fluctuations near the optimal laser power density will not have great influence on drift velocity. When the laser linewidth is wide, the power density should be set strictly. The optimum linewidth is related to laser power density, temperature and buffer gas pressure. As the laser power density increases, the value of optimum linewidth first increases rapidly and then decreases slowly. The value of optimal linewidth also increases linearly with the increase of temperature, and it decreases with the increase of buffer gas pressure. In conclusion, the laser linewidth does play a key role in the process of light-induced drift. The results of this study can provide a theoretical basis for future experiments, and be a good reference to the selection of exciting light.
We present a model for light-induced drift (LID) in the Na--noble-gas system which should enable direct comparison with experiment. In contrast to previous theories of LID based on a two-level description of the optical absorbers and on a simplified collision treatment, the present model is based on a realistic description of laser-driven Na atoms immersed in a buffer gas. Starting from the generalized Bloch equations, we introduce a rate-equation model for the velocity distributions in the four important Na levels. The velocity-changing and fine-structure-changing collisions are described using composite Keilson-Storer collision kernels in which all adjustable parameters have been eliminated by using available literature data. We apply the model in numerical calculations of LID as a function of all experimentally accessible parameters. It is found that the ground-state hyperfine splitting can have large effects on LID, whereas the excited-state fine-structure splitting has not. The paper establishes criteria for optimum LID effects; when using a single-frequency laser the maximum attainable drift velocity is predicted to be 13.8 m/s. Using a proper set of boundary conditions, we find a pressure dependence of LID qualitatively different from the predictions based on previous work. Finally, the influence of the collision model is investigated. We find that LID is independent of the shape of the collision kernel, indicating that a strong-collision model is always valid.
A new light-induced drift effect is discussed in which a white-light source separates a gas mixture containing a single optically active (absorbing) species and a buffer gas which does not interact with the light. A three-level model with one upper level and two closely spaced lower levels is used for the active atoms, and strong collisions with the more abundant surrounding buffer gas atoms are assumed. The intensity spectrum in the vapor (including the effects of hyperfine pumping), and the resulting drift velocity are calculated as a function of optical depth into the vapor.
The authors calculate the light-induced drift velocity of multi-level atoms in the strong collision approximation. The solution is presented in a general form which can be easily applied to various systems. Specific calculations of drift velocities are presented for the system Rb:Ar for the cases of single- and multi-frequency laser excitations. A calculation is also presented for the case of a white light excitation spectrum with a spectral dip, which could be caused by absorption of light by another substance in the vapour, for instance in stellar atmospheres.
Using Lamb's model, we analyze the effects of gain saturation by strong traveling-wave fields in dilute laser media. Using approximate solutions of an integral equation for the population inversion density (PID), the index of refraction and incremental gain are studied for arbitrarily strong fields. Effects of atomic motion are included for a Maxwellian velocity distribution, but pressure effects are neglected. The case of a monochromatic field leads to the saturation results of Gordon, White, and Rigden, which are studied as a function of frequency. For a small ratio of natural to Doppler linewidths, there is a transition from inhomogeneous to homogeneous broadening for sufficiently strong fields. An effect of particular interest is the generation of waves at $2{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$, $2{\ensuremath{\omega}}_{2}\ensuremath{-}{\ensuremath{\omega}}_{1}$, and higher order sidebands by two strong input signals at ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$. The source of the parametric gain at these frequencies is the time-dependent gain saturation due to the presence of multiple strong fields. For ${\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$ small compared to the decay rates ${\ensuremath{\gamma}}_{a}$ and ${\ensuremath{\gamma}}_{b}$ of the laser levels, the gain at these intermodulation sidebands is computed as a function of the field strengths. The limiting cases of homogeneous and inhomogeneous (due to atomic motion) broadening are studied in detail. These two cases give essentially the same results, for a given unsaturated gain. Numerical results indicate that a first-order side-band intensity at least 10% as large as that of the inducing fields can be easily observed in practice. The integral equation for the PID is converted into an infinite set of linear algebraic equations for a typical solid-state laser. The conditions under which this set of equations can be limited to a finite number is discussed, and the dependence of the sideband gain on ${\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$ is calculated. For large ${\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$, the gain at the mth sideband decreases as ${({\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2})}^{\ensuremath{-}m}$.