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Journal of Kufa Physics

Theoretical Calculations of the Diffusion and Friction Coefficients for Neutral Atoms that Moving in a Laser Field

Haider Кamil Hanoon

Published Dec 10, 2019• 0 citations
Publisher

Abstract

This research aimed to study the friction and diffusion coefficients of neutral atoms that moving and interact with a laser field .The Mathcad 14 program used to calculate the results. The theoretical model was solved and shown the effect of different optical parameters on the diffusion and friction of neutral atoms .The different values of ellipticity (Ɛ) were used to find the friction and diffusion coefficients ,for each value of ellipticity we found that the relationship between the natural width of excited level( γ) and the difference(δ) between the frequency of laser field(ω) and the atomic resonance (ω0 ) has strong effect on the friction coefficient of atoms .The effect of Rabi frequency (Ω ) on the diffusion coefficient has been investigated .In this research the results showed that each of the parameters δ and Ω has effect on the diffusion of atom and the Rabi frequency has more influence. The dependence of the friction and diffusion coefficients on the natural width of the excited level was studied. The measuring of the friction and diffusion coefficients of atom very important to control the movement and then localize it, this have many applications in physics fields.

DOI
10.31257/2018/jkp/2019/110208

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This research aimed to study the friction and diffusion coefficients of neutral atoms that moving and interact with a laser field .The Mathcad 14 program used to calculate the results. The theoretical model was solved and shown the effect of different optical parameters on the diffusion and friction of neutral atoms .The different values of ellipticity (Ɛ) were used to find the friction and diffusion coefficients ,for each value of ellipticity we found that the relationship between the natural width of excited level( γ) and the difference(δ) between the frequency of laser field(ω) and the atomic resonance (ω0 ) has strong effect on the friction coefficient of atoms .The effect of Rabi frequency (Ω ) on the diffusion coefficient has been investigated .In this research the results showed that each of the parameters δ and Ω has effect on the diffusion of atom and the Rabi frequency has more influence. The dependence of the friction and diffusion coefficients on the natural width of the excited level was studied. The measuring of the friction and diffusion coefficients of atom very important to control the movement and then localize it, this have many applications in physics fields.
The motion of slow atoms with degenerate energy levels in a resonant, nonuniformly polarized laser field is described by the Fokker-Planck equation for the atomic distribution function in phase space in terms of the semiclassical approach. Field gradient expansions are used for the spatially nonuniform coefficients of the equation. For closed atomic transitions J g =J→J e =J+1 (J g and J e are the total angular momenta of the ground and excited states, respectively), new analytical results are presented for the light pressure force and the friction and diffusion coefficients in momentum space. These results allow the kinetic effects (laser cooling, localization in optical potential wells, etc.) in a field of arbitrary one-, two-, or three-dimensional configuration to be investigated. In several cases, the new contributions to the friction coefficient are interpreted qualitatively.
We examine the kinetics of atoms with their ground and excited states being degenerate in the projection of angular momentum. The atoms are located in a standing wave with uniform elliptical polarization. Using the j g =1/2→j e =1/2 transition as an example, we show that the friction and diffusion of atoms strongly depend on the ellipticity of the field. For instance, in the low saturation limit the frictional force contains, in addition to the ordinary Doppler friction term, a term that can be interpreted as Sisyphean friction. Under certain conditions, the contributions reflecting the degeneracy of the ground state are dominant, with the result that the values of the friction and diffusion coefficients (and hence the rate of kinetic processes) may differ from the values predicted by the two-level atomic model by several orders of magnitude.
Methods are presented that allow numerical calculations of the friction and momentum diffusion coefficients for atomic motion in laser fields with periodicity in one, two, and three dimensions. Polarization gradients in the fields lead to increased friction on atoms with a Zeeman sublevel structure, and new features arising in the cases of motion in two and three dimensions are discussed. There is a marked position dependence of the calculated quantities, and the consequence for the forces on atoms following specified trajectories is studied. Temperatures determined from the position-averaged friction and diffusion coefficients scale with the laser power divided by the frequency detuning, except in some special configurations. Of relevance for experiments on cooling, the relative merits of four different laser configurations in three dimensions are studied.
This work discusses the effect of a high-intensity standing wave laser field on the motion of neutral atoms moving with a relatively high velocity. The analysis involves a detailed calculation of the force acting on the atoms and the calculation of the diffusion tensor associated with the fluctuations of the quantum force operator. The high-intensity laser field limit corresponds to a Rabi frequency much greater than the natural rate of the atom. The general results are valid for any atomic velocity. Results are then specialized to the case of slow and fast atoms where the Doppler shift of the laser frequency due to the atomic motion is either smaller or larger than the natural decay rate of the atom. The results obtained for the force and diffusion tensor are applied to a particular ideal experiment that studies the evolution of a fast atomic beam crossing a high-intensity laser beam. The theories developed previously, for a similar laser configuration, discuss only the low atomic velocities case and not the more realistic case of fast atoms. Here, an approximate solution of the equation for the distribution is obtained. Starting from the approximate distribution function, the deflection angle and dispersion angle for themore » atomic beam with respect to the free motion are calculated.« less
The authors have studied resonance collisions amongst atoms dressed by a strong laser field. The equations of motion have been solved numerically to yield collisional transition rates for various values of the Rabi frequency (V) due to the laser and its detuning ( Delta ) from the atomic transition frequency ( omega 0 ). The atoms are assumed to follow classical rectilinear paths and only undergo binary collisions. The resonance interaction is taken to be the first-order dipole-dipole interaction acting within the ground and resonance levels of a pair of atoms. A qualitative explanation is offered for the results obtained by splitting the Hamiltonian into parts that represent the collision-free evolution of the system at the Rabi frequency, the 'normal' resonance interaction, and the 'dressed interaction' responsible for opening new scattering channels. The latter interaction depends upon the relative strengths of the resonance interaction (R), the generalized Rabi frequency ( Omega ) and the ratio V/ Delta .
The kinetics of atoms in a bichromatic field formed by waves with an arbitrary elliptical polarisation is considered. Analytical expressions are derived for the force and the friction and diffusion coefficients within the model of an atom with the j g = 1/2 → j e = 3/2 optical transition. These expressions are presented in the general form as an expansion in gradients of light field parameters. Some specific features of the kinetics of atoms are found, which are due to the interference contributions to the friction and diffusion coefficients. The kinetics of atoms in the field of an optical lattice formed as a result of the interference of a wave with a uniform elliptical polarisation and a nonuniformly polarised dissipative field is analysed.