Dipole gradient force

This possibility is based on the use of what is known as the dipole (gradient) force that I proposed many years ago to control the motion of neutral atoms [5]. In the case of atoms in a light field in the vicinity of the resonance frequency coo, this force may be expressed in the form... 

The motion of a two-level atom in a spatially inhomogeneous laser field is generally governed by the dipole gradient force, the radiation pressure force, and the diffusion of momentmn. A detailed and consistent analysis of the motion of two-level atoms in light fields can be foimd in Minogin and Letokhov (1987) and Kazantsev et al. (1990), and here I shall restrict myself to a brief amvey of the basic formulas. 

This is done by treating the particle as a point dipole and using Maxwell s equations to solve for the electric field within the beam. It is convenient to analyze the trapping force in terms of two separate components the scattering force, Fscm, and the gradient force, Fy. The scattering force arises due to absorption and reradiation by the dipole, whereas the gradient force arises due to the interaction between the induced dipole and the electric field. The dipole moment can be calculated by... 

In the above, /(r) = (c/87r) o( ) the intensity of the laser beam at the point r Is = cl4n) h yld) is the saturation intensity d=d- e is the projection of the dipole moment matrix element of the polarization vector e of the laser beam A is the detuning of the laser field frequency cu with respect to the atomic transition frequency tuo, that is, A = lo — loo, and the quantity 27 defines the rate of spontaneous decay of the atom from the upper level e) to the lower level g), that is, the Einstein coefficient A. Figure 5.6 shows the dependence of the radiation pressure force and the gradient force on the projection v =v of the atomic velocity on the propagation direction of a Gaussian laser beam for the case of strong saturation of the D-line of Na. 

In the reflection of atoms by an evanescent wave, the amplitude of the light field does not necessarily change adiabatically slowly in comparison with the relaxation of the internal atomic motion. In this case eqn (7.6) for the light gradient (dipole) force acting on the atom is only the zeroth-order term in an expansion of the force in powers of the inverse interaction time (Ol shanii et al. 1992). The next term in the expansion gives rise to a dissipative part in the gradient force. Such nonadiabaticity can happen if the time of interaction of the atom with the field is comparable to 7 F In this case the specular character of the reflection of atoms can be disturbed. 

McClelland and Scheinfein (1991), and Gallatin and Gould (1991). McClelland and Scheinfein found solutions of the classical equations for paraxial rays in the field of the gradient force and estimated on that basis the spherical, chromatic, diffusion, and diffraction aberrations. It follows from these estimates that the main contribution to the width of the focal spot is, as a rule, the contribution from the diffraction aberrations, the contribution from the dipole force fluctuations sometimes also being substantial. 

Pulay P, FogarasI G, Pang F and Boggs J E 1979 Systematic ab initio gradient calculation of molecular geometries, force constants and dipole moment derivatives J. Am. Chem. Soc. 101 2550... 

Forces of Adsorption. Adsorption may be classified as chemisorption or physical adsorption, depending on the nature of the surface forces. In physical adsorption the forces are relatively weak, involving mainly van der Waals (induced dipole—induced dipole) interactions, supplemented in many cases by electrostatic contributions from field gradient—dipole or —quadmpole interactions. By contrast, in chemisorption there is significant electron transfer, equivalent to the formation of a chemical bond between the sorbate and the soHd surface. Such interactions are both stronger and more specific than the forces of physical adsorption and are obviously limited to monolayer coverage. The differences in the general features of physical and chemisorption systems (Table 1) can be understood on the basis of this difference in the nature of the surface forces. 

Pulay, P., G. Fogarasi, F. Pang, and J. E. Boggs. 1979b. Systematic Ab Initio Gradient Calculation of Molecular Geometries, Force Constants, and Dipole Moment Derivatives. J. Am. Chem. Soc. 101, 2550-2560. 

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