Laser focusing of an atomic beam

we conclude that the force effecting the focusing of an atom in a beam should be proportional to the atomic displacement. This criterion must be satisfied for the force to produce a true image if this criterion is not met, the image is blurred, that is, there are aberrations. 

A particle-optical approach can also be used for the treatment of focusing of atoms by laser light (McClelland and Scheinfein 1991). In this approach the atoms are treated as classical particles that move in the potential field of a laser beam. This method was originally developed for charged particle optics, for calculation of trajectories in a cylindrically symmetric potential field. The equation of motion can be derived from the Lagrangian L = Mv /2 — U p, z), where U p, z) is the potential energy eqn (6.1) and 2 is the axis of symmetry. In cylindrical coordinates, the radial equation of motion is 

By making the assumption that the potential energy U p,z) is less than the kinetic energy of the atom Eq U p, z) -C Eq), and that dp/dz -C 1 (both conditions are usually valid in real experimental situations), the equation simplifies to 

The quadratic radial dependence of the potential is a necessary condition for the focusing of atoms. Expanding the real potential U(p, z) and keeping only the lowest quadratic term in the expansion, we find 

The focusing of an atomic beam by means of the gradient force was demonstrated first at Bell Laboratories (Bjorkholm et al. 1978, 1980). In the scheme used there, the atomic lens was created by a CW dye laser, which was focused to 200 pm and superimposed upon an atomic beam of sodium. The laser power was 50 mW and the frequency detuning A was —2 GHz. The atomic beam propagated along and inside a narrow Gaussian laser beam. The laser frequency was tuned below the atomic transition frequency, so that the gradient force was directed toward the laser beam axis. The radial potential here is determined by eqn (6.1), with the saturation parameter 

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Balykin, V. I., and Letokhov, V. S. (1987). The possibility of deep laser focusing of an atomic beam into A-region. Optics Communications, 64, 151-156. 

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