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Focusing of Atomic Beams

V. I. Balykin, Vladilen S Letokhov

Published Apr 23, 2020• 0 citations

Abstract

The principal element in any sort of optics is a lens. It is essential to create laser field configurations capable of focusing neutral atomic beams. There are two possibilities for focusing an atomic beam by laser light: by using the gradient force or by using the light pressure force. 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 the true “image”: if this criteria is not met, the image is blurred, i.e. there are aberrations. An approach to treat the focusing of atomic beam by laser light is to use the path integral technique to calculate the evolution of atomic wave function as it propagates in laser field. A particle-optical approach also can be used for treatment of focusing of atoms by laser light. The quadratic radial dependence of the potential is a necessary condition for focusing of atoms.

DOI: 10.1201/9780429333378-4

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The principal element in any sort of optics is a lens. It is essential to create laser field configurations capable of focusing neutral atomic beams. There are two possibilities for focusing an atomic beam by laser light: by using the gradient force or by using the light pressure force. 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 the true “image”: if this criteria is not met, the image is blurred, i.e. there are aberrations. An approach to treat the focusing of atomic beam by laser light is to use the path integral technique to calculate the evolution of atomic wave function as it propagates in laser field. A particle-optical approach also can be used for treatment of focusing of atoms by laser light. The quadratic radial dependence of the potential is a necessary condition for focusing of atoms.

The focusing of an atomic beam using near-resonant laser light is considered. Path-integral techniques are employed to transform the problem into a standard diffraction integral. This approach is general and allows us to deal with thick laser lenses. Starting from the basic form of the potential energy for an atom in a laser beam, we derive the propagation kernel for the atomic wave function for the particular case of a TEM01*, or doughnut, mode laser beam. Both the full three-dimensional propagation kernel and its paraxial approximation are discussed. We show that the paraxial case can be obtained from the three-dimensional case by a stationary-phase approximation of the propagation equation. Numerical results for the focusing of a Gaussian atomic beam are presented. These results show that spot diameters on the order of 20 Å are obtainable for many reasonable choices of laser and atomic beam parameters and that for most of these cases the thin-lens approximation is not valid. The effects of the lowest-order aberrations are also briefly discussed. Spherical aberration is found to contribute significantly to the focal spot diameter, at least for the doughnut mode laser beam considered here.

Recently, the focusing of an atomic beam using a laser has been considered by Balykin and Letokhov.1 Their calculations explicitly assume the thin lens approximation. Here, using path integral techniques, we derive the focal length and lowest-order aberrations of the laser atomic beam lens as a function of both laser and atomic beam parameters without making the thin lens approximation. Starting from the basic form of the potential energy for an atom in a laser beam, the propagation kernel is derived for the TEM(01)* or donut mode beam. From this result the focal length and lowest-order aberrations can be found for any atomic beam profile. We consider in particular a Gaussian atomic beam. Both the full 3-D propagation kernel and its paraxial approximation are discussed. We show how the paraxial case can be obtained from the 3-D case via a stationary phase approximation of the propagation equation.

In the field of atom optics, there has been much interests in developing components such as lenses, mirrors, beam splitters and waveguides to manipulate neutral atoms. Especially many clever methods to focus neutral atoms have been developed. The lenses have been constructed using the static electrical and magnetic fields, Fresnel zone plates, and radiation pressure forces. Before the laser cooling and trapping techniques were invented, the electrostatic fields could not be used for manipulating neutral atoms because of its weak interaction energy with atoms. After the cold atoms were available, it has been possible to manipulate atoms with weak electrostatic interaction energy. We developed an atom lens system using electrostatic fields.