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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Wide optical lenses for atomic beams

Ole Steuernagel

Published Jun 1, 2009• 0 citations
Publisher

Abstract

The field of atom-optics offers considerable potential in fundamental and applied physics, both for imaging atoms and their deposition (to create nano-structures). Here we work in the paraxial approximation throughout and can therefore assume that the scalar modes represent (e. g., linearly polarized) electro-magnetic laser-field modes. For atomic lens design, based on the optical dipole force, it is necessary to coherently superpose suitable laser modes in order to create wide thin parabolic lenses with large numerical apertures. Only in this manner can the tiny diffraction limits promised by the extraordinary smallness of the de Broglie wavelengths of atomic beams be realized.

DOI
10.1109/cleoe-eqec.2009.5192927

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The field of atom-optics offers considerable potential in fundamental and applied physics, both for imaging atoms and their deposition (to create nano-structures). Here we work in the paraxial approximation throughout and can therefore assume that the scalar modes represent (e. g., linearly polarized) electro-magnetic laser-field modes. For atomic lens design, based on the optical dipole force, it is necessary to coherently superpose suitable laser modes in order to create wide thin parabolic lenses with large numerical apertures. Only in this manner can the tiny diffraction limits promised by the extraordinary smallness of the de Broglie wavelengths of atomic beams be realized.
The use of a TEM01*-mode laser beam has been proposed as a means of focusing an atomic beam to nanometer- scale spot diameters. We have analyzed the classical trajectories of atoms through a TEM01*-mode laser beam, using methods developed for particle optics. The differential equation that describes the properties of the: first- order paraxial lens hi exactly the same form as the bell-shaped magnetic Newtonian lens that was first analyzed by Glaser for the focusing of electrons in an electron-microscope objective. We calculate the first-order properties of the lens, obtaining cardinal elements that are valid over the entire operating range of the lens including the thick and the immersion regimes. Contributions to the spot size are discussed, including four aberrations plus diffraction and atomic-beam-collimation effects. Explicit expressions for spherical chromatic, spontaneous-emission, and dipole-fluctuation aberrations are obtained. Examples are discussed for a sodium atomic beam, showing that subnanometer-diameter spots may be achieved with reasonable laser and atomic- beam parameters. Optimization of the lens is also discussed.
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.