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arXiv:0810.4486 · Physical Review A

Optical lenses for atomic beams

Ole Steuernagel

Published Jan 23, 2009• 8 citations
arXivHTMLPDF

Abstract

Superpositions of paraxial laser beam modes to generate atom-optical lenses based on the optical dipole force are investigated theoretically. Thin, wide, parabolic, cylindrical, and circular atom lenses with numerical apertures much greater than those reported in the literature to date can be synthesized. This superposition approach promises to make high-quality atom beam imaging and nanodeposition feasible.

DOI
10.1103/physreva.79.013421

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Superpositions of paraxial laser beam modes to generate atom-optical lenses based on the optical dipole force are investigated theoretically. Thin, wide, parabolic, cylindrical, and circular atom lenses with numerical apertures much greater than those reported in the literature to date can be synthesized. This superposition approach promises to make high-quality atom beam imaging and nanodeposition feasible.
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.
We show that light force lenses can be used to focus a thermal beam of neutral atoms with extremely high resolution (\ensuremath{\sim}20 nm) and high contrast (\ensuremath{\sim}10:1), finally making such atom-optical lenses viable for proposed applications. Our (cylindrical) lenses for sodium atoms are created by the dipole force within each period of a standing wave. We determine the spatial distribution of the focused atoms (with nanometer resolution) by allowing the atoms to deposit on a substrate and scanning with a UHV scanning tunneling microscope. We find that the requirements for optimum focusing are very large, positive detuning; short focal lengths; and a well-collimated atomic beam. These dependences can be thoroughly understood from a simple theoretical model. \textcopyright{}1996 The American Physical Society.
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.
Atomic beam focusing by an atomic microlens formed by the optical field diffracted from a circular aperture in a metallic screen is considered for an aperture diameter smaller than the wavelength of the field. Analytic expressions are derived for the dipole gradient force acting on an atom in the field of diffracted radiation. It is shown that the action of the gradient force makes it possible to focus the atomic beam into a spot with a diameter on the order of a few nanometers. Numerical estimates are obtained for the focusing properties of the atomic microlens in the model describing the dipole interaction of Rb atoms with laser radiation in the vicinity of the D line.
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.