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Journal de Physique II

Laser near rield lens for atoms

V. I. Balykin, В. В. Климов, Vladilen S Letokhov

Published Nov 1, 1994• 14 citations
Publisher

Abstract

We suggest and examine an atom optics focusing element based on the near field arising in the diffraction of laser radiation by an aperture of small size (less than an optical wavelength) in a thin conducting screen. The quasi-resonant interaction potential of the atom and the near field is found to be close to the potential of the ideal lens. Within the quasi-classical dynamics of atoms we consider the role of chromatic, spherical aberration. Taking the diffraction aberrations into account we find that it is possible to focus atoms into spot with radius 4-7 nm.

DOI
10.1051/jp2:1994244

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We suggest and examine an atom optics focusing element based on the near field arising in the diffraction of laser radiation by an aperture of small size (less than an optical wavelength) in a thin conducting screen. The quasi-resonant interaction potential of the atom and the near field is found to be close to the potential of the ideal lens. Within the quasi-classical dynamics of atoms we consider the role of chromatic, spherical aberration. Taking the diffraction aberrations into account we find that it is possible to focus atoms into spot with radius 4-7 nm.
This paper examines the focusing of an atomic beam by the near field of laser radiation diffracted by a small aperture. The wave properties of the atom are taken into consideration within the framework of an approximate Schrödinger equation. The possibility is demonstrated of focusing an atomic beam into a spot some 3 nm across, the atomic and laser beam characteristics being quite acceptable. The main contribution to the spot size is shown to be from spherical aberrations and diffraction effects, the chromatic aberrations of the atomic beam with a 5% velocity distribution broadening having a lesser effect.
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.
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.
The focusing of atoms after interacting with both far-detuned and resonant standing wave fields in the thin-lens regime is considered. Exact quantum expressions for the Fourier components of the density (that include all spherical aberration) are used to study the focusing numerically. The following lens parameters and density profiles are calculated as functions of the pulsed field area $\ensuremath{\theta}:$ the position of the focal plane, peak atomic density, atomic density pattern at the focus, focal spot size, depth of focus, and background density. The lens parameters are compared to asymptotic, analytical results derived from a scalar diffraction theory for which spherical aberration is small but non-negligible $(\ensuremath{\theta}\ensuremath{\gg}1).$ Within the diffraction theory analytical expressions show that the focused atoms in the far-detuned case have an approximately constant background density $0.5(1\ensuremath{-}0.635{\ensuremath{\theta}}^{\ensuremath{-}1/2})$ while the peak density behaves as $3.83{\ensuremath{\theta}}^{1/2},$ the focal distance as ${\ensuremath{\theta}}^{\ensuremath{-}1}(1+1.27{\ensuremath{\theta}}^{\ensuremath{-}1/2})$ ${L}_{T}/2\ensuremath{\pi},$ the depth of focus as ${0.304L}_{T}{\ensuremath{\theta}}^{\ensuremath{-}3/2},$ and the focal spot size $0.0592\ensuremath{\lambda}{\ensuremath{\theta}}^{\ensuremath{-}3/4},$ where LT{L}_{T}LT​ is the Talbot distance and \ensuremath{\lambda} is the wavelength of the light. Focusing by the resonant standing wave field leads to a new effect, a Rabi-like oscillation of the atom density. For the far-detuned lens, chromatic aberration is studied quantitatively with the exact Fourier results. Similarly, the degradation of the focus that results from angular divergence in beams or thermal velocity distributions in traps is studied quantitatively with the exact Fourier method and understood analytically using the asymptotic results. Overall, we show that strong thin-lens focusing is possible with modest laser powers and with currently achievable atomic beam characteristics.
We analyze focusing of atomic beams by the atom near-field microlenses produced by the laser fields diffracted on the apertures in the metallic screens. Analysis of the focusing properties of the atom microlenses is given in a model describing dipole interaction of atoms with a far-off-resonance laser light. Two types of the atom microlenses are considered: The Bethe-type microlens with aperture less than the light wavelength and the Fresnel-type microlens with aperture about the wavelength. It is shown that both types of the atom microlenses are able to produce strong dipole gradient forces which can focus the atomic beams. However, while the Bethe-atom microlens is able to produce sharp focusing of the beams the Fresnel-atom microlens possesses weak focusing property due to high anharmonicity of the gradient force. We conclude that the Bethe-atom microlens can be considered as a promising tool of the atom optics potentially able to focus atomic beams into spot sizes about nanometers.
We propose a lens for atoms with reduced chromatic aberrations and calculate its focal length and spot size. In our scheme a two-level atom interacts with a near-resonant standing light wave formed by two running waves of slightly different wave vectors, and a far-detuned running wave propagating perpendicularly to the standing wave. We show that within the Raman-Nath approximation and for an adiabatically slow atom-light interaction, the phase acquired by the atom is independent of the incident atomic velocity.