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Japanese Journal of Applied Physics

Use of Bessel J1 Laser Beam to Focus an Atomic Beam into a Nano-scale Dot

Kenji Okamoto, Yasushi Inouye, Satoshi Kawata

Published Jul 1, 2001• 9 citations
Publisher

Abstract

We propose a novel scheme to guide atomic beams with submicrometer spot sizes and beam propagation lengths of more than 1 centimeter. By using a Bessel J 1 beam for guiding atoms, the atoms are confined to the center dark region of the doughnut mode of J 1 beam. Our numerical analysis results show that a guided atomic beam maintains its width which is less than 100 nm. We also propose a scheme which combines the Bessel J 1 beam with a magneto-optical trap and a Bessel J 0 beam, where the unfocused part of an atomic flux, i.e., the background component, is suppressed.

DOI
10.1143/jjap.40.4544

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Conference on Lasers and Electro-Optics•Nov 27, 2002•0 citations
We propose a novel scheme to guide atomic beams with submicrometer spot sizes and beam propagation lengths of more than 1 centimeter. By using a Bessel J 1 beam for guiding atoms, the atoms are confined to the center dark region of the doughnut mode of J 1 beam. Our numerical analysis results show that a guided atomic beam maintains its width which is less than 100 nm. We also propose a scheme which combines the Bessel J 1 beam with a magneto-optical trap and a Bessel J 0 beam, where the unfocused part of an atomic flux, i.e., the background component, is suppressed.
Atomic beam focusing by a gradient (dipole) force of the near resonant first order Bessel beam is considered in the paraxial approximation. The first order Bessel beam (J1) is a nondivergent laser beam whose intensity profile is the square of the first-order Bessel function of the first kind. A co-propagating J1 beam, tuned above resonance, provides the minimum rate of spontaneous emission on axis where the intensity is minimum. It has a steeper intensity gradient and a longer interaction range than does TEM01*. Numerical results for the focal length and the atomic beam density distribution in the focal plane are presented. Focusing limitations due to aberrations are discussed. The results are compared with those of the TEM01* mode beam.
A doughnut-shaped light beam has been generated from a Gaussian mode (TEM 00 ). Upon splitting the pump beam into two equal-intensity components and introducing unequal convergences with a phase delay while they are recombined, a doughnut mode results. The output beam is tunable and has a long propagation length. The evanescent field generated by a 360 mW (at 780 nm wavelength) beam creates an optical field of 600 nm decay length with a 5.75 neV repulsive dipole potential. Thus cold Rb atoms (at a temperature of 10 μK or less) released from a magneto-optical trap can be reflected by the funnel surface, with the result that the atoms are ultimately collected at the bottom.
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.
This thesis is concerned with the guiding of cold atoms using optical forces, which is of great importance in the field of atom optics. Atomic beams can be used for precision sensor equipment, building nano-scale structures, construction of quantum computers and to further the understanding of the properties of atoms. Atoms are guided along light beams using the dipole force; there are two regimes under which this force works. Typically red-detuned guides are used (atoms are attracted towards the light) such guides, however, require large detuning and high powers. In this thesis we investigate the use of blue-detuned (atoms are repelled from the light) hollow light beams of moderate power (a few hundred mW) and confine atoms in the dark centre of the beams. Several magneto-optical traps (MOTs) have been constructed to exploit different guiding geometries. Hollow beams have been generated using a variety of methods; in particular the use of a computer controlled spatial light modulator (SLM) has provided great versatility and simplicity to the experimental arrangements. First, experiments were performed with a low-velocity intense source (LVIS) of atoms. A co-linear LG beam significantly enhances the observed flux, however, considerable difficulties are encountered loading atoms into oblique guides. Imaging a hole in the walls of the light tube was used to improve the loading efficiency. Second, guiding a free-falling atom cloud is performed using a non-diffracting Bessel beam. It is found that while the potential of the Bessel beam is steeper than equivalent LG beams the power distribution across the beam severely limits its usefulness. The next study investigated higher-order LG guide beams generated with an SLM. High order modes have a narrower profile so confine the atoms with less interaction with the guide beam, leading to a more natural guide (as opposed to a pushing force). Finally the SLM was used to create non-trivial beam shapes for beam splitters and interferometers.
We have performed continuous slowing of an atomic beam to load a magneto-optical trap (MOT) on axis. To avoid the undesirable effects of the strong slowing laser on the performance of the MOT, a dark spot in the center of the slowing laser beam is used. We varied the spot size and the slowing-laser frequency and intensity to optimize the number of trapped atoms. Our ``dark-spot'' slowing increased the number of trapped atoms by a factor of 30, allowing us to trap $\ensuremath{\sim}{10}^{9}$ atoms in the MOT.